####Accident _Collision from 2023.01.01 to 2023.06.30

####🌰0. data cleaning

data02 <- read.csv("/Users/a20010228/Desktop/data try/Accident _Collision.csv")
library(fpp3)
## ── Attaching packages ────────────────────────────────────────────── fpp3 0.5 ──
## ✔ tibble      3.2.1     ✔ tsibble     1.1.3
## ✔ dplyr       1.1.4     ✔ tsibbledata 0.4.1
## ✔ tidyr       1.3.1     ✔ feasts      0.3.1
## ✔ lubridate   1.9.3     ✔ fable       0.3.3
## ✔ ggplot2     3.5.1     ✔ fabletools  0.3.3
## ── Conflicts ───────────────────────────────────────────────── fpp3_conflicts ──
## ✖ lubridate::date()    masks base::date()
## ✖ dplyr::filter()      masks stats::filter()
## ✖ tsibble::intersect() masks base::intersect()
## ✖ tsibble::interval()  masks lubridate::interval()
## ✖ dplyr::lag()         masks stats::lag()
## ✖ tsibble::setdiff()   masks base::setdiff()
## ✖ tsibble::union()     masks base::union()
view(data02)
head(data02)
##   collision_index collision_year collision_reference location_easting_osgr
## 1   2023010419171           2023           010419171                525060
## 2   2023010419183           2023           010419183                535463
## 3   2023010419189           2023           010419189                508702
## 4   2023010419191           2023           010419191                520341
## 5   2023010419192           2023           010419192                527255
## 6   2023010419198           2023           010419198                524780
##   location_northing_osgr longitude  latitude police_force
## 1                 170416 -0.202878 51.418974            1
## 2                 198745 -0.042464 51.671155            1
## 3                 177696 -0.435789 51.487777            1
## 4                 190175 -0.263972 51.597575            1
## 5                 176963 -0.168976 51.477324            1
## 6                 184471 -0.201941 51.545349            1
##   legacy_collision_severity number_of_vehicles number_of_casualties       date
## 1                         3                  1                    1 01/01/2023
## 2                         3                  3                    2 01/01/2023
## 3                         3                  2                    1 01/01/2023
## 4                         3                  2                    1 01/01/2023
## 5                         3                  2                    1 01/01/2023
## 6                         3                  1                    1 01/01/2023
##   day_of_week  time local_authority_district local_authority_ons_district
## 1           1 01:24                       -1                    E09000024
## 2           1 02:25                       -1                    E09000010
## 3           1 03:50                       -1                    E09000017
## 4           1 02:13                       -1                    E09000003
## 5           1 01:42                       -1                    E09000032
## 6           1 02:10                       -1                    E09000005
##   local_authority_highway first_road_class first_road_number road_type
## 1               E09000024                5                 0         2
## 2               E09000010                6                 0         6
## 3               E09000017                3               437         1
## 4               E09000003                3                 5         6
## 5               E09000032                3              3220         6
## 6               E09000005                3                 5         6
##   speed_limit junction_detail junction_control second_road_class
## 1          20               9                4                 5
## 2          30               3                4                 6
## 3          30               1                4                 6
## 4          30               3                4                 6
## 5          30               8                4                 6
## 6          30               0               -1                 0
##   second_road_number pedestrian_crossing_human_control
## 1                  0                                 2
## 2                  0                                 0
## 3                  0                                 0
## 4                  0                                 0
## 5                  0                                 0
## 6                 -1                                 2
##   pedestrian_crossing_physical_facilities light_conditions weather_conditions
## 1                                       5                4                  8
## 2                                       1                4                  1
## 3                                       0                4                  1
## 4                                       0                4                  9
## 5                                       0                4                  1
## 6                                       5                4                  1
##   road_surface_conditions special_conditions_at_site carriageway_hazards
## 1                       2                          0                   0
## 2                       1                          0                   0
## 3                       1                          0                   0
## 4                       1                          0                   0
## 5                       1                          0                   0
## 6                       1                          0                   0
##   urban_or_rural_area did_police_officer_attend_scene_of_collision
## 1                  -1                                            1
## 2                  -1                                            1
## 3                  -1                                            1
## 4                  -1                                            1
## 5                  -1                                            1
## 6                  -1                                            1
##   trunk_road_flag lsoa_of_collision_location
## 1              -1                  E01003383
## 2              -1                  E01001547
## 3              -1                  E01002448
## 4              -1                  E01000129
## 5              -1                  E01004583
## 6              -1                  E01000974
names(data02)
##  [1] "collision_index"                             
##  [2] "collision_year"                              
##  [3] "collision_reference"                         
##  [4] "location_easting_osgr"                       
##  [5] "location_northing_osgr"                      
##  [6] "longitude"                                   
##  [7] "latitude"                                    
##  [8] "police_force"                                
##  [9] "legacy_collision_severity"                   
## [10] "number_of_vehicles"                          
## [11] "number_of_casualties"                        
## [12] "date"                                        
## [13] "day_of_week"                                 
## [14] "time"                                        
## [15] "local_authority_district"                    
## [16] "local_authority_ons_district"                
## [17] "local_authority_highway"                     
## [18] "first_road_class"                            
## [19] "first_road_number"                           
## [20] "road_type"                                   
## [21] "speed_limit"                                 
## [22] "junction_detail"                             
## [23] "junction_control"                            
## [24] "second_road_class"                           
## [25] "second_road_number"                          
## [26] "pedestrian_crossing_human_control"           
## [27] "pedestrian_crossing_physical_facilities"     
## [28] "light_conditions"                            
## [29] "weather_conditions"                          
## [30] "road_surface_conditions"                     
## [31] "special_conditions_at_site"                  
## [32] "carriageway_hazards"                         
## [33] "urban_or_rural_area"                         
## [34] "did_police_officer_attend_scene_of_collision"
## [35] "trunk_road_flag"                             
## [36] "lsoa_of_collision_location"
dim(data02)
## [1] 49316    36
summary(data02)
##  collision_index    collision_year collision_reference location_easting_osgr
##  Length:49316       Min.   :2023   Length:49316        Length:49316         
##  Class :character   1st Qu.:2023   Class :character    Class :character     
##  Mode  :character   Median :2023   Mode  :character    Mode  :character     
##                     Mean   :2023                                            
##                     3rd Qu.:2023                                            
##                     Max.   :2023                                            
##  location_northing_osgr  longitude           latitude          police_force  
##  Length:49316           Length:49316       Length:49316       Min.   : 1.00  
##  Class :character       Class :character   Class :character   1st Qu.: 4.00  
##  Mode  :character       Mode  :character   Mode  :character   Median :22.00  
##                                                               Mean   :27.15  
##                                                               3rd Qu.:44.00  
##                                                               Max.   :99.00  
##  legacy_collision_severity number_of_vehicles number_of_casualties
##  Min.   :1.000             Min.   : 1.000     Min.   : 1.000      
##  1st Qu.:3.000             1st Qu.: 1.000     1st Qu.: 1.000      
##  Median :3.000             Median : 2.000     Median : 1.000      
##  Mean   :2.752             Mean   : 1.815     Mean   : 1.271      
##  3rd Qu.:3.000             3rd Qu.: 2.000     3rd Qu.: 1.000      
##  Max.   :3.000             Max.   :17.000     Max.   :70.000      
##      date            day_of_week        time           local_authority_district
##  Length:49316       Min.   :1.000   Length:49316       Min.   :-1              
##  Class :character   1st Qu.:3.000   Class :character   1st Qu.:-1              
##  Mode  :character   Median :4.000   Mode  :character   Median :-1              
##                     Mean   :4.113                      Mean   :-1              
##                     3rd Qu.:6.000                      3rd Qu.:-1              
##                     Max.   :7.000                      Max.   :-1              
##  local_authority_ons_district local_authority_highway first_road_class
##  Length:49316                 Length:49316            Min.   :1.000   
##  Class :character             Class :character        1st Qu.:3.000   
##  Mode  :character             Mode  :character        Median :4.000   
##                                                       Mean   :4.243   
##                                                       3rd Qu.:6.000   
##                                                       Max.   :6.000   
##  first_road_number   road_type      speed_limit   junction_detail 
##  Min.   :  -1.0    Min.   :1.000   Min.   :-1.0   Min.   : 0.000  
##  1st Qu.:   0.0    1st Qu.:6.000   1st Qu.:30.0   1st Qu.: 0.000  
##  Median :  27.0    Median :6.000   Median :30.0   Median : 3.000  
##  Mean   : 774.4    Mean   :5.307   Mean   :35.7   Mean   : 4.676  
##  3rd Qu.: 525.0    3rd Qu.:6.000   3rd Qu.:40.0   3rd Qu.: 3.000  
##  Max.   :9204.0    Max.   :9.000   Max.   :70.0   Max.   :99.000  
##  junction_control second_road_class second_road_number
##  Min.   :-1.000   Min.   :-1.000    Min.   :  -1.0    
##  1st Qu.:-1.000   1st Qu.: 0.000    1st Qu.:  -1.0    
##  Median : 2.000   Median : 3.000    Median :   0.0    
##  Mean   : 1.759   Mean   : 3.109    Mean   : 216.4    
##  3rd Qu.: 4.000   3rd Qu.: 6.000    3rd Qu.:   0.0    
##  Max.   : 9.000   Max.   : 9.000    Max.   :9999.0    
##  pedestrian_crossing_human_control pedestrian_crossing_physical_facilities
##  Min.   :-1.0000                   Min.   :-1.000                         
##  1st Qu.: 0.0000                   1st Qu.: 0.000                         
##  Median : 0.0000                   Median : 0.000                         
##  Mean   : 0.4287                   Mean   : 1.233                         
##  3rd Qu.: 0.0000                   3rd Qu.: 1.000                         
##  Max.   : 9.0000                   Max.   : 9.000                         
##  light_conditions weather_conditions road_surface_conditions
##  Min.   :-1.000   Min.   :-1.000     Min.   :-1.000         
##  1st Qu.: 1.000   1st Qu.: 1.000     1st Qu.: 1.000         
##  Median : 1.000   Median : 1.000     Median : 1.000         
##  Mean   : 1.932   Mean   : 1.643     Mean   : 1.366         
##  3rd Qu.: 4.000   3rd Qu.: 1.000     3rd Qu.: 1.000         
##  Max.   : 7.000   Max.   : 9.000     Max.   : 9.000         
##  special_conditions_at_site carriageway_hazards urban_or_rural_area
##  Min.   :-1.0000            Min.   :-1.0000     Min.   :-1         
##  1st Qu.: 0.0000            1st Qu.: 0.0000     1st Qu.:-1         
##  Median : 0.0000            Median : 0.0000     Median :-1         
##  Mean   : 0.2999            Mean   : 0.2395     Mean   :-1         
##  3rd Qu.: 0.0000            3rd Qu.: 0.0000     3rd Qu.:-1         
##  Max.   : 9.0000            Max.   : 9.0000     Max.   :-1         
##  did_police_officer_attend_scene_of_collision trunk_road_flag
##  Min.   :-1.000                               Min.   :-1     
##  1st Qu.: 1.000                               1st Qu.:-1     
##  Median : 1.000                               Median :-1     
##  Mean   : 1.527                               Mean   :-1     
##  3rd Qu.: 2.000                               3rd Qu.:-1     
##  Max.   : 3.000                               Max.   :-1     
##  lsoa_of_collision_location
##  Length:49316              
##  Class :character          
##  Mode  :character          
##                            
##                            
## 
#####Next, do data cleaning:

#💚1. load
library(dplyr)
library(tidyr)

#💚2. Identify missing values

missing_vals <- colSums(is.na(data02))
print(missing_vals)     #All elements are 0: "Not NA"
##                              collision_index 
##                                            0 
##                               collision_year 
##                                            0 
##                          collision_reference 
##                                            0 
##                        location_easting_osgr 
##                                            0 
##                       location_northing_osgr 
##                                            0 
##                                    longitude 
##                                            0 
##                                     latitude 
##                                            0 
##                                 police_force 
##                                            0 
##                    legacy_collision_severity 
##                                            0 
##                           number_of_vehicles 
##                                            0 
##                         number_of_casualties 
##                                            0 
##                                         date 
##                                            0 
##                                  day_of_week 
##                                            0 
##                                         time 
##                                            0 
##                     local_authority_district 
##                                            0 
##                 local_authority_ons_district 
##                                            0 
##                      local_authority_highway 
##                                            0 
##                             first_road_class 
##                                            0 
##                            first_road_number 
##                                            0 
##                                    road_type 
##                                            0 
##                                  speed_limit 
##                                            0 
##                              junction_detail 
##                                            0 
##                             junction_control 
##                                            0 
##                            second_road_class 
##                                            0 
##                           second_road_number 
##                                            0 
##            pedestrian_crossing_human_control 
##                                            0 
##      pedestrian_crossing_physical_facilities 
##                                            0 
##                             light_conditions 
##                                            0 
##                           weather_conditions 
##                                            0 
##                      road_surface_conditions 
##                                            0 
##                   special_conditions_at_site 
##                                            0 
##                          carriageway_hazards 
##                                            0 
##                          urban_or_rural_area 
##                                            0 
## did_police_officer_attend_scene_of_collision 
##                                            0 
##                              trunk_road_flag 
##                                            0 
##                   lsoa_of_collision_location 
##                                            0
#ALL 0, SO there is NO missing values at all

#💚3. Correct data types
str(data02)  #Make sure all columns have the correct data type
## 'data.frame':    49316 obs. of  36 variables:
##  $ collision_index                             : chr  "2023010419171" "2023010419183" "2023010419189" "2023010419191" ...
##  $ collision_year                              : int  2023 2023 2023 2023 2023 2023 2023 2023 2023 2023 ...
##  $ collision_reference                         : chr  "010419171" "010419183" "010419189" "010419191" ...
##  $ location_easting_osgr                       : chr  "525060" "535463" "508702" "520341" ...
##  $ location_northing_osgr                      : chr  "170416" "198745" "177696" "190175" ...
##  $ longitude                                   : chr  "-0.202878" "-0.042464" "-0.435789" "-0.263972" ...
##  $ latitude                                    : chr  "51.418974" "51.671155" "51.487777" "51.597575" ...
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : int  3 3 3 3 3 3 3 3 3 3 ...
##  $ number_of_vehicles                          : int  1 3 2 2 2 1 2 1 1 2 ...
##  $ number_of_casualties                        : int  1 2 1 1 1 1 1 1 1 1 ...
##  $ date                                        : chr  "01/01/2023" "01/01/2023" "01/01/2023" "01/01/2023" ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ time                                        : chr  "01:24" "02:25" "03:50" "02:13" ...
##  $ local_authority_district                    : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ local_authority_ons_district                : chr  "E09000024" "E09000010" "E09000017" "E09000003" ...
##  $ local_authority_highway                     : chr  "E09000024" "E09000010" "E09000017" "E09000003" ...
##  $ first_road_class                            : int  5 6 3 3 3 3 3 3 3 5 ...
##  $ first_road_number                           : int  0 0 437 5 3220 5 3 406 10 0 ...
##  $ road_type                                   : int  2 6 1 6 6 6 6 3 6 6 ...
##  $ speed_limit                                 : int  20 30 30 30 30 30 20 50 20 20 ...
##  $ junction_detail                             : int  9 3 1 3 8 0 6 0 0 3 ...
##  $ junction_control                            : int  4 4 4 4 4 -1 2 -1 -1 4 ...
##  $ second_road_class                           : int  5 6 6 6 6 0 3 0 0 6 ...
##  $ second_road_number                          : int  0 0 0 0 0 -1 3202 -1 -1 0 ...
##  $ pedestrian_crossing_human_control           : int  2 0 0 0 0 2 0 0 0 1 ...
##  $ pedestrian_crossing_physical_facilities     : int  5 1 0 0 0 5 0 0 4 4 ...
##  $ light_conditions                            : int  4 4 4 4 4 4 4 1 4 1 ...
##  $ weather_conditions                          : int  8 1 1 9 1 1 1 1 1 1 ...
##  $ road_surface_conditions                     : int  2 1 1 1 1 1 2 1 1 1 ...
##  $ special_conditions_at_site                  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ carriageway_hazards                         : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ urban_or_rural_area                         : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ did_police_officer_attend_scene_of_collision: int  1 1 1 1 1 1 1 1 1 1 ...
##  $ trunk_road_flag                             : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ lsoa_of_collision_location                  : chr  "E01003383" "E01001547" "E01002448" "E01000129" ...
nrow(data02)   
## [1] 49316
cat("There is no missing values at all")
## There is no missing values at all
#💚5. Identify and handle invalid data 
#Filter out invalid rows("NULL", -1, unrecorded variable number and recorded "Unknown" rows given stats19) 
#We only study severity at Junctions, hence rid all "0" in 'junction_detail' column #0: Not at or within 20 metres
data3<- data02 %>%
  filter(collision_year == 2023, location_easting_osgr != "NULL", location_northing_osgr != "NULL", longitude != "NULL", latitude!= "NULL",  number_of_casualties >=0, day_of_week %in% 1:7, first_road_class  %in% 1:6,  first_road_number != -1, road_type %in% c(1,2,3,6,7), speed_limit > 0, junction_detail %in% c(0:3,3:9), junction_control %in% 1:4, second_road_class  %in% 1:6,  second_road_number != -1, pedestrian_crossing_human_control  %in% 0:2, pedestrian_crossing_physical_facilities  %in%  c(0,1,4,5,7,8) ,light_conditions %in% c(1,4,5,6,7), weather_conditions %in% 1:8, road_surface_conditions %in% 1:5, special_conditions_at_site  %in% 0:7, carriageway_hazards %in% c(0,1,2,3,6,7), did_police_officer_attend_scene_of_collision  == 1:2, lsoa_of_collision_location != "-1" )
nrow(data3)  
## [1] 9550
view(data3)

#Rid "Unknown" or "9" rows in "road_type" and "weather_conditions"

#💚6. Validate the cleaned data
str(data3)
## 'data.frame':    9550 obs. of  36 variables:
##  $ collision_index                             : chr  "2023010419171" "2023010419189" "2023010419192" "2023010419201" ...
##  $ collision_year                              : int  2023 2023 2023 2023 2023 2023 2023 2023 2023 2023 ...
##  $ collision_reference                         : chr  "010419171" "010419189" "010419192" "010419201" ...
##  $ location_easting_osgr                       : chr  "525060" "508702" "527255" "532189" ...
##  $ location_northing_osgr                      : chr  "170416" "177696" "176963" "179517" ...
##  $ longitude                                   : chr  "-0.202878" "-0.435789" "-0.168976" "-0.097014" ...
##  $ latitude                                    : chr  "51.418974" "51.487777" "51.477324" "51.499145" ...
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : int  3 3 3 3 3 3 3 3 3 3 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ date                                        : chr  "01/01/2023" "01/01/2023" "01/01/2023" "01/01/2023" ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ time                                        : chr  "01:24" "03:50" "01:42" "03:00" ...
##  $ local_authority_district                    : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ local_authority_ons_district                : chr  "E09000024" "E09000017" "E09000032" "E09000028" ...
##  $ local_authority_highway                     : chr  "E09000024" "E09000017" "E09000032" "E09000028" ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : int  2 1 6 6 1 3 2 2 6 6 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : int  9 1 8 6 1 6 3 6 9 3 ...
##  $ junction_control                            : int  4 4 4 2 4 2 4 2 4 4 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : int  2 0 0 0 0 0 0 0 0 0 ...
##  $ pedestrian_crossing_physical_facilities     : int  5 0 0 0 0 5 0 4 0 0 ...
##  $ light_conditions                            : int  4 4 4 4 4 4 6 4 4 1 ...
##  $ weather_conditions                          : int  8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : int  2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ carriageway_hazards                         : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ urban_or_rural_area                         : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ did_police_officer_attend_scene_of_collision: int  1 1 1 1 1 1 1 1 1 1 ...
##  $ trunk_road_flag                             : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ lsoa_of_collision_location                  : chr  "E01003383" "E01002448" "E01004583" "E01003927" ...
summary(data3)
##  collision_index    collision_year collision_reference location_easting_osgr
##  Length:9550        Min.   :2023   Length:9550         Length:9550          
##  Class :character   1st Qu.:2023   Class :character    Class :character     
##  Mode  :character   Median :2023   Mode  :character    Mode  :character     
##                     Mean   :2023                                            
##                     3rd Qu.:2023                                            
##                     Max.   :2023                                            
##  location_northing_osgr  longitude           latitude          police_force 
##  Length:9550            Length:9550        Length:9550        Min.   : 1.0  
##  Class :character       Class :character   Class :character   1st Qu.: 4.0  
##  Mode  :character       Mode  :character   Mode  :character   Median :20.0  
##                                                               Mean   :22.7  
##                                                               3rd Qu.:43.0  
##                                                               Max.   :63.0  
##  legacy_collision_severity number_of_vehicles number_of_casualties
##  Min.   :1.000             Min.   :1.00       Min.   : 1.000      
##  1st Qu.:3.000             1st Qu.:1.00       1st Qu.: 1.000      
##  Median :3.000             Median :2.00       Median : 1.000      
##  Mean   :2.739             Mean   :1.84       Mean   : 1.292      
##  3rd Qu.:3.000             3rd Qu.:2.00       3rd Qu.: 1.000      
##  Max.   :3.000             Max.   :8.00       Max.   :17.000      
##      date            day_of_week        time           local_authority_district
##  Length:9550        Min.   :1.000   Length:9550        Min.   :-1              
##  Class :character   1st Qu.:2.000   Class :character   1st Qu.:-1              
##  Mode  :character   Median :4.000   Mode  :character   Median :-1              
##                     Mean   :4.097                      Mean   :-1              
##                     3rd Qu.:6.000                      3rd Qu.:-1              
##                     Max.   :7.000                      Max.   :-1              
##  local_authority_ons_district local_authority_highway first_road_class
##  Length:9550                  Length:9550             Min.   :1.000   
##  Class :character             Class :character        1st Qu.:3.000   
##  Mode  :character             Mode  :character        Median :4.000   
##                                                       Mean   :4.294   
##                                                       3rd Qu.:6.000   
##                                                       Max.   :6.000   
##  first_road_number   road_type      speed_limit    junction_detail
##  Min.   :   0.0    Min.   :1.000   Min.   :20.00   Min.   :1.000  
##  1st Qu.:   0.0    1st Qu.:6.000   1st Qu.:30.00   1st Qu.:3.000  
##  Median :  41.0    Median :6.000   Median :30.00   Median :3.000  
##  Mean   : 851.9    Mean   :5.153   Mean   :33.02   Mean   :4.281  
##  3rd Qu.: 602.0    3rd Qu.:6.000   3rd Qu.:30.00   3rd Qu.:6.000  
##  Max.   :9204.0    Max.   :7.000   Max.   :70.00   Max.   :9.000  
##  junction_control second_road_class second_road_number
##  Min.   :1.000    Min.   :1.000     Min.   :   0.0    
##  1st Qu.:4.000    1st Qu.:5.000     1st Qu.:   0.0    
##  Median :4.000    Median :6.000     Median :   0.0    
##  Mean   :3.579    Mean   :5.318     Mean   : 397.6    
##  3rd Qu.:4.000    3rd Qu.:6.000     3rd Qu.:   0.0    
##  Max.   :4.000    Max.   :6.000     Max.   :6547.0    
##  pedestrian_crossing_human_control pedestrian_crossing_physical_facilities
##  Min.   :0.00000                   Min.   :0.0                            
##  1st Qu.:0.00000                   1st Qu.:0.0                            
##  Median :0.00000                   Median :0.0                            
##  Mean   :0.04911                   Mean   :1.2                            
##  3rd Qu.:0.00000                   3rd Qu.:1.0                            
##  Max.   :2.00000                   Max.   :8.0                            
##  light_conditions weather_conditions road_surface_conditions
##  Min.   :1.000    Min.   :1.000      Min.   :1.000          
##  1st Qu.:1.000    1st Qu.:1.000      1st Qu.:1.000          
##  Median :1.000    Median :1.000      Median :1.000          
##  Mean   :1.895    Mean   :1.365      Mean   :1.268          
##  3rd Qu.:4.000    3rd Qu.:1.000      3rd Qu.:1.000          
##  Max.   :7.000    Max.   :8.000      Max.   :5.000          
##  special_conditions_at_site carriageway_hazards urban_or_rural_area
##  Min.   :0.00000            Min.   :0.00000     Min.   :-1         
##  1st Qu.:0.00000            1st Qu.:0.00000     1st Qu.:-1         
##  Median :0.00000            Median :0.00000     Median :-1         
##  Mean   :0.07424            Mean   :0.04838     Mean   :-1         
##  3rd Qu.:0.00000            3rd Qu.:0.00000     3rd Qu.:-1         
##  Max.   :7.00000            Max.   :7.00000     Max.   :-1         
##  did_police_officer_attend_scene_of_collision trunk_road_flag
##  Min.   :1.000                                Min.   :-1     
##  1st Qu.:1.000                                1st Qu.:-1     
##  Median :1.000                                Median :-1     
##  Mean   :1.138                                Mean   :-1     
##  3rd Qu.:1.000                                3rd Qu.:-1     
##  Max.   :2.000                                Max.   :-1     
##  lsoa_of_collision_location
##  Length:9550               
##  Class :character          
##  Mode  :character          
##                            
##                            
## 
dim(data3)
## [1] 9550   36
#💚7. Visualization
library(ggplot2)
#ggplot(data3, aes(x = legacy_collision_severity)) + geom_bar() + theme_minimal()
# Visualization: Crash Severity Bar Plot
ggplot(data3, aes(x = as.factor(legacy_collision_severity), fill = as.factor(legacy_collision_severity))) +
  geom_bar() +
  scale_fill_manual(
    name = "Severity Levels",
    values = c("1" = "red", "2" = "orange", "3" = "green"),
    labels = c("1 = Fatal", "2 = Serious", "3 = Slight")
  ) +
  labs(
    title = "Distribution of Crash Severity",
    x = "Crash Severity",
    y = "Count"
  ) +
  theme_minimal()

# Visualization: Speed Limit Histogram
ggplot(data3, aes(x = speed_limit)) + geom_histogram(binwidth = 5) + theme_minimal()

####🌰1 Modeling of Mutinomial Logit Regression(defaulted baseline):

EDA,then fit Mutinomial model on :💛3_1:full model(20 predictors: 11 factor, 9 numeric), #💛3_2: fit shorted model (17 predictors), #💛3_3:fit reduced model (13 predictors), 💛4_2: fit stepwise best model (12 predictors: 6 factors, 6 numeric).

For all 4 models using data4 and new dataset dwrite1, severity Baseline is 3: Slight, junction_detail Baseline is 3 (T or staggered junction), junction_control Baseline is: 4 (Give way or uncontrolled), did_police_officer_attend_scene_of_collision Baseline is: 2(No). # y is “legacy_collision_severity”, X are given in each case. ####Next, carry analysis for Best model: step_test in 💚5 ~ 💚10 #💚5. Relative Risk Ratio and Output tables #💚6. predicted probabilities by fitting best model #💚7. Predict Probability of another dataset using best model #💚8. Table 2 that extracts parameter estimates and goodness-of-fit measures from the multinomial model (step_test) #💚9. Evaluate performances of two models by the F-measure, the G-mean, and the AUC

#💚0. Load necessary libraries
library(ggplot2)
library(GGally)
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
library(dplyr)
library(foreign)
library(nnet)
library(ggplot2)
library(reshape2)
## 
## Attaching package: 'reshape2'
## The following object is masked from 'package:tidyr':
## 
##     smiths
str(data3)
## 'data.frame':    9550 obs. of  36 variables:
##  $ collision_index                             : chr  "2023010419171" "2023010419189" "2023010419192" "2023010419201" ...
##  $ collision_year                              : int  2023 2023 2023 2023 2023 2023 2023 2023 2023 2023 ...
##  $ collision_reference                         : chr  "010419171" "010419189" "010419192" "010419201" ...
##  $ location_easting_osgr                       : chr  "525060" "508702" "527255" "532189" ...
##  $ location_northing_osgr                      : chr  "170416" "177696" "176963" "179517" ...
##  $ longitude                                   : chr  "-0.202878" "-0.435789" "-0.168976" "-0.097014" ...
##  $ latitude                                    : chr  "51.418974" "51.487777" "51.477324" "51.499145" ...
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : int  3 3 3 3 3 3 3 3 3 3 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ date                                        : chr  "01/01/2023" "01/01/2023" "01/01/2023" "01/01/2023" ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ time                                        : chr  "01:24" "03:50" "01:42" "03:00" ...
##  $ local_authority_district                    : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ local_authority_ons_district                : chr  "E09000024" "E09000017" "E09000032" "E09000028" ...
##  $ local_authority_highway                     : chr  "E09000024" "E09000017" "E09000032" "E09000028" ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : int  2 1 6 6 1 3 2 2 6 6 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : int  9 1 8 6 1 6 3 6 9 3 ...
##  $ junction_control                            : int  4 4 4 2 4 2 4 2 4 4 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : int  2 0 0 0 0 0 0 0 0 0 ...
##  $ pedestrian_crossing_physical_facilities     : int  5 0 0 0 0 5 0 4 0 0 ...
##  $ light_conditions                            : int  4 4 4 4 4 4 6 4 4 1 ...
##  $ weather_conditions                          : int  8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : int  2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ carriageway_hazards                         : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ urban_or_rural_area                         : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ did_police_officer_attend_scene_of_collision: int  1 1 1 1 1 1 1 1 1 1 ...
##  $ trunk_road_flag                             : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ lsoa_of_collision_location                  : chr  "E01003383" "E01002448" "E01004583" "E01003927" ...
head(data3)
##   collision_index collision_year collision_reference location_easting_osgr
## 1   2023010419171           2023           010419171                525060
## 2   2023010419189           2023           010419189                508702
## 3   2023010419192           2023           010419192                527255
## 4   2023010419201           2023           010419201                532189
## 5   2023010419259           2023           010419259                532454
## 6   2023010419278           2023           010419278                532076
##   location_northing_osgr longitude  latitude police_force
## 1                 170416 -0.202878 51.418974            1
## 2                 177696 -0.435789 51.487777            1
## 3                 176963 -0.168976 51.477324            1
## 4                 179517 -0.097014 51.499145            1
## 5                 185214 -0.091059 51.550279            1
## 6                 187483 -0.095656 51.570757            1
##   legacy_collision_severity number_of_vehicles number_of_casualties       date
## 1                         3                  1                    1 01/01/2023
## 2                         3                  2                    1 01/01/2023
## 3                         3                  2                    1 01/01/2023
## 4                         3                  2                    1 01/01/2023
## 5                         3                  2                    3 01/01/2023
## 6                         3                  1                    1 01/01/2023
##   day_of_week  time local_authority_district local_authority_ons_district
## 1           1 01:24                       -1                    E09000024
## 2           1 03:50                       -1                    E09000017
## 3           1 01:42                       -1                    E09000032
## 4           1 03:00                       -1                    E09000028
## 5           1 17:15                       -1                    E09000019
## 6           1 21:15                       -1                    E09000012
##   local_authority_highway first_road_class first_road_number road_type
## 1               E09000024                5                 0         2
## 2               E09000017                3               437         1
## 3               E09000032                3              3220         6
## 4               E09000028                3                 3         6
## 5               E09000019                6                 0         1
## 6               E09000012                3               503         3
##   speed_limit junction_detail junction_control second_road_class
## 1          20               9                4                 5
## 2          30               1                4                 6
## 3          30               8                4                 6
## 4          20               6                2                 3
## 5          20               1                4                 6
## 6          30               6                2                 3
##   second_road_number pedestrian_crossing_human_control
## 1                  0                                 2
## 2                  0                                 0
## 3                  0                                 0
## 4               3202                                 0
## 5                  0                                 0
## 6                105                                 0
##   pedestrian_crossing_physical_facilities light_conditions weather_conditions
## 1                                       5                4                  8
## 2                                       0                4                  1
## 3                                       0                4                  1
## 4                                       0                4                  1
## 5                                       0                4                  2
## 6                                       5                4                  2
##   road_surface_conditions special_conditions_at_site carriageway_hazards
## 1                       2                          0                   0
## 2                       1                          0                   0
## 3                       1                          0                   0
## 4                       2                          0                   0
## 5                       2                          0                   0
## 6                       2                          0                   0
##   urban_or_rural_area did_police_officer_attend_scene_of_collision
## 1                  -1                                            1
## 2                  -1                                            1
## 3                  -1                                            1
## 4                  -1                                            1
## 5                  -1                                            1
## 6                  -1                                            1
##   trunk_road_flag lsoa_of_collision_location
## 1              -1                  E01003383
## 2              -1                  E01002448
## 3              -1                  E01004583
## 4              -1                  E01003927
## 5              -1                  E01002779
## 6              -1                  E01033701
summary(data3)
##  collision_index    collision_year collision_reference location_easting_osgr
##  Length:9550        Min.   :2023   Length:9550         Length:9550          
##  Class :character   1st Qu.:2023   Class :character    Class :character     
##  Mode  :character   Median :2023   Mode  :character    Mode  :character     
##                     Mean   :2023                                            
##                     3rd Qu.:2023                                            
##                     Max.   :2023                                            
##  location_northing_osgr  longitude           latitude          police_force 
##  Length:9550            Length:9550        Length:9550        Min.   : 1.0  
##  Class :character       Class :character   Class :character   1st Qu.: 4.0  
##  Mode  :character       Mode  :character   Mode  :character   Median :20.0  
##                                                               Mean   :22.7  
##                                                               3rd Qu.:43.0  
##                                                               Max.   :63.0  
##  legacy_collision_severity number_of_vehicles number_of_casualties
##  Min.   :1.000             Min.   :1.00       Min.   : 1.000      
##  1st Qu.:3.000             1st Qu.:1.00       1st Qu.: 1.000      
##  Median :3.000             Median :2.00       Median : 1.000      
##  Mean   :2.739             Mean   :1.84       Mean   : 1.292      
##  3rd Qu.:3.000             3rd Qu.:2.00       3rd Qu.: 1.000      
##  Max.   :3.000             Max.   :8.00       Max.   :17.000      
##      date            day_of_week        time           local_authority_district
##  Length:9550        Min.   :1.000   Length:9550        Min.   :-1              
##  Class :character   1st Qu.:2.000   Class :character   1st Qu.:-1              
##  Mode  :character   Median :4.000   Mode  :character   Median :-1              
##                     Mean   :4.097                      Mean   :-1              
##                     3rd Qu.:6.000                      3rd Qu.:-1              
##                     Max.   :7.000                      Max.   :-1              
##  local_authority_ons_district local_authority_highway first_road_class
##  Length:9550                  Length:9550             Min.   :1.000   
##  Class :character             Class :character        1st Qu.:3.000   
##  Mode  :character             Mode  :character        Median :4.000   
##                                                       Mean   :4.294   
##                                                       3rd Qu.:6.000   
##                                                       Max.   :6.000   
##  first_road_number   road_type      speed_limit    junction_detail
##  Min.   :   0.0    Min.   :1.000   Min.   :20.00   Min.   :1.000  
##  1st Qu.:   0.0    1st Qu.:6.000   1st Qu.:30.00   1st Qu.:3.000  
##  Median :  41.0    Median :6.000   Median :30.00   Median :3.000  
##  Mean   : 851.9    Mean   :5.153   Mean   :33.02   Mean   :4.281  
##  3rd Qu.: 602.0    3rd Qu.:6.000   3rd Qu.:30.00   3rd Qu.:6.000  
##  Max.   :9204.0    Max.   :7.000   Max.   :70.00   Max.   :9.000  
##  junction_control second_road_class second_road_number
##  Min.   :1.000    Min.   :1.000     Min.   :   0.0    
##  1st Qu.:4.000    1st Qu.:5.000     1st Qu.:   0.0    
##  Median :4.000    Median :6.000     Median :   0.0    
##  Mean   :3.579    Mean   :5.318     Mean   : 397.6    
##  3rd Qu.:4.000    3rd Qu.:6.000     3rd Qu.:   0.0    
##  Max.   :4.000    Max.   :6.000     Max.   :6547.0    
##  pedestrian_crossing_human_control pedestrian_crossing_physical_facilities
##  Min.   :0.00000                   Min.   :0.0                            
##  1st Qu.:0.00000                   1st Qu.:0.0                            
##  Median :0.00000                   Median :0.0                            
##  Mean   :0.04911                   Mean   :1.2                            
##  3rd Qu.:0.00000                   3rd Qu.:1.0                            
##  Max.   :2.00000                   Max.   :8.0                            
##  light_conditions weather_conditions road_surface_conditions
##  Min.   :1.000    Min.   :1.000      Min.   :1.000          
##  1st Qu.:1.000    1st Qu.:1.000      1st Qu.:1.000          
##  Median :1.000    Median :1.000      Median :1.000          
##  Mean   :1.895    Mean   :1.365      Mean   :1.268          
##  3rd Qu.:4.000    3rd Qu.:1.000      3rd Qu.:1.000          
##  Max.   :7.000    Max.   :8.000      Max.   :5.000          
##  special_conditions_at_site carriageway_hazards urban_or_rural_area
##  Min.   :0.00000            Min.   :0.00000     Min.   :-1         
##  1st Qu.:0.00000            1st Qu.:0.00000     1st Qu.:-1         
##  Median :0.00000            Median :0.00000     Median :-1         
##  Mean   :0.07424            Mean   :0.04838     Mean   :-1         
##  3rd Qu.:0.00000            3rd Qu.:0.00000     3rd Qu.:-1         
##  Max.   :7.00000            Max.   :7.00000     Max.   :-1         
##  did_police_officer_attend_scene_of_collision trunk_road_flag
##  Min.   :1.000                                Min.   :-1     
##  1st Qu.:1.000                                1st Qu.:-1     
##  Median :1.000                                Median :-1     
##  Mean   :1.138                                Mean   :-1     
##  3rd Qu.:1.000                                3rd Qu.:-1     
##  Max.   :2.000                                Max.   :-1     
##  lsoa_of_collision_location
##  Length:9550               
##  Class :character          
##  Mode  :character          
##                            
##                            
## 
nrow(data3)/nrow(data02)
## [1] 0.1936491
str(data02)
## 'data.frame':    49316 obs. of  36 variables:
##  $ collision_index                             : chr  "2023010419171" "2023010419183" "2023010419189" "2023010419191" ...
##  $ collision_year                              : int  2023 2023 2023 2023 2023 2023 2023 2023 2023 2023 ...
##  $ collision_reference                         : chr  "010419171" "010419183" "010419189" "010419191" ...
##  $ location_easting_osgr                       : chr  "525060" "535463" "508702" "520341" ...
##  $ location_northing_osgr                      : chr  "170416" "198745" "177696" "190175" ...
##  $ longitude                                   : chr  "-0.202878" "-0.042464" "-0.435789" "-0.263972" ...
##  $ latitude                                    : chr  "51.418974" "51.671155" "51.487777" "51.597575" ...
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : int  3 3 3 3 3 3 3 3 3 3 ...
##  $ number_of_vehicles                          : int  1 3 2 2 2 1 2 1 1 2 ...
##  $ number_of_casualties                        : int  1 2 1 1 1 1 1 1 1 1 ...
##  $ date                                        : chr  "01/01/2023" "01/01/2023" "01/01/2023" "01/01/2023" ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ time                                        : chr  "01:24" "02:25" "03:50" "02:13" ...
##  $ local_authority_district                    : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ local_authority_ons_district                : chr  "E09000024" "E09000010" "E09000017" "E09000003" ...
##  $ local_authority_highway                     : chr  "E09000024" "E09000010" "E09000017" "E09000003" ...
##  $ first_road_class                            : int  5 6 3 3 3 3 3 3 3 5 ...
##  $ first_road_number                           : int  0 0 437 5 3220 5 3 406 10 0 ...
##  $ road_type                                   : int  2 6 1 6 6 6 6 3 6 6 ...
##  $ speed_limit                                 : int  20 30 30 30 30 30 20 50 20 20 ...
##  $ junction_detail                             : int  9 3 1 3 8 0 6 0 0 3 ...
##  $ junction_control                            : int  4 4 4 4 4 -1 2 -1 -1 4 ...
##  $ second_road_class                           : int  5 6 6 6 6 0 3 0 0 6 ...
##  $ second_road_number                          : int  0 0 0 0 0 -1 3202 -1 -1 0 ...
##  $ pedestrian_crossing_human_control           : int  2 0 0 0 0 2 0 0 0 1 ...
##  $ pedestrian_crossing_physical_facilities     : int  5 1 0 0 0 5 0 0 4 4 ...
##  $ light_conditions                            : int  4 4 4 4 4 4 4 1 4 1 ...
##  $ weather_conditions                          : int  8 1 1 9 1 1 1 1 1 1 ...
##  $ road_surface_conditions                     : int  2 1 1 1 1 1 2 1 1 1 ...
##  $ special_conditions_at_site                  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ carriageway_hazards                         : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ urban_or_rural_area                         : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ did_police_officer_attend_scene_of_collision: int  1 1 1 1 1 1 1 1 1 1 ...
##  $ trunk_road_flag                             : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ lsoa_of_collision_location                  : chr  "E01003383" "E01001547" "E01002448" "E01000129" ...
#Rid 13 character columns and 2 constant(always equal to -1) columns among all 36 columns of data3, we get data4 with 21 columns 
data4 <- data3[,c(8:11,13,18:32,34)]  #21 columns
view(data4)
names(data4)
##  [1] "police_force"                                
##  [2] "legacy_collision_severity"                   
##  [3] "number_of_vehicles"                          
##  [4] "number_of_casualties"                        
##  [5] "day_of_week"                                 
##  [6] "first_road_class"                            
##  [7] "first_road_number"                           
##  [8] "road_type"                                   
##  [9] "speed_limit"                                 
## [10] "junction_detail"                             
## [11] "junction_control"                            
## [12] "second_road_class"                           
## [13] "second_road_number"                          
## [14] "pedestrian_crossing_human_control"           
## [15] "pedestrian_crossing_physical_facilities"     
## [16] "light_conditions"                            
## [17] "weather_conditions"                          
## [18] "road_surface_conditions"                     
## [19] "special_conditions_at_site"                  
## [20] "carriageway_hazards"                         
## [21] "did_police_officer_attend_scene_of_collision"
dim(data4)
## [1] 9550   21
head(data4)
##   police_force legacy_collision_severity number_of_vehicles
## 1            1                         3                  1
## 2            1                         3                  2
## 3            1                         3                  2
## 4            1                         3                  2
## 5            1                         3                  2
## 6            1                         3                  1
##   number_of_casualties day_of_week first_road_class first_road_number road_type
## 1                    1           1                5                 0         2
## 2                    1           1                3               437         1
## 3                    1           1                3              3220         6
## 4                    1           1                3                 3         6
## 5                    3           1                6                 0         1
## 6                    1           1                3               503         3
##   speed_limit junction_detail junction_control second_road_class
## 1          20               9                4                 5
## 2          30               1                4                 6
## 3          30               8                4                 6
## 4          20               6                2                 3
## 5          20               1                4                 6
## 6          30               6                2                 3
##   second_road_number pedestrian_crossing_human_control
## 1                  0                                 2
## 2                  0                                 0
## 3                  0                                 0
## 4               3202                                 0
## 5                  0                                 0
## 6                105                                 0
##   pedestrian_crossing_physical_facilities light_conditions weather_conditions
## 1                                       5                4                  8
## 2                                       0                4                  1
## 3                                       0                4                  1
## 4                                       0                4                  1
## 5                                       0                4                  2
## 6                                       5                4                  2
##   road_surface_conditions special_conditions_at_site carriageway_hazards
## 1                       2                          0                   0
## 2                       1                          0                   0
## 3                       1                          0                   0
## 4                       2                          0                   0
## 5                       2                          0                   0
## 6                       2                          0                   0
##   did_police_officer_attend_scene_of_collision
## 1                                            1
## 2                                            1
## 3                                            1
## 4                                            1
## 5                                            1
## 6                                            1
data4$legacy_collision_severity[1]
## [1] 3
#visualize it
ggplot(data4, aes(x = legacy_collision_severity)) + geom_bar() + theme_minimal()

# caculate propotion of each category in all severity categories
#caculate total rows
total_rows <- nrow(data4)

#Count the frequency of each value
count_1 <- sum(data4$legacy_collision_severity == 1)
count_2 <- sum(data4$legacy_collision_severity == 2)
count_3 <- sum(data4$legacy_collision_severity == 3)

prop_1 <- count_1 / total_rows
prop_2 <- count_2 / total_rows
prop_3 <- count_3 / total_rows

cat("Number of rows where legacy_collision_severity == 1 is", count_1, "\n")
## Number of rows where legacy_collision_severity == 1 is 104
cat("Proportion of rows where legacy_collision_severity == 1 is", prop_1, "\n\n")
## Proportion of rows where legacy_collision_severity == 1 is 0.01089005
cat("Number of rows where legacy_collision_severity == 2 is", count_2, "\n")
## Number of rows where legacy_collision_severity == 2 is 2280
cat("Proportion of rows where legacy_collision_severity == 2 is", prop_2, "\n\n")
## Proportion of rows where legacy_collision_severity == 2 is 0.2387435
cat("Number of rows where legacy_collision_severity == 3 is", count_3, "\n")
## Number of rows where legacy_collision_severity == 3 is 7166
cat("Proportion of rows where legacy_collision_severity == 3 is", prop_3, "\n")
## Proportion of rows where legacy_collision_severity == 3 is 0.7503665
####Table 1 in https://www.mdpi.com/2071-1050/14/6/3188

#💚1. Plot the count and percentage distribution of the selected factors for the model development.
#💛1_1: 6 bar plots of Count distribution of the 6 selected numeric factors
# Load necessary libraries
library(ggplot2)
library(dplyr)
library(reshape2)

# Define the function to calculate count and percentage
create_plot_data <- function(data, group_col) {
  data %>%
    group_by(!!sym(group_col), legacy_collision_severity) %>%
    summarise(Count = n()) %>%
    mutate(Percentage = Count / sum(Count) * 100)
}

# Example for one variable: First Road Class
#9 numeric predictors
plot_police_force <- create_plot_data(data4, "police_force")
## `summarise()` has grouped output by 'police_force'. You can override using the
## `.groups` argument.
plot_number_of_vehicles <- create_plot_data(data4, "number_of_vehicles")
## `summarise()` has grouped output by 'number_of_vehicles'. You can override
## using the `.groups` argument.
plot_number_of_casualties <- create_plot_data(data4, "number_of_casualties")
## `summarise()` has grouped output by 'number_of_casualties'. You can override
## using the `.groups` argument.
plot_speed_limit <- create_plot_data(data4, "speed_limit")
## `summarise()` has grouped output by 'speed_limit'. You can override using the
## `.groups` argument.
plot_day_of_week  <- create_plot_data(data4, "day_of_week")
## `summarise()` has grouped output by 'day_of_week'. You can override using the
## `.groups` argument.
plot_first_road_class <- create_plot_data(data4, "first_road_class")
## `summarise()` has grouped output by 'first_road_class'. You can override using
## the `.groups` argument.
plot_first_road_number <- create_plot_data(data4, "first_road_number")
## `summarise()` has grouped output by 'first_road_number'. You can override using
## the `.groups` argument.
plot_second_road_class <- create_plot_data(data4, "second_road_class")
## `summarise()` has grouped output by 'second_road_class'. You can override using
## the `.groups` argument.
plot_second_road_number <- create_plot_data(data4, "second_road_number")
## `summarise()` has grouped output by 'second_road_number'. You can override
## using the `.groups` argument.
# List of plot data
plot_data_list <- list(
  "Police Force" = plot_police_force,
  "Number of Vehicles" = plot_number_of_vehicles,
  "Number of Casualties" = plot_number_of_casualties,
  "Day of week" = plot_day_of_week,
  "Speed Limit" = plot_speed_limit,
  "First Road Class" = plot_first_road_class,
  "First Road Number" = plot_first_road_number,
  "Second Road Class" = plot_second_road_class,
  "Second Road Number" = plot_second_road_number
)

# Function to create count and percentage bar plots
plot_factor_distribution <- function(plot_data, title) {
  ggplot(plot_data, aes(x = as.factor(!!sym(names(plot_data)[1])), y = Count, fill = as.factor(legacy_collision_severity))) +
    geom_bar(stat = "identity", position = "dodge") +
    labs(title = title, x = names(plot_data)[1], y = "Count") +
    theme_minimal() +
    scale_fill_manual(name = "Severity", values = c("red", "orange", "green"), 
                      labels = c("Fatal", "Serious", "Slight"))
}


# Create plots for each factor
plots <- lapply(names(plot_data_list), function(factor_name) {
  plot_factor_distribution(plot_data_list[[factor_name]], paste("Count Distribution for", factor_name))
})

# Optionally, print plots in a loop
for (i in seq_along(plots)) {
  print(plots[[i]])
}

#💛1_2:Table for the count and percentage distribution of the 6 selected categorical factors for the model development.
#Table 1&2 in https://www.mdpi.com/2071-1050/14/6/3188

library(dplyr)

library(tidyr)

# List of significant variables
significant_vars <- c("police_force", "number_of_vehicles", "number_of_casualties", "speed_limit", 
                      "junction_detail", "junction_control", "second_road_class", "second_road_number", 
                      "pedestrian_crossing_human_control", "light_conditions", "road_surface_conditions", 
                      "did_police_officer_attend_scene_of_collision")

# Function to calculate count and percentage for each variable
calc_count_percentage <- function(data, var_name) {
  data %>%
    group_by(!!sym(var_name), legacy_collision_severity) %>%
    summarise(Count = n()) %>%
    group_by(!!sym(var_name)) %>%
    mutate(Total = sum(Count)) %>%
    spread(legacy_collision_severity, Count, fill = 0) %>%
    mutate(Fatal_Perc = round((`1` / Total) * 100, 2),
           Serious_Perc = round((`2` / Total) * 100, 2),
           Slight_Perc = round((`3` / Total) * 100, 2)) %>%
    rename(Fatal_Count = `1`, Serious_Count = `2`, Slight_Count = `3`)
}

# Apply the function to each significant variable and combine the results into a list
results_list <- lapply(significant_vars, function(var) {
  calc_count_percentage(data4, var)
})
## `summarise()` has grouped output by 'police_force'. You can override using the
## `.groups` argument.
## `summarise()` has grouped output by 'number_of_vehicles'. You can override
## using the `.groups` argument.
## `summarise()` has grouped output by 'number_of_casualties'. You can override
## using the `.groups` argument.
## `summarise()` has grouped output by 'speed_limit'. You can override using the
## `.groups` argument.
## `summarise()` has grouped output by 'junction_detail'. You can override using
## the `.groups` argument.
## `summarise()` has grouped output by 'junction_control'. You can override using
## the `.groups` argument.
## `summarise()` has grouped output by 'second_road_class'. You can override using
## the `.groups` argument.
## `summarise()` has grouped output by 'second_road_number'. You can override
## using the `.groups` argument.
## `summarise()` has grouped output by 'pedestrian_crossing_human_control'. You
## can override using the `.groups` argument.
## `summarise()` has grouped output by 'light_conditions'. You can override using
## the `.groups` argument.
## `summarise()` has grouped output by 'road_surface_conditions'. You can override
## using the `.groups` argument.
## `summarise()` has grouped output by
## 'did_police_officer_attend_scene_of_collision'. You can override using the
## `.groups` argument.
# Name the list elements by variable names for clarity
names(results_list) <- significant_vars

# Display the results for each variable
for (var_name in significant_vars) {
  cat("\nResults for:", var_name, "\n")
  print(results_list[[var_name]])
}    ##Table 3.1
## 
## Results for: police_force 
## # A tibble: 40 × 8
## # Groups:   police_force [40]
##    police_force Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##           <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
##  1            1  2304          14           527         1763       0.61
##  2            4   361           4           130          227       1.11
##  3            5   257           2            53          202       0.78
##  4            6   195           3            65          127       1.54
##  5            7   222           2            35          185       0.9 
##  6           10   112           2            22           88       1.79
##  7           11    35           3            14           18       8.57
##  8           12   131           2            25          104       1.53
##  9           13   580           8           167          405       1.38
## 10           14   280           1            85          194       0.36
## # ℹ 30 more rows
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
## 
## Results for: number_of_vehicles 
## # A tibble: 8 × 8
## # Groups:   number_of_vehicles [8]
##   number_of_vehicles Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##                <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
## 1                  1  2446          43           764         1639       1.76
## 2                  2  6388          43          1371         4974       0.67
## 3                  3   571          17           121          433       2.98
## 4                  4   110           1            16           93       0.91
## 5                  5    22           0             6           16       0   
## 6                  6     8           0             2            6       0   
## 7                  7     3           0             0            3       0   
## 8                  8     2           0             0            2       0   
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
## 
## Results for: number_of_casualties 
## # A tibble: 10 × 8
## # Groups:   number_of_casualties [10]
##    number_of_casualties Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##                   <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
##  1                    1  7598          72          1823         5703       0.95
##  2                    2  1399          15           309         1075       1.07
##  3                    3   367          10            97          260       2.72
##  4                    4   122           4            28           90       3.28
##  5                    5    49           3            17           29       6.12
##  6                    6    10           0             5            5       0   
##  7                    7     1           0             0            1       0   
##  8                    8     2           0             0            2       0   
##  9                   12     1           0             0            1       0   
## 10                   17     1           0             1            0       0   
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
## 
## Results for: speed_limit 
## # A tibble: 6 × 8
## # Groups:   speed_limit [6]
##   speed_limit Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##         <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
## 1          20  1654          17           394         1243       1.03
## 2          30  5736          42          1341         4353       0.73
## 3          40   857          13           188          656       1.52
## 4          50   374           8           101          265       2.14
## 5          60   781          24           223          534       3.07
## 6          70   148           0            33          115       0   
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
## 
## Results for: junction_detail 
## # A tibble: 8 × 8
## # Groups:   junction_detail [8]
##   junction_detail Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##             <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
## 1               1  1089           5           203          881       0.46
## 2               2   242           2            52          188       0.83
## 3               3  4679          51          1192         3436       1.09
## 4               5   185           3            54          128       1.62
## 5               6  1642          18           406         1218       1.1 
## 6               7   275           4            50          221       1.45
## 7               8   370           4            90          276       1.08
## 8               9  1068          17           233          818       1.59
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
## 
## Results for: junction_control 
## # A tibble: 4 × 8
## # Groups:   junction_control [4]
##   junction_control Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##              <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
## 1                1   125           0            21          104       0   
## 2                2  1767          15           366         1386       0.85
## 3                3   112           0            29           83       0   
## 4                4  7546          89          1864         5593       1.18
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
## 
## Results for: second_road_class 
## # A tibble: 6 × 8
## # Groups:   second_road_class [6]
##   second_road_class Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##               <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
## 1                 1    41           0             8           33       0   
## 2                 2     9           0             4            5       0   
## 3                 3  1500          14           314         1172       0.93
## 4                 4   685           3           162          520       0.44
## 5                 5   402           1           102          299       0.25
## 6                 6  6913          86          1690         5137       1.24
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
## 
## Results for: second_road_number 
## # A tibble: 1,004 × 8
## # Groups:   second_road_number [1,004]
##    second_road_number Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##                 <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
##  1                  0  7315          87          1792         5436       1.19
##  2                  1    25           1             4           20       4   
##  3                  2    12           0             5            7       0   
##  4                  3    17           0             3           14       0   
##  5                  4    26           1             3           22       3.85
##  6                  5    13           1             3            9       7.69
##  7                  6    17           0             5           12       0   
##  8                  7     1           0             0            1       0   
##  9                 10    14           0             3           11       0   
## 10                 11     7           0             0            7       0   
## # ℹ 994 more rows
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
## 
## Results for: pedestrian_crossing_human_control 
## # A tibble: 3 × 8
## # Groups:   pedestrian_crossing_human_control [3]
##   pedestrian_crossing_…¹ Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##                    <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
## 1                      0  9289         104          2230         6955       1.12
## 2                      1    53           0             9           44       0   
## 3                      2   208           0            41          167       0   
## # ℹ abbreviated name: ¹​pedestrian_crossing_human_control
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
## 
## Results for: light_conditions 
## # A tibble: 5 × 8
## # Groups:   light_conditions [5]
##   light_conditions Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##              <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
## 1                1  6963          54          1626         5283       0.78
## 2                4  2208          42           556         1610       1.9 
## 3                5    57           2            20           35       3.51
## 4                6   235           4            65          166       1.7 
## 5                7    87           2            13           72       2.3 
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
## 
## Results for: road_surface_conditions 
## # A tibble: 5 × 8
## # Groups:   road_surface_conditions [5]
##   road_surface_conditi…¹ Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##                    <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
## 1                      1  7330          75          1797         5458       1.02
## 2                      2  2035          27           451         1557       1.33
## 3                      3    30           0             4           26       0   
## 4                      4   151           1            28          122       0.66
## 5                      5     4           1             0            3      25   
## # ℹ abbreviated name: ¹​road_surface_conditions
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
## 
## Results for: did_police_officer_attend_scene_of_collision 
## # A tibble: 2 × 8
## # Groups:   did_police_officer_attend_scene_of_collision [2]
##   did_police_officer_a…¹ Total Fatal_Count Serious_Count Slight_Count Fatal_Perc
##                    <int> <int>       <dbl>         <dbl>        <dbl>      <dbl>
## 1                      1  8236         103          2107         6026       1.25
## 2                      2  1314           1           173         1140       0.08
## # ℹ abbreviated name: ¹​did_police_officer_attend_scene_of_collision
## # ℹ 2 more variables: Serious_Perc <dbl>, Slight_Perc <dbl>
#💛1_3: Figure 2.1

library(DiagrammeR)
grViz("
digraph flowchart {
  
  # 定义图表方向
  graph [layout = dot, rankdir = TB]
  
  # 定义节点
  node [shape = ellipse, style=filled, color=lightblue]
  A [label = 'Great Britain STATS19 crash database\nN = 49,316\nStudy period = 2023.1-2023.6']
  
  node [shape = box, style=filled, color=lightgray]
  B [label = 'Vehicle-pedestrian crashes\nN = 9,550\nChapter 4']
  C [label = 'Data pre-processing\nChapter 4']
  
  node [shape = parallelogram, style=filled, color=lightblue]
  D [label = 'Multinomial Logistic models\nChapter 3.2']
  E [label = 'Ordinal Logistic models\nChapter 3.3']
  F [label = 'Significant explanatory variables\nRelative Risk Ratios\nPredicted Probability\nChapter 5.3.1.1 and 5.3.1.2']
  G [label = 'Propotional Odds Ratios\nPredicted Probability\nMarginal Effects\nParallel Regression Assumption\nChapter 5.3.2.1 ~ 5.3.2.4']
  
  
  node [shape = box, style=filled, color=lightgray]
 
  
  node [shape = diamond, style=filled, color=lightblue]
  H [label = 'Parameter Estimates\nGoodness of Fit Measures\nRMSE\nAUC Values\nChapter 5.2.1 ~ 5.2.3 and 5.4']
  
  node [shape = ellipse, style=filled, color=lightgray]
  I [label = 'Conclusions and Recommendations\nChapter 6']
  
  # 定义边
  A -> B
  B -> C
  C -> D
  C -> E
  D -> F
  E -> G
  F -> H
  G -> H
  H -> I
}
")
####


#💚2. EDA: Generate pair plots for the dataset data4

#💛2_1: using ggpairs() function
# Select a subset of columns if the dataset data4 is large to avoid cluttered plots
data4_subset1 <- data4 %>%
  select(legacy_collision_severity, police_force, number_of_vehicles, number_of_casualties, day_of_week ) 
# Create pair plots
ggpairs(data4_subset1)

str(data4)
## 'data.frame':    9550 obs. of  21 variables:
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : int  3 3 3 3 3 3 3 3 3 3 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : int  2 1 6 6 1 3 2 2 6 6 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : int  9 1 8 6 1 6 3 6 9 3 ...
##  $ junction_control                            : int  4 4 4 2 4 2 4 2 4 4 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : int  2 0 0 0 0 0 0 0 0 0 ...
##  $ pedestrian_crossing_physical_facilities     : int  5 0 0 0 0 5 0 4 0 0 ...
##  $ light_conditions                            : int  4 4 4 4 4 4 6 4 4 1 ...
##  $ weather_conditions                          : int  8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : int  2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ carriageway_hazards                         : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ did_police_officer_attend_scene_of_collision: int  1 1 1 1 1 1 1 1 1 1 ...
data4_subset2 <- data4 %>%
  select(legacy_collision_severity, first_road_class, first_road_number, road_type, speed_limit, junction_detail, junction_control)
ggpairs(data4_subset2)

data4_subset3 <- data4 %>%
  select(legacy_collision_severity, second_road_class, second_road_number, pedestrian_crossing_human_control, pedestrian_crossing_physical_facilities, light_conditions, weather_conditions) 
ggpairs(data4_subset3)

data4_subset4 <- data4 %>%
  select(legacy_collision_severity, road_surface_conditions, special_conditions_at_site, carriageway_hazards, did_police_officer_attend_scene_of_collision) 
ggpairs(data4_subset4)

#💛2_2: using pairs() function
pairs(data4[,c(2,1,3,4,5)])

pairs(data4[,c(2,6:11)])

pairs(data4[,c(2,12:17)])

pairs(data4[,c(2,18:21)])

#💚3. fit Mutinomial model            💜
#defaulted Baseline of "severity" is "1": Fatal
view(data4)
str(data4)   #All numeric (21 variables)
## 'data.frame':    9550 obs. of  21 variables:
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : int  3 3 3 3 3 3 3 3 3 3 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : int  2 1 6 6 1 3 2 2 6 6 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : int  9 1 8 6 1 6 3 6 9 3 ...
##  $ junction_control                            : int  4 4 4 2 4 2 4 2 4 4 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : int  2 0 0 0 0 0 0 0 0 0 ...
##  $ pedestrian_crossing_physical_facilities     : int  5 0 0 0 0 5 0 4 0 0 ...
##  $ light_conditions                            : int  4 4 4 4 4 4 6 4 4 1 ...
##  $ weather_conditions                          : int  8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : int  2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ carriageway_hazards                         : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ did_police_officer_attend_scene_of_collision: int  1 1 1 1 1 1 1 1 1 1 ...
#💛3_1: fit full model(20 predictors: 11 factors, 9 numeric) with Baseline of response: 3 Slight                  💜1
library(nnet)
is.factor(data4$legacy_collision_severity[1])
## [1] FALSE
#💙3_1_1 convert response to a factor
data4$legacy_collision_severity <- as.factor(data4$legacy_collision_severity)
data4$legacy_collision_severity[1]   #defaulted Baseline is 1:Fatal
## [1] 3
## Levels: 1 2 3
#Change baseline of response from 1:Fatal to 3: Slight
data4$legacy_collision_severity <- relevel(data4$legacy_collision_severity, ref = "3")
data4$legacy_collision_severity[1] #new Baseline is 3:Slight 
## [1] 3
## Levels: 3 1 2
########
str(data4)  #1 response factor, 20 numeric
## 'data.frame':    9550 obs. of  21 variables:
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : Factor w/ 3 levels "3","1","2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : int  2 1 6 6 1 3 2 2 6 6 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : int  9 1 8 6 1 6 3 6 9 3 ...
##  $ junction_control                            : int  4 4 4 2 4 2 4 2 4 4 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : int  2 0 0 0 0 0 0 0 0 0 ...
##  $ pedestrian_crossing_physical_facilities     : int  5 0 0 0 0 5 0 4 0 0 ...
##  $ light_conditions                            : int  4 4 4 4 4 4 6 4 4 1 ...
##  $ weather_conditions                          : int  8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : int  2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ carriageway_hazards                         : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ did_police_officer_attend_scene_of_collision: int  1 1 1 1 1 1 1 1 1 1 ...
#💙3_1_2 Turn Numeric predictors(11) into Factors with Defaulted baseline respectively, according to comparison table of Stats19 below: https://assets.publishing.service.gov.uk/media/60d0cc548fa8f57ce4615110/stats19.pdf
##11 Baselines
data4$pedestrian_crossing_human_control <- as.factor(data4$pedestrian_crossing_human_control) #Baseline: 0 (None within 50 metres)
data4$road_type <- as.factor(data4$road_type)  #Baseline: 1
data4$junction_detail <- as.factor(data4$junction_detail) #Baseline: 1

data4$junction_control <- as.factor(data4$junction_control) #Baseline: 1
data4$pedestrian_crossing_physical_facilities <- as.factor(data4$pedestrian_crossing_physical_facilities) #Baseline: 0(No physical crossing facility within 50m)
data4$light_conditions <- as.factor(data4$light_conditions) #Baseline: 1 (Daylight)
data4$weather_conditions <- as.factor(data4$weather_conditions) #Baseline: 1 (Fine without high winds)
data4$road_surface_conditions <- as.factor(data4$road_surface_conditions) #Baseline: 1 (Dry)
data4$special_conditions_at_site <- as.factor(data4$special_conditions_at_site)#Baseline: 0  (None)
data4$carriageway_hazards <- as.factor(data4$carriageway_hazards) #Baseline: 0 (None)
data4$did_police_officer_attend_scene_of_collision <- as.factor(data4$did_police_officer_attend_scene_of_collision) #Baseline: 1

str(data4)    #1 response factor, 20 predictors: 11 factor, 9 numeric
## 'data.frame':    9550 obs. of  21 variables:
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : Factor w/ 3 levels "3","1","2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : Factor w/ 5 levels "1","2","3","6",..: 2 1 4 4 1 3 2 2 4 4 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : Factor w/ 8 levels "1","2","3","5",..: 8 1 7 5 1 5 3 5 8 3 ...
##  $ junction_control                            : Factor w/ 4 levels "1","2","3","4": 4 4 4 2 4 2 4 2 4 4 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : Factor w/ 3 levels "0","1","2": 3 1 1 1 1 1 1 1 1 1 ...
##  $ pedestrian_crossing_physical_facilities     : Factor w/ 6 levels "0","1","4","5",..: 4 1 1 1 1 4 1 3 1 1 ...
##  $ light_conditions                            : Factor w/ 5 levels "1","4","5","6",..: 2 2 2 2 2 2 4 2 2 1 ...
##  $ weather_conditions                          : Factor w/ 8 levels "1","2","3","4",..: 8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : Factor w/ 5 levels "1","2","3","4",..: 2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : Factor w/ 8 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ carriageway_hazards                         : Factor w/ 6 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ did_police_officer_attend_scene_of_collision: Factor w/ 2 levels "1","2": 1 1 1 1 1 1 1 1 1 1 ...
#💙3_1_3 Change baseline of specific 3 predictors

data4$junction_detail <- relevel(data4$junction_detail, ref = "3")
data4$junction_detail[1]  #Baseline: 3 (T or staggered junction)
## [1] 9
## Levels: 3 1 2 5 6 7 8 9
data4$junction_control <- relevel(data4$junction_control, ref = "4")
data4$junction_control[1] #Baseline: 4 (Give way or uncontrolled)
## [1] 4
## Levels: 4 1 2 3
data4$did_police_officer_attend_scene_of_collision <- relevel(data4$did_police_officer_attend_scene_of_collision, ref = "2")

data4$did_police_officer_attend_scene_of_collision[1]#Baseline: 2 (No)
## [1] 1
## Levels: 2 1
#💙3_1_4 fit full model(20 predictors: 11 factors, 9 numeric) with defaulted Baseline of resposne: 1 Fatal
str(data4)
## 'data.frame':    9550 obs. of  21 variables:
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : Factor w/ 3 levels "3","1","2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : Factor w/ 5 levels "1","2","3","6",..: 2 1 4 4 1 3 2 2 4 4 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : Factor w/ 8 levels "3","1","2","5",..: 8 2 7 5 2 5 1 5 8 1 ...
##  $ junction_control                            : Factor w/ 4 levels "4","1","2","3": 1 1 1 3 1 3 1 3 1 1 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : Factor w/ 3 levels "0","1","2": 3 1 1 1 1 1 1 1 1 1 ...
##  $ pedestrian_crossing_physical_facilities     : Factor w/ 6 levels "0","1","4","5",..: 4 1 1 1 1 4 1 3 1 1 ...
##  $ light_conditions                            : Factor w/ 5 levels "1","4","5","6",..: 2 2 2 2 2 2 4 2 2 1 ...
##  $ weather_conditions                          : Factor w/ 8 levels "1","2","3","4",..: 8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : Factor w/ 5 levels "1","2","3","4",..: 2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : Factor w/ 8 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ carriageway_hazards                         : Factor w/ 6 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ did_police_officer_attend_scene_of_collision: Factor w/ 2 levels "2","1": 2 2 2 2 2 2 2 2 2 2 ...
full_test <- multinom(legacy_collision_severity~., data = data4)
## # weights:  180 (118 variable)
## initial  value 10491.747357 
## iter  10 value 6402.520219
## iter  20 value 5975.571105
## iter  30 value 5682.303843
## iter  40 value 5607.082472
## iter  50 value 5576.438268
## iter  60 value 5562.486611
## iter  70 value 5561.863329
## iter  80 value 5561.256155
## iter  90 value 5561.114478
## iter 100 value 5561.091132
## final  value 5561.091132 
## stopped after 100 iterations
summary(full_test)   ##Residual Deviance: 11122.18 AIC: 11358.18
## Call:
## multinom(formula = legacy_collision_severity ~ ., data = data4)
## 
## Coefficients:
##   (Intercept)  police_force number_of_vehicles number_of_casualties day_of_week
## 1   -9.649336 -0.0002603854         -0.4435874            0.2821931 0.033646727
## 2   -1.623632 -0.0033539057         -0.4237118            0.0593945 0.008926054
##   first_road_class first_road_number road_type2  road_type3 road_type6
## 1      0.060726049      9.000039e-05 -0.3174556 -0.85976618 -0.5542447
## 2     -0.008681604      1.697736e-05 -0.2515685 -0.01148905  0.0568374
##   road_type7 speed_limit junction_detail1 junction_detail2 junction_detail5
## 1  0.2239049 0.045845846       -1.2783805       -0.4937728       -0.3539749
## 2  0.1044930 0.007873401       -0.3192354       -0.1578201        0.1202851
##   junction_detail6 junction_detail7 junction_detail8 junction_detail9
## 1       0.12853599        0.6321293      -0.15935560        0.3160721
## 2       0.03997728       -0.3472000      -0.09359557       -0.2130548
##   junction_control1 junction_control2 junction_control3 second_road_class
## 1       -19.3304623        -0.0539519     -9.8526330318        0.23723608
## 2        -0.5663018        -0.3036329     -0.0006324719        0.05272483
##   second_road_number pedestrian_crossing_human_control1
## 1       5.303346e-05                        -13.1291641
## 2       5.009628e-05                         -0.5134329
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                         -9.4643030                               -0.1389320
## 2                         -0.2263456                               -0.2414344
##   pedestrian_crossing_physical_facilities4
## 1                               0.57729933
## 2                               0.02003174
##   pedestrian_crossing_physical_facilities5
## 1                               -0.4969318
## 2                                0.1004731
##   pedestrian_crossing_physical_facilities7
## 1                             -13.81440362
## 2                               0.05436394
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.2895445         1.2081215         1.7839651
## 2                                0.1313142         0.1674304         0.7006969
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.06687944         1.2946794         -0.10906583         -15.0747536
## 2       -0.04898701        -0.4876633         -0.08968094           0.1383215
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         1.157493198         1.125282639          -8.0317966
## 2        -0.006637487        -0.008499294          -0.1475138
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1          -13.628079          -0.3894472               -0.1582056
## 2           -0.200857           0.0234403               -0.1907727
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1                -4.911645               -0.8320947                 1.484379
## 2                -0.824147               -0.4492597               -13.666844
##   special_conditions_at_site1 special_conditions_at_site2
## 1                  -12.127460                   -2.928582
## 2                   -1.098886                    1.003969
##   special_conditions_at_site3 special_conditions_at_site4
## 1                 -13.3502704                  0.59501806
## 2                   0.2673735                 -0.04677051
##   special_conditions_at_site5 special_conditions_at_site6
## 1                 -11.5920766                  -10.853101
## 2                  -0.4631856                   -1.024815
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   -8.907198          -10.7946592          -0.33427025
## 2                    1.291973            0.4316188           0.03124668
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1          -13.1815425            1.6841315           -11.434012
## 2            0.7183624           -0.4566238             0.590187
##   did_police_officer_attend_scene_of_collision1
## 1                                     2.8213299
## 2                                     0.8693817
## 
## Std. Errors:
##   (Intercept) police_force number_of_vehicles number_of_casualties day_of_week
## 1 0.006883285  0.005540718         0.02229413           0.08012842  0.04963468
## 2 0.014285587  0.001391530         0.04147174           0.03579138  0.01239533
##   first_road_class first_road_number   road_type2  road_type3  road_type6
## 1       0.07715662      5.979452e-05 0.0003941961 0.005315322 0.004981006
## 2       0.01915109      1.620450e-05 0.0066941979 0.049392388 0.044181288
##     road_type7 speed_limit junction_detail1 junction_detail2 junction_detail5
## 1 0.0005175358 0.007288014      0.001343273     0.0005850073      0.001762981
## 2 0.0028615356 0.002193569      0.075670016     0.0054192610      0.011154106
##   junction_detail6 junction_detail7 junction_detail8 junction_detail9
## 1      0.002344953     0.0003871143      0.001211368      0.002671039
## 2      0.068072959     0.0122019725      0.014102407      0.079615019
##   junction_control1 junction_control2 junction_control3 second_road_class
## 1      2.179850e-12       0.005058009      9.690439e-09        0.07448496
## 2      1.236231e-03       0.050349913      2.398642e-03        0.02196781
##   second_road_number pedestrian_crossing_human_control1
## 1       9.674306e-05                       6.346776e-10
## 2       2.248322e-05                       6.020673e-04
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                       7.327329e-08                             0.0007649916
## 2                       5.700382e-03                             0.0133277535
##   pedestrian_crossing_physical_facilities4
## 1                              0.005784734
## 2                              0.078705078
##   pedestrian_crossing_physical_facilities5
## 1                              0.002135923
## 2                              0.050278825
##   pedestrian_crossing_physical_facilities7
## 1                             9.670815e-11
## 2                             7.721476e-04
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                             0.0004267612       0.008163959      0.0003210215
## 2                             0.0079222245       0.058870686      0.0014119723
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       0.001460050      0.0005882037         0.002974713        1.244954e-11
## 2       0.005888787      0.0007840681         0.027895839        7.048062e-04
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1        0.0003975037        0.0007287123        1.620607e-08
## 2        0.0007144411        0.0014868491        1.549681e-04
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1        5.351479e-10        0.0003669845              0.002439978
## 2        3.045100e-04        0.0030533694              0.048477183
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1             4.481396e-08             0.0001457525             1.885225e-04
## 2             2.433617e-04             0.0014995198             3.353128e-10
##   special_conditions_at_site1 special_conditions_at_site2
## 1                2.450033e-09                5.287748e-07
## 2                2.709103e-04                1.705175e-04
##   special_conditions_at_site3 special_conditions_at_site4
## 1                2.614023e-10                0.0004704346
## 2                6.703465e-04                0.0010769200
##   special_conditions_at_site5 special_conditions_at_site6
## 1                1.392063e-09                1.770430e-09
## 2                2.174103e-04                2.310177e-04
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                9.387168e-09         1.680322e-09         0.0001409420
## 2                3.421237e-04         4.246618e-04         0.0007913176
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1         3.817691e-10         0.0003041781         1.324792e-09
## 2         3.427446e-04         0.0004218098         3.791659e-04
##   did_police_officer_attend_scene_of_collision1
## 1                                   0.007009982
## 2                                   0.079023688
## 
## Residual Deviance: 11122.18 
## AIC: 11358.18
summary(full_test)$coefficients
##   (Intercept)  police_force number_of_vehicles number_of_casualties day_of_week
## 1   -9.649336 -0.0002603854         -0.4435874            0.2821931 0.033646727
## 2   -1.623632 -0.0033539057         -0.4237118            0.0593945 0.008926054
##   first_road_class first_road_number road_type2  road_type3 road_type6
## 1      0.060726049      9.000039e-05 -0.3174556 -0.85976618 -0.5542447
## 2     -0.008681604      1.697736e-05 -0.2515685 -0.01148905  0.0568374
##   road_type7 speed_limit junction_detail1 junction_detail2 junction_detail5
## 1  0.2239049 0.045845846       -1.2783805       -0.4937728       -0.3539749
## 2  0.1044930 0.007873401       -0.3192354       -0.1578201        0.1202851
##   junction_detail6 junction_detail7 junction_detail8 junction_detail9
## 1       0.12853599        0.6321293      -0.15935560        0.3160721
## 2       0.03997728       -0.3472000      -0.09359557       -0.2130548
##   junction_control1 junction_control2 junction_control3 second_road_class
## 1       -19.3304623        -0.0539519     -9.8526330318        0.23723608
## 2        -0.5663018        -0.3036329     -0.0006324719        0.05272483
##   second_road_number pedestrian_crossing_human_control1
## 1       5.303346e-05                        -13.1291641
## 2       5.009628e-05                         -0.5134329
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                         -9.4643030                               -0.1389320
## 2                         -0.2263456                               -0.2414344
##   pedestrian_crossing_physical_facilities4
## 1                               0.57729933
## 2                               0.02003174
##   pedestrian_crossing_physical_facilities5
## 1                               -0.4969318
## 2                                0.1004731
##   pedestrian_crossing_physical_facilities7
## 1                             -13.81440362
## 2                               0.05436394
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.2895445         1.2081215         1.7839651
## 2                                0.1313142         0.1674304         0.7006969
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.06687944         1.2946794         -0.10906583         -15.0747536
## 2       -0.04898701        -0.4876633         -0.08968094           0.1383215
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         1.157493198         1.125282639          -8.0317966
## 2        -0.006637487        -0.008499294          -0.1475138
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1          -13.628079          -0.3894472               -0.1582056
## 2           -0.200857           0.0234403               -0.1907727
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1                -4.911645               -0.8320947                 1.484379
## 2                -0.824147               -0.4492597               -13.666844
##   special_conditions_at_site1 special_conditions_at_site2
## 1                  -12.127460                   -2.928582
## 2                   -1.098886                    1.003969
##   special_conditions_at_site3 special_conditions_at_site4
## 1                 -13.3502704                  0.59501806
## 2                   0.2673735                 -0.04677051
##   special_conditions_at_site5 special_conditions_at_site6
## 1                 -11.5920766                  -10.853101
## 2                  -0.4631856                   -1.024815
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   -8.907198          -10.7946592          -0.33427025
## 2                    1.291973            0.4316188           0.03124668
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1          -13.1815425            1.6841315           -11.434012
## 2            0.7183624           -0.4566238             0.590187
##   did_police_officer_attend_scene_of_collision1
## 1                                     2.8213299
## 2                                     0.8693817
coef(summary(full_test))     #coeffcient matrix 
##   (Intercept)  police_force number_of_vehicles number_of_casualties day_of_week
## 1   -9.649336 -0.0002603854         -0.4435874            0.2821931 0.033646727
## 2   -1.623632 -0.0033539057         -0.4237118            0.0593945 0.008926054
##   first_road_class first_road_number road_type2  road_type3 road_type6
## 1      0.060726049      9.000039e-05 -0.3174556 -0.85976618 -0.5542447
## 2     -0.008681604      1.697736e-05 -0.2515685 -0.01148905  0.0568374
##   road_type7 speed_limit junction_detail1 junction_detail2 junction_detail5
## 1  0.2239049 0.045845846       -1.2783805       -0.4937728       -0.3539749
## 2  0.1044930 0.007873401       -0.3192354       -0.1578201        0.1202851
##   junction_detail6 junction_detail7 junction_detail8 junction_detail9
## 1       0.12853599        0.6321293      -0.15935560        0.3160721
## 2       0.03997728       -0.3472000      -0.09359557       -0.2130548
##   junction_control1 junction_control2 junction_control3 second_road_class
## 1       -19.3304623        -0.0539519     -9.8526330318        0.23723608
## 2        -0.5663018        -0.3036329     -0.0006324719        0.05272483
##   second_road_number pedestrian_crossing_human_control1
## 1       5.303346e-05                        -13.1291641
## 2       5.009628e-05                         -0.5134329
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                         -9.4643030                               -0.1389320
## 2                         -0.2263456                               -0.2414344
##   pedestrian_crossing_physical_facilities4
## 1                               0.57729933
## 2                               0.02003174
##   pedestrian_crossing_physical_facilities5
## 1                               -0.4969318
## 2                                0.1004731
##   pedestrian_crossing_physical_facilities7
## 1                             -13.81440362
## 2                               0.05436394
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.2895445         1.2081215         1.7839651
## 2                                0.1313142         0.1674304         0.7006969
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.06687944         1.2946794         -0.10906583         -15.0747536
## 2       -0.04898701        -0.4876633         -0.08968094           0.1383215
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         1.157493198         1.125282639          -8.0317966
## 2        -0.006637487        -0.008499294          -0.1475138
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1          -13.628079          -0.3894472               -0.1582056
## 2           -0.200857           0.0234403               -0.1907727
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1                -4.911645               -0.8320947                 1.484379
## 2                -0.824147               -0.4492597               -13.666844
##   special_conditions_at_site1 special_conditions_at_site2
## 1                  -12.127460                   -2.928582
## 2                   -1.098886                    1.003969
##   special_conditions_at_site3 special_conditions_at_site4
## 1                 -13.3502704                  0.59501806
## 2                   0.2673735                 -0.04677051
##   special_conditions_at_site5 special_conditions_at_site6
## 1                 -11.5920766                  -10.853101
## 2                  -0.4631856                   -1.024815
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   -8.907198          -10.7946592          -0.33427025
## 2                    1.291973            0.4316188           0.03124668
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1          -13.1815425            1.6841315           -11.434012
## 2            0.7183624           -0.4566238             0.590187
##   did_police_officer_attend_scene_of_collision1
## 1                                     2.8213299
## 2                                     0.8693817
# 2-tailed Z- statistic test
z <- summary(full_test)$coefficients/summary(full_test)$standard.errors
z
##   (Intercept) police_force number_of_vehicles number_of_casualties day_of_week
## 1  -1401.8505  -0.04699488          -19.89705             3.521761   0.6778875
## 2   -113.6552  -2.41022831          -10.21688             1.659464   0.7201144
##   first_road_class first_road_number road_type2   road_type3  road_type6
## 1        0.7870491          1.505161 -805.32404 -161.7524033 -111.271644
## 2       -0.4533215          1.047694  -37.58008   -0.2326076    1.286459
##   road_type7 speed_limit junction_detail1 junction_detail2 junction_detail5
## 1  432.63647    6.290581      -951.690894       -844.04554       -200.78205
## 2   36.51642    3.589311        -4.218783        -29.12207         10.78393
##   junction_detail6 junction_detail7 junction_detail8 junction_detail9
## 1       54.8138963       1632.92694      -131.550069       118.333009
## 2        0.5872711        -28.45442        -6.636851        -2.676062
##   junction_control1 junction_control2 junction_control3 second_road_class
## 1     -8.867796e+12        -10.666627     -1.016738e+09          3.185020
## 2     -4.580874e+02         -6.030455     -2.636791e-01          2.400095
##   second_road_number pedestrian_crossing_human_control1
## 1          0.5481888                      -2.068635e+10
## 2          2.2281632                      -8.527832e+02
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                      -1.291644e+08                               -181.61241
## 2                      -3.970709e+01                                -18.11516
##   pedestrian_crossing_physical_facilities4
## 1                               99.7970359
## 2                                0.2545165
##   pedestrian_crossing_physical_facilities5
## 1                              -232.654343
## 2                                 1.998318
##   pedestrian_crossing_physical_facilities7
## 1                            -1.428463e+11
## 2                             7.040615e+01
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                678.46961        147.982308          5557.152
## 2                                 16.57542          2.844037           496.254
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1        -45.806264         2201.0733           -36.66432       -1.210869e+12
## 2         -8.318691         -621.9656            -3.21485        1.962547e+02
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         2911.905809         1544.206939       -4.956042e+08
## 2           -9.290461           -5.716312       -9.518983e+02
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1       -2.546600e+10        -1061.208868                -64.83895
## 2       -6.596074e+02            7.676864                 -3.93531
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1            -1.096008e+08               -5708.9584             7.873748e+03
## 2            -3.386511e+03                -299.6024            -4.075849e+10
##   special_conditions_at_site1 special_conditions_at_site2
## 1               -4.949916e+09                -5538429.375
## 2               -4.056272e+03                    5887.778
##   special_conditions_at_site3 special_conditions_at_site4
## 1               -5.107174e+10                  1264.82620
## 2                3.988587e+02                   -43.42989
##   special_conditions_at_site5 special_conditions_at_site6
## 1               -8.327264e+09               -6.130205e+09
## 2               -2.130467e+03               -4.436089e+03
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1               -9.488695e+08        -6.424160e+09          -2371.68609
## 2                3.776332e+03         1.016382e+03             39.48691
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1        -3.452753e+10             5536.663        -8.630795e+09
## 2         2.095911e+03            -1082.535         1.556540e+03
##   did_police_officer_attend_scene_of_collision1
## 1                                     402.47319
## 2                                      11.00153
pnorm(abs(z), 0, 1)       #Normal Distribution assumption
##   (Intercept) police_force number_of_vehicles number_of_casualties day_of_week
## 1           1    0.5187413                  1            0.9997857   0.7510785
## 2           1    0.9920287                  1            0.9514888   0.7642727
##   first_road_class first_road_number road_type2 road_type3 road_type6
## 1        0.7843734         0.9338587          1  1.0000000  1.0000000
## 2        0.6748414         0.8526102          1  0.5919669  0.9008585
##   road_type7 speed_limit junction_detail1 junction_detail2 junction_detail5
## 1          1   1.0000000        1.0000000                1                1
## 2          1   0.9998342        0.9999877                1                1
##   junction_detail6 junction_detail7 junction_detail8 junction_detail9
## 1        1.0000000                1                1        1.0000000
## 2        0.7214892                1                1        0.9962754
##   junction_control1 junction_control2 junction_control3 second_road_class
## 1                 1                 1         1.0000000         0.9992763
## 2                 1                 1         0.6039864         0.9918046
##   second_road_number pedestrian_crossing_human_control1
## 1          0.7082189                                  1
## 2          0.9870652                                  1
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                                  1                                        1
## 2                                  1                                        1
##   pedestrian_crossing_physical_facilities4
## 1                                1.0000000
## 2                                0.6004517
##   pedestrian_crossing_physical_facilities5
## 1                                1.0000000
## 2                                0.9771589
##   pedestrian_crossing_physical_facilities7
## 1                                        1
## 2                                        1
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                        1         1.0000000                 1
## 2                                        1         0.9977727                 1
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1                 1                 1           1.0000000                   1
## 2                 1                 1           0.9993474                   1
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1                   1                   1                   1
## 2                   1                   1                   1
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1                   1                   1                1.0000000
## 2                   1                   1                0.9999585
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1                        1                        1                        1
## 2                        1                        1                        1
##   special_conditions_at_site1 special_conditions_at_site2
## 1                           1                           1
## 2                           1                           1
##   special_conditions_at_site3 special_conditions_at_site4
## 1                           1                           1
## 2                           1                           1
##   special_conditions_at_site5 special_conditions_at_site6
## 1                           1                           1
## 2                           1                           1
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                           1                    1                    1
## 2                           1                    1                    1
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1                    1                    1                    1
## 2                    1                    1                    1
##   did_police_officer_attend_scene_of_collision1
## 1                                             1
## 2                                             1
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p
##   (Intercept) police_force number_of_vehicles number_of_casualties day_of_week
## 1           0   0.96251731                  0         0.0004286911   0.4978430
## 2           0   0.01594254                  0         0.0970223019   0.4714546
##   first_road_class first_road_number road_type2 road_type3 road_type6
## 1        0.4312531         0.1322826          0  0.0000000   0.000000
## 2        0.6503172         0.2947796          0  0.8160661   0.198283
##   road_type7  speed_limit junction_detail1 junction_detail2 junction_detail5
## 1          0 3.162797e-10     0.000000e+00                0                0
## 2          0 3.315537e-04     2.456243e-05                0                0
##   junction_detail6 junction_detail7 junction_detail8 junction_detail9
## 1        0.0000000                0     0.000000e+00      0.000000000
## 2        0.5570216                0     3.204548e-11      0.007449276
##   junction_control1 junction_control2 junction_control3 second_road_class
## 1                 0      0.000000e+00         0.0000000        0.00144744
## 2                 0      1.634991e-09         0.7920272        0.01639082
##   second_road_number pedestrian_crossing_human_control1
## 1         0.58356229                                  0
## 2         0.02586963                                  0
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                                  0                                        0
## 2                                  0                                        0
##   pedestrian_crossing_physical_facilities4
## 1                                0.0000000
## 2                                0.7990966
##   pedestrian_crossing_physical_facilities5
## 1                               0.00000000
## 2                               0.04568224
##   pedestrian_crossing_physical_facilities7
## 1                                        0
## 2                                        0
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                        0       0.000000000                 0
## 2                                        0       0.004454593                 0
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1                 0                 0         0.000000000                   0
## 2                 0                 0         0.001305127                   0
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1                   0        0.000000e+00                   0
## 2                   0        1.088605e-08                   0
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1                   0        0.000000e+00             0.000000e+00
## 2                   0        1.620926e-14             8.308938e-05
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1                        0                        0                        0
## 2                        0                        0                        0
##   special_conditions_at_site1 special_conditions_at_site2
## 1                           0                           0
## 2                           0                           0
##   special_conditions_at_site3 special_conditions_at_site4
## 1                           0                           0
## 2                           0                           0
##   special_conditions_at_site5 special_conditions_at_site6
## 1                           0                           0
## 2                           0                           0
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                           0                    0                    0
## 2                           0                    0                    0
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1                    0                    0                    0
## 2                    0                    0                    0
##   did_police_officer_attend_scene_of_collision1
## 1                                             0
## 2                                             0
summary(full_test)$coefficients
##   (Intercept)  police_force number_of_vehicles number_of_casualties day_of_week
## 1   -9.649336 -0.0002603854         -0.4435874            0.2821931 0.033646727
## 2   -1.623632 -0.0033539057         -0.4237118            0.0593945 0.008926054
##   first_road_class first_road_number road_type2  road_type3 road_type6
## 1      0.060726049      9.000039e-05 -0.3174556 -0.85976618 -0.5542447
## 2     -0.008681604      1.697736e-05 -0.2515685 -0.01148905  0.0568374
##   road_type7 speed_limit junction_detail1 junction_detail2 junction_detail5
## 1  0.2239049 0.045845846       -1.2783805       -0.4937728       -0.3539749
## 2  0.1044930 0.007873401       -0.3192354       -0.1578201        0.1202851
##   junction_detail6 junction_detail7 junction_detail8 junction_detail9
## 1       0.12853599        0.6321293      -0.15935560        0.3160721
## 2       0.03997728       -0.3472000      -0.09359557       -0.2130548
##   junction_control1 junction_control2 junction_control3 second_road_class
## 1       -19.3304623        -0.0539519     -9.8526330318        0.23723608
## 2        -0.5663018        -0.3036329     -0.0006324719        0.05272483
##   second_road_number pedestrian_crossing_human_control1
## 1       5.303346e-05                        -13.1291641
## 2       5.009628e-05                         -0.5134329
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                         -9.4643030                               -0.1389320
## 2                         -0.2263456                               -0.2414344
##   pedestrian_crossing_physical_facilities4
## 1                               0.57729933
## 2                               0.02003174
##   pedestrian_crossing_physical_facilities5
## 1                               -0.4969318
## 2                                0.1004731
##   pedestrian_crossing_physical_facilities7
## 1                             -13.81440362
## 2                               0.05436394
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.2895445         1.2081215         1.7839651
## 2                                0.1313142         0.1674304         0.7006969
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.06687944         1.2946794         -0.10906583         -15.0747536
## 2       -0.04898701        -0.4876633         -0.08968094           0.1383215
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         1.157493198         1.125282639          -8.0317966
## 2        -0.006637487        -0.008499294          -0.1475138
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1          -13.628079          -0.3894472               -0.1582056
## 2           -0.200857           0.0234403               -0.1907727
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1                -4.911645               -0.8320947                 1.484379
## 2                -0.824147               -0.4492597               -13.666844
##   special_conditions_at_site1 special_conditions_at_site2
## 1                  -12.127460                   -2.928582
## 2                   -1.098886                    1.003969
##   special_conditions_at_site3 special_conditions_at_site4
## 1                 -13.3502704                  0.59501806
## 2                   0.2673735                 -0.04677051
##   special_conditions_at_site5 special_conditions_at_site6
## 1                 -11.5920766                  -10.853101
## 2                  -0.4631856                   -1.024815
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   -8.907198          -10.7946592          -0.33427025
## 2                    1.291973            0.4316188           0.03124668
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1          -13.1815425            1.6841315           -11.434012
## 2            0.7183624           -0.4566238             0.590187
##   did_police_officer_attend_scene_of_collision1
## 1                                     2.8213299
## 2                                     0.8693817
#💛3_2: fit shorted model by taking unions of siginificant predictors in two equations  (17 predictors), or by ridding all 3 predictors that are Not significant in both equations  💜2
shorted_test <- multinom(legacy_collision_severity ~ police_force + number_of_vehicles + number_of_casualties + road_type + speed_limit + junction_detail + junction_control + second_road_class + second_road_number + pedestrian_crossing_human_control + pedestrian_crossing_physical_facilities + light_conditions + weather_conditions + road_surface_conditions + special_conditions_at_site + carriageway_hazards + did_police_officer_attend_scene_of_collision , data = data4)
## # weights:  171 (112 variable)
## initial  value 10491.747357 
## iter  10 value 6388.020793
## iter  20 value 6055.003701
## iter  30 value 5834.866476
## iter  40 value 5685.754049
## iter  50 value 5601.891843
## iter  60 value 5569.910986
## iter  70 value 5565.320318
## iter  80 value 5563.865743
## iter  90 value 5563.480910
## iter 100 value 5563.379110
## final  value 5563.379110 
## stopped after 100 iterations
summary(shorted_test)   #Residual Deviance: 11126.76  AIC: 11350.76
## Call:
## multinom(formula = legacy_collision_severity ~ police_force + 
##     number_of_vehicles + number_of_casualties + road_type + speed_limit + 
##     junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     pedestrian_crossing_physical_facilities + light_conditions + 
##     weather_conditions + road_surface_conditions + special_conditions_at_site + 
##     carriageway_hazards + did_police_officer_attend_scene_of_collision, 
##     data = data4)
## 
## Coefficients:
##   (Intercept)  police_force number_of_vehicles number_of_casualties road_type2
## 1   -9.322459  0.0005148806         -0.4483758           0.28023017 -0.2346986
## 2   -1.632246 -0.0033754407         -0.4218705           0.06027876 -0.2523894
##     road_type3 road_type6 road_type7 speed_limit junction_detail1
## 1 -0.837605688 -0.4893581  0.2471879 0.044600445       -1.2512712
## 2 -0.009658725  0.0522579  0.1004321 0.008099421       -0.3150009
##   junction_detail2 junction_detail5 junction_detail6 junction_detail7
## 1       -0.4110820       -0.4135562       0.14492943        0.6351918
## 2       -0.1581355        0.1216332       0.03735784       -0.3490824
##   junction_detail8 junction_detail9 junction_control1 junction_control2
## 1      -0.15970414        0.3262966        -7.3081914        -0.0531227
## 2      -0.08874936       -0.2134031        -0.5680115        -0.2950320
##   junction_control3 second_road_class second_road_number
## 1      -6.846010301        0.26422178       7.777301e-05
## 2       0.008566192        0.05412671       5.388216e-05
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                          -7.231865                         -9.5052291
## 2                          -0.502265                         -0.2284233
##   pedestrian_crossing_physical_facilities1
## 1                               -0.1274308
## 2                               -0.2347681
##   pedestrian_crossing_physical_facilities4
## 1                               0.55501485
## 2                               0.03013617
##   pedestrian_crossing_physical_facilities5
## 1                               -0.5173743
## 2                                0.1077542
##   pedestrian_crossing_physical_facilities7
## 1                               -5.3644300
## 2                                0.0478872
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.3058574         1.2127820         1.7437589
## 2                                0.1355307         0.1689736         0.6886369
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.08467625         1.2985187         -0.10272497          -6.2106207
## 2       -0.05561107        -0.4882985         -0.08589124           0.1405358
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         1.182114065         1.096416515          -4.5037924
## 2        -0.002328235        -0.007455071          -0.1493311
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1          -6.4260762         -0.36283677               -0.1521375
## 2          -0.2099111          0.02689139               -0.1907029
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1               -2.8099169               -0.8371797                 1.543703
## 2               -0.8143634               -0.4516657                -7.880520
##   special_conditions_at_site1 special_conditions_at_site2
## 1                   -7.235519                   -2.185902
## 2                   -1.094812                    1.023523
##   special_conditions_at_site3 special_conditions_at_site4
## 1                   -6.263508                  0.58785807
## 2                    0.283695                 -0.04521761
##   special_conditions_at_site5 special_conditions_at_site6
## 1                  -6.7555938                   -5.354714
## 2                  -0.4631181                   -1.016474
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   -5.281094           -6.1497110          -0.32413102
## 2                    1.289926            0.4278019           0.03111096
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1           -6.2712488            1.6980761           -6.2032021
## 2            0.7068268           -0.4623049            0.5878164
##   did_police_officer_attend_scene_of_collision1
## 1                                     2.7950073
## 2                                     0.8706988
## 
## Std. Errors:
##   (Intercept) police_force number_of_vehicles number_of_casualties  road_type2
## 1 0.005670886  0.005497405         0.01678708           0.07989293 0.001190441
## 2 0.025120048  0.001389960         0.04164802           0.03576161 0.054492666
##    road_type3  road_type6  road_type7 speed_limit junction_detail1
## 1 0.002326322 0.006416303 0.001265597 0.007236497     0.0008872457
## 2 0.087457427 0.066350751 0.029776237 0.002253740     0.0859349636
##   junction_detail2 junction_detail5 junction_detail6 junction_detail7
## 1     0.0005940152      0.002047974       0.00211857     0.0006381236
## 2     0.0387291668      0.027234679       0.06931968     0.0214490476
##   junction_detail8 junction_detail9 junction_control1 junction_control2
## 1      0.002183416      0.002621959      1.290669e-07       0.002633738
## 2      0.125604094      0.080766571      4.736002e-03       0.089173985
##   junction_control3 second_road_class second_road_number
## 1      1.705965e-07        0.04142907       9.166148e-05
## 2      5.347357e-03        0.01968236       2.181037e-05
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                       9.092679e-08                       4.833600e-08
## 2                       2.741817e-03                       2.485395e-02
##   pedestrian_crossing_physical_facilities1
## 1                              0.001767239
## 2                              0.116957242
##   pedestrian_crossing_physical_facilities4
## 1                              0.002667852
## 2                              0.095355425
##   pedestrian_crossing_physical_facilities5
## 1                              0.001202182
## 2                              0.101477972
##   pedestrian_crossing_physical_facilities7
## 1                             2.228353e-07
## 2                             2.625009e-03
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                              0.002674276       0.005284383      0.0002777629
## 2                              0.127116951       0.059034391      0.0018612560
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       0.001952626       0.000607484         0.003513579        2.380145e-07
## 2       0.066101278       0.002673323         0.105876754        4.277768e-03
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1        0.0005557404        0.0007864487        2.021262e-07
## 2        0.0062382815        0.0112894632        5.626645e-04
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1        1.841972e-07          0.00161575              0.003015195
## 2        2.320508e-03          0.12835081              0.075171887
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1             2.374845e-07             0.0003277564             1.233033e-04
## 2             5.333886e-04             0.0348428617             4.920202e-07
##   special_conditions_at_site1 special_conditions_at_site2
## 1                3.803918e-08                8.417229e-07
## 2                3.420777e-04                2.914436e-04
##   special_conditions_at_site3 special_conditions_at_site4
## 1                1.108105e-07                0.0003290944
## 2                1.469170e-03                0.0022724608
##   special_conditions_at_site5 special_conditions_at_site6
## 1                9.998701e-08                1.050985e-07
## 2                1.046176e-03                3.985250e-04
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                1.471311e-07          1.03623e-07         0.0001342594
## 2                1.666994e-03          1.19183e-03         0.0039862547
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1         1.402213e-07         0.0001833229         2.840343e-07
## 2         9.399609e-04         0.0010929982         2.000345e-03
##   did_police_officer_attend_scene_of_collision1
## 1                                   0.005565053
## 2                                   0.079999647
## 
## Residual Deviance: 11126.76 
## AIC: 11350.76
#💜2 shorted model has larger Residual Deviance, and smaller AIC compared to 💜1 full model
summary(shorted_test)$coefficients
##   (Intercept)  police_force number_of_vehicles number_of_casualties road_type2
## 1   -9.322459  0.0005148806         -0.4483758           0.28023017 -0.2346986
## 2   -1.632246 -0.0033754407         -0.4218705           0.06027876 -0.2523894
##     road_type3 road_type6 road_type7 speed_limit junction_detail1
## 1 -0.837605688 -0.4893581  0.2471879 0.044600445       -1.2512712
## 2 -0.009658725  0.0522579  0.1004321 0.008099421       -0.3150009
##   junction_detail2 junction_detail5 junction_detail6 junction_detail7
## 1       -0.4110820       -0.4135562       0.14492943        0.6351918
## 2       -0.1581355        0.1216332       0.03735784       -0.3490824
##   junction_detail8 junction_detail9 junction_control1 junction_control2
## 1      -0.15970414        0.3262966        -7.3081914        -0.0531227
## 2      -0.08874936       -0.2134031        -0.5680115        -0.2950320
##   junction_control3 second_road_class second_road_number
## 1      -6.846010301        0.26422178       7.777301e-05
## 2       0.008566192        0.05412671       5.388216e-05
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                          -7.231865                         -9.5052291
## 2                          -0.502265                         -0.2284233
##   pedestrian_crossing_physical_facilities1
## 1                               -0.1274308
## 2                               -0.2347681
##   pedestrian_crossing_physical_facilities4
## 1                               0.55501485
## 2                               0.03013617
##   pedestrian_crossing_physical_facilities5
## 1                               -0.5173743
## 2                                0.1077542
##   pedestrian_crossing_physical_facilities7
## 1                               -5.3644300
## 2                                0.0478872
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.3058574         1.2127820         1.7437589
## 2                                0.1355307         0.1689736         0.6886369
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.08467625         1.2985187         -0.10272497          -6.2106207
## 2       -0.05561107        -0.4882985         -0.08589124           0.1405358
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         1.182114065         1.096416515          -4.5037924
## 2        -0.002328235        -0.007455071          -0.1493311
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1          -6.4260762         -0.36283677               -0.1521375
## 2          -0.2099111          0.02689139               -0.1907029
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1               -2.8099169               -0.8371797                 1.543703
## 2               -0.8143634               -0.4516657                -7.880520
##   special_conditions_at_site1 special_conditions_at_site2
## 1                   -7.235519                   -2.185902
## 2                   -1.094812                    1.023523
##   special_conditions_at_site3 special_conditions_at_site4
## 1                   -6.263508                  0.58785807
## 2                    0.283695                 -0.04521761
##   special_conditions_at_site5 special_conditions_at_site6
## 1                  -6.7555938                   -5.354714
## 2                  -0.4631181                   -1.016474
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   -5.281094           -6.1497110          -0.32413102
## 2                    1.289926            0.4278019           0.03111096
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1           -6.2712488            1.6980761           -6.2032021
## 2            0.7068268           -0.4623049            0.5878164
##   did_police_officer_attend_scene_of_collision1
## 1                                     2.7950073
## 2                                     0.8706988
coef(summary(shorted_test))
##   (Intercept)  police_force number_of_vehicles number_of_casualties road_type2
## 1   -9.322459  0.0005148806         -0.4483758           0.28023017 -0.2346986
## 2   -1.632246 -0.0033754407         -0.4218705           0.06027876 -0.2523894
##     road_type3 road_type6 road_type7 speed_limit junction_detail1
## 1 -0.837605688 -0.4893581  0.2471879 0.044600445       -1.2512712
## 2 -0.009658725  0.0522579  0.1004321 0.008099421       -0.3150009
##   junction_detail2 junction_detail5 junction_detail6 junction_detail7
## 1       -0.4110820       -0.4135562       0.14492943        0.6351918
## 2       -0.1581355        0.1216332       0.03735784       -0.3490824
##   junction_detail8 junction_detail9 junction_control1 junction_control2
## 1      -0.15970414        0.3262966        -7.3081914        -0.0531227
## 2      -0.08874936       -0.2134031        -0.5680115        -0.2950320
##   junction_control3 second_road_class second_road_number
## 1      -6.846010301        0.26422178       7.777301e-05
## 2       0.008566192        0.05412671       5.388216e-05
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                          -7.231865                         -9.5052291
## 2                          -0.502265                         -0.2284233
##   pedestrian_crossing_physical_facilities1
## 1                               -0.1274308
## 2                               -0.2347681
##   pedestrian_crossing_physical_facilities4
## 1                               0.55501485
## 2                               0.03013617
##   pedestrian_crossing_physical_facilities5
## 1                               -0.5173743
## 2                                0.1077542
##   pedestrian_crossing_physical_facilities7
## 1                               -5.3644300
## 2                                0.0478872
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.3058574         1.2127820         1.7437589
## 2                                0.1355307         0.1689736         0.6886369
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.08467625         1.2985187         -0.10272497          -6.2106207
## 2       -0.05561107        -0.4882985         -0.08589124           0.1405358
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         1.182114065         1.096416515          -4.5037924
## 2        -0.002328235        -0.007455071          -0.1493311
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1          -6.4260762         -0.36283677               -0.1521375
## 2          -0.2099111          0.02689139               -0.1907029
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1               -2.8099169               -0.8371797                 1.543703
## 2               -0.8143634               -0.4516657                -7.880520
##   special_conditions_at_site1 special_conditions_at_site2
## 1                   -7.235519                   -2.185902
## 2                   -1.094812                    1.023523
##   special_conditions_at_site3 special_conditions_at_site4
## 1                   -6.263508                  0.58785807
## 2                    0.283695                 -0.04521761
##   special_conditions_at_site5 special_conditions_at_site6
## 1                  -6.7555938                   -5.354714
## 2                  -0.4631181                   -1.016474
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   -5.281094           -6.1497110          -0.32413102
## 2                    1.289926            0.4278019           0.03111096
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1           -6.2712488            1.6980761           -6.2032021
## 2            0.7068268           -0.4623049            0.5878164
##   did_police_officer_attend_scene_of_collision1
## 1                                     2.7950073
## 2                                     0.8706988
#2-tailed Z- statistic test
z <- summary(shorted_test)$coefficients/summary(shorted_test)$standard.errors
z
##   (Intercept) police_force number_of_vehicles number_of_casualties  road_type2
## 1 -1643.91590   0.09365885          -26.70958             3.507571 -197.152617
## 2   -64.97784  -2.42844457          -10.12943             1.685572   -4.631622
##     road_type3  road_type6 road_type7 speed_limit junction_detail1
## 1 -360.0558415 -76.2679217 195.313371    6.163265     -1410.287057
## 2   -0.1104392   0.7876007   3.372895    3.593770        -3.665573
##   junction_detail2 junction_detail5 junction_detail6 junction_detail7
## 1      -692.039534      -201.934341       68.4090823        995.40550
## 2        -4.083112         4.466114        0.5389212        -16.27496
##   junction_detail8 junction_detail9 junction_control1 junction_control2
## 1      -73.1441643        124.44763     -5.662329e+07        -20.170080
## 2       -0.7065801         -2.64222     -1.199348e+02         -3.308499
##   junction_control3 second_road_class second_road_number
## 1     -4.012985e+07          6.377690          0.8484809
## 2      1.601949e+00          2.750011          2.4704836
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                      -7.953503e+07                      -1.966491e+08
## 2                      -1.831869e+02                      -9.190625e+00
##   pedestrian_crossing_physical_facilities1
## 1                               -72.107314
## 2                                -2.007299
##   pedestrian_crossing_physical_facilities4
## 1                              208.0380927
## 2                                0.3160404
##   pedestrian_crossing_physical_facilities5
## 1                              -430.362774
## 2                                 1.061848
##   pedestrian_crossing_physical_facilities7
## 1                            -2.407352e+07
## 2                             1.824268e+01
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                               114.370167        229.503073         6277.8692
## 2                                 1.066189          2.862291          369.9851
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1        -43.365329          2137.536          -29.236562       -2.609346e+07
## 2         -0.841301          -182.656           -0.811238        3.285261e+01
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1        2127.0976964        1394.1360374         -22282083.9
## 2          -0.3732173          -0.6603565              -265.4
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1       -3.488693e+07        -224.5625140               -50.456939
## 2       -9.045910e+01           0.2095148                -2.536892
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1            -11832000.660              -2554.27392                 12519.55
## 2                -1526.773                -12.96293             -16016658.17
##   special_conditions_at_site1 special_conditions_at_site2
## 1               -1.902123e+08                -2596937.234
## 2               -3.200479e+03                    3511.908
##   special_conditions_at_site3 special_conditions_at_site4
## 1               -5.652452e+07                  1786.28986
## 2                1.930989e+02                   -19.89808
##   special_conditions_at_site5 special_conditions_at_site6
## 1               -67564715.074                -50949475.07
## 2                    -442.677                    -2550.59
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1               -35893790.111        -5.934700e+07         -2414.214500
## 2                     773.804         3.589454e+02             7.804558
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1        -4.472393e+07            9262.7588        -2.183962e+07
## 2         7.519747e+02            -422.9695         2.938576e+02
##   did_police_officer_attend_scene_of_collision1
## 1                                     502.24270
## 2                                      10.88378
pnorm(abs(z), 0, 1)       #Normal Distribution assumption
##   (Intercept) police_force number_of_vehicles number_of_casualties road_type2
## 1           1    0.5373099                  1            0.9997739  1.0000000
## 2           1    0.9924181                  1            0.9540609  0.9999982
##   road_type3 road_type6 road_type7 speed_limit junction_detail1
## 1  1.0000000  1.0000000  1.0000000    1.000000        1.0000000
## 2  0.5439695  0.7845348  0.9996281    0.999837        0.9998766
##   junction_detail2 junction_detail5 junction_detail6 junction_detail7
## 1        1.0000000         1.000000        1.0000000                1
## 2        0.9999778         0.999996        0.7050294                1
##   junction_detail8 junction_detail9 junction_control1 junction_control2
## 1        1.0000000        1.0000000                 1          1.000000
## 2        0.7600863        0.9958818                 1          0.999531
##   junction_control3 second_road_class second_road_number
## 1         1.0000000         1.0000000          0.8019149
## 2         0.9454165         0.9970203          0.9932535
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                                  1                                  1
## 2                                  1                                  1
##   pedestrian_crossing_physical_facilities1
## 1                                1.0000000
## 2                                0.9776411
##   pedestrian_crossing_physical_facilities4
## 1                                1.0000000
## 2                                0.6240141
##   pedestrian_crossing_physical_facilities5
## 1                                1.0000000
## 2                                0.8558476
##   pedestrian_crossing_physical_facilities7
## 1                                        1
## 2                                        1
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                1.0000000          1.000000                 1
## 2                                0.8568309          0.997897                 1
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1         1.0000000                 1           1.0000000                   1
## 2         0.7999103                 1           0.7913855                   1
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1           1.0000000           1.0000000                   1
## 2           0.6455066           0.7454875                   1
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1                   1           1.0000000                1.0000000
## 2                   1           0.5829768                0.9944079
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1                        1                        1                        1
## 2                        1                        1                        1
##   special_conditions_at_site1 special_conditions_at_site2
## 1                           1                           1
## 2                           1                           1
##   special_conditions_at_site3 special_conditions_at_site4
## 1                           1                           1
## 2                           1                           1
##   special_conditions_at_site5 special_conditions_at_site6
## 1                           1                           1
## 2                           1                           1
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                           1                    1                    1
## 2                           1                    1                    1
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1                    1                    1                    1
## 2                    1                    1                    1
##   did_police_officer_attend_scene_of_collision1
## 1                                             1
## 2                                             1
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p
##   (Intercept) police_force number_of_vehicles number_of_casualties   road_type2
## 1           0   0.92538016                  0         0.0004522171 0.000000e+00
## 2           0   0.01516374                  0         0.0918782827 3.628121e-06
##   road_type3 road_type6   road_type7  speed_limit junction_detail1
## 1  0.0000000  0.0000000 0.0000000000 7.126015e-10     0.0000000000
## 2  0.9120611  0.4309303 0.0007438224 3.259281e-04     0.0002467855
##   junction_detail2 junction_detail5 junction_detail6 junction_detail7
## 1     0.000000e+00     0.000000e+00        0.0000000                0
## 2     4.443658e-05     7.965335e-06        0.5899413                0
##   junction_detail8 junction_detail9 junction_control1 junction_control2
## 1        0.0000000      0.000000000                 0      0.0000000000
## 2        0.4798274      0.008236452                 0      0.0009379767
##   junction_control3 second_road_class second_road_number
## 1         0.0000000      1.797791e-10         0.39617022
## 2         0.1091669      5.959332e-03         0.01349305
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                                  0                                  0
## 2                                  0                                  0
##   pedestrian_crossing_physical_facilities1
## 1                               0.00000000
## 2                               0.04471789
##   pedestrian_crossing_physical_facilities4
## 1                                0.0000000
## 2                                0.7519718
##   pedestrian_crossing_physical_facilities5
## 1                                0.0000000
## 2                                0.2883048
##   pedestrian_crossing_physical_facilities7
## 1                                        0
## 2                                        0
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.0000000       0.000000000                 0
## 2                                0.2863383       0.004205911                 0
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1         0.0000000                 0            0.000000                   0
## 2         0.4001794                 0            0.417229                   0
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1           0.0000000           0.0000000                   0
## 2           0.7089867           0.5090251                   0
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1                   0           0.0000000               0.00000000
## 2                   0           0.8340464               0.01118415
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1                        0                        0                        0
## 2                        0                        0                        0
##   special_conditions_at_site1 special_conditions_at_site2
## 1                           0                           0
## 2                           0                           0
##   special_conditions_at_site3 special_conditions_at_site4
## 1                           0                           0
## 2                           0                           0
##   special_conditions_at_site5 special_conditions_at_site6
## 1                           0                           0
## 2                           0                           0
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                           0                    0         0.000000e+00
## 2                           0                    0         5.995204e-15
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1                    0                    0                    0
## 2                    0                    0                    0
##   did_police_officer_attend_scene_of_collision1
## 1                                             0
## 2                                             0
#💛3_3: fit reduced model (13 predictors) by ridding all 4 predictors that are Not significant in both equations, or, "taking union minus taking intersection" 💜3  
#♥1. model fitting
data4$legacy_collision_severity[1]   #Baseline:3
## [1] 3
## Levels: 3 1 2
reduced_test <- multinom(legacy_collision_severity ~  number_of_vehicles + number_of_casualties + speed_limit + junction_detail + junction_control +  pedestrian_crossing_human_control + pedestrian_crossing_physical_facilities + light_conditions + weather_conditions + road_surface_conditions + special_conditions_at_site + carriageway_hazards +  did_police_officer_attend_scene_of_collision, data = data4)
## # weights:  150 (98 variable)
## initial  value 10491.747357 
## iter  10 value 6345.731364
## iter  20 value 5845.884145
## iter  30 value 5682.192208
## iter  40 value 5610.751781
## iter  50 value 5594.598005
## iter  60 value 5580.418176
## iter  70 value 5574.466712
## final  value 5574.465295 
## converged
summary(reduced_test)  ##Residual Deviance: 11148.93 AIC: 11344.93  💜3
## Call:
## multinom(formula = legacy_collision_severity ~ number_of_vehicles + 
##     number_of_casualties + speed_limit + junction_detail + junction_control + 
##     pedestrian_crossing_human_control + pedestrian_crossing_physical_facilities + 
##     light_conditions + weather_conditions + road_surface_conditions + 
##     special_conditions_at_site + carriageway_hazards + did_police_officer_attend_scene_of_collision, 
##     data = data4)
## 
## Coefficients:
##   (Intercept) number_of_vehicles number_of_casualties speed_limit
## 1   -8.078260         -0.4660840           0.26447275 0.041477697
## 2   -1.288353         -0.4155048           0.05977593 0.006199458
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1       -1.2814101       -0.2417272      -0.58474797       0.13544816
## 2       -0.3918679       -0.1965509       0.09509609       0.04596641
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.4838749      -0.07098145        0.3234438       -15.7209642
## 2       -0.3469858      -0.07912671       -0.2040596        -0.5992423
##   junction_control2 junction_control3 pedestrian_crossing_human_control1
## 1        -0.2682920      -14.08467657                         -9.7133442
## 2        -0.3089527        0.02255284                         -0.4829515
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                        -24.8529157                               -0.1079675
## 2                         -0.2194514                               -0.2291976
##   pedestrian_crossing_physical_facilities4
## 1                                0.5115622
## 2                                0.0258380
##   pedestrian_crossing_physical_facilities5
## 1                              -0.57336761
## 2                               0.09496456
##   pedestrian_crossing_physical_facilities7
## 1                              -7.85735237
## 2                               0.00837761
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.2758907         1.1783276         1.7251576
## 2                                0.1406324         0.1704131         0.6815443
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.05242388         1.2340997         -0.14154709           -8.982988
## 2       -0.05277091        -0.4871037         -0.07531591            0.161815
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         1.171154592        1.0017658540          -4.3837374
## 2        -0.008899186        0.0008380705          -0.1233909
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1           -8.511244         -0.34336710               -0.1382315
## 2           -0.244166          0.04011264               -0.1952008
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1               -4.9015342               -0.7732497                 1.539861
## 2               -0.8297849               -0.4466436                -8.965658
##   special_conditions_at_site1 special_conditions_at_site2
## 1                   -8.379892                   -1.531607
## 2                   -1.086071                    1.007642
##   special_conditions_at_site3 special_conditions_at_site4
## 1                  -7.5745771                  0.60805518
## 2                   0.2977358                 -0.04888975
##   special_conditions_at_site5 special_conditions_at_site6
## 1                  -7.2552430                   -6.448164
## 2                  -0.4207747                   -1.003790
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   -5.341084           -7.8581690          -0.30150875
## 2                    1.270619            0.4732286           0.04209324
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1           -6.3922111            1.6207326            -6.862983
## 2            0.6919408           -0.4424418             0.574678
##   did_police_officer_attend_scene_of_collision1
## 1                                     2.7802828
## 2                                     0.8550327
## 
## Std. Errors:
##   (Intercept) number_of_vehicles number_of_casualties speed_limit
## 1   1.0853780         0.17685490           0.09028682 0.008419956
## 2   0.1334009         0.04365336           0.03602610 0.002328491
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1       0.48324404        0.7351794        0.6670217       0.29463682
## 2       0.08838527        0.1635089        0.1730637       0.07254195
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.5464745        0.5287492       0.28831332      6.793306e-09
## 2        0.1656608        0.1280829       0.08306445      2.439774e-01
##   junction_control2 junction_control3 pedestrian_crossing_human_control1
## 1        0.36880746      3.151637e-08                       4.395674e-06
## 2        0.08902075      2.222137e-01                       3.723151e-01
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                       5.531897e-12                                0.5304161
## 2                       1.832731e-01                                0.1208538
##   pedestrian_crossing_physical_facilities4
## 1                               0.35939203
## 2                               0.09880024
##   pedestrian_crossing_physical_facilities5
## 1                                0.5177200
## 2                                0.1045311
##   pedestrian_crossing_physical_facilities7
## 1                             7.993761e-06
## 2                             5.134729e-01
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.5276145        0.22866856         0.7710412
## 2                                0.1309620        0.06012149         0.2895364
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1         0.5549027         0.7469739           0.4140806        7.607646e-06
## 2         0.1599786         0.3092343           0.1097073        4.243526e-01
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1           0.6206454           0.7064847        0.0002902471
## 2           0.2590991           0.3030261        1.1574780619
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1        1.789597e-05           0.7414908                0.3010863
## 2        5.136290e-01           0.1577582                0.0800514
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1             9.716749e-06                 1.040002             1.3640613933
## 2             6.625875e-01                 0.219967             0.0001065846
##   special_conditions_at_site1 special_conditions_at_site2
## 1                1.777748e-05                 0.003793689
## 2                5.375575e-01                 1.418848994
##   special_conditions_at_site3 special_conditions_at_site4
## 1                1.101709e-05                   0.7432835
## 2                5.166558e-01                   0.2411244
##   special_conditions_at_site5 special_conditions_at_site6
## 1                3.293412e-05                6.497204e-05
## 2                6.567681e-01                1.075568e+00
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                6.432941e-05         8.109637e-06            1.0384835
## 2                6.233580e-01         4.609435e-01            0.2466329
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1         0.0001032864            1.0789642         3.454301e-05
## 2         0.5845351860            0.5641896         5.998423e-01
##   did_police_officer_attend_scene_of_collision1
## 1                                    1.00701533
## 2                                    0.08677085
## 
## Residual Deviance: 11148.93 
## AIC: 11344.93
#💜3 reduced model has larger Residual Deviance, and smaller AIC compared to 💜2 full model, hence 💜3 > 💜2 > 💜1 by AIC

summary(reduced_test)$coefficients
##   (Intercept) number_of_vehicles number_of_casualties speed_limit
## 1   -8.078260         -0.4660840           0.26447275 0.041477697
## 2   -1.288353         -0.4155048           0.05977593 0.006199458
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1       -1.2814101       -0.2417272      -0.58474797       0.13544816
## 2       -0.3918679       -0.1965509       0.09509609       0.04596641
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.4838749      -0.07098145        0.3234438       -15.7209642
## 2       -0.3469858      -0.07912671       -0.2040596        -0.5992423
##   junction_control2 junction_control3 pedestrian_crossing_human_control1
## 1        -0.2682920      -14.08467657                         -9.7133442
## 2        -0.3089527        0.02255284                         -0.4829515
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                        -24.8529157                               -0.1079675
## 2                         -0.2194514                               -0.2291976
##   pedestrian_crossing_physical_facilities4
## 1                                0.5115622
## 2                                0.0258380
##   pedestrian_crossing_physical_facilities5
## 1                              -0.57336761
## 2                               0.09496456
##   pedestrian_crossing_physical_facilities7
## 1                              -7.85735237
## 2                               0.00837761
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.2758907         1.1783276         1.7251576
## 2                                0.1406324         0.1704131         0.6815443
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.05242388         1.2340997         -0.14154709           -8.982988
## 2       -0.05277091        -0.4871037         -0.07531591            0.161815
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         1.171154592        1.0017658540          -4.3837374
## 2        -0.008899186        0.0008380705          -0.1233909
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1           -8.511244         -0.34336710               -0.1382315
## 2           -0.244166          0.04011264               -0.1952008
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1               -4.9015342               -0.7732497                 1.539861
## 2               -0.8297849               -0.4466436                -8.965658
##   special_conditions_at_site1 special_conditions_at_site2
## 1                   -8.379892                   -1.531607
## 2                   -1.086071                    1.007642
##   special_conditions_at_site3 special_conditions_at_site4
## 1                  -7.5745771                  0.60805518
## 2                   0.2977358                 -0.04888975
##   special_conditions_at_site5 special_conditions_at_site6
## 1                  -7.2552430                   -6.448164
## 2                  -0.4207747                   -1.003790
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   -5.341084           -7.8581690          -0.30150875
## 2                    1.270619            0.4732286           0.04209324
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1           -6.3922111            1.6207326            -6.862983
## 2            0.6919408           -0.4424418             0.574678
##   did_police_officer_attend_scene_of_collision1
## 1                                     2.7802828
## 2                                     0.8550327
coef(summary(reduced_test))
##   (Intercept) number_of_vehicles number_of_casualties speed_limit
## 1   -8.078260         -0.4660840           0.26447275 0.041477697
## 2   -1.288353         -0.4155048           0.05977593 0.006199458
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1       -1.2814101       -0.2417272      -0.58474797       0.13544816
## 2       -0.3918679       -0.1965509       0.09509609       0.04596641
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.4838749      -0.07098145        0.3234438       -15.7209642
## 2       -0.3469858      -0.07912671       -0.2040596        -0.5992423
##   junction_control2 junction_control3 pedestrian_crossing_human_control1
## 1        -0.2682920      -14.08467657                         -9.7133442
## 2        -0.3089527        0.02255284                         -0.4829515
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                        -24.8529157                               -0.1079675
## 2                         -0.2194514                               -0.2291976
##   pedestrian_crossing_physical_facilities4
## 1                                0.5115622
## 2                                0.0258380
##   pedestrian_crossing_physical_facilities5
## 1                              -0.57336761
## 2                               0.09496456
##   pedestrian_crossing_physical_facilities7
## 1                              -7.85735237
## 2                               0.00837761
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.2758907         1.1783276         1.7251576
## 2                                0.1406324         0.1704131         0.6815443
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.05242388         1.2340997         -0.14154709           -8.982988
## 2       -0.05277091        -0.4871037         -0.07531591            0.161815
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         1.171154592        1.0017658540          -4.3837374
## 2        -0.008899186        0.0008380705          -0.1233909
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1           -8.511244         -0.34336710               -0.1382315
## 2           -0.244166          0.04011264               -0.1952008
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1               -4.9015342               -0.7732497                 1.539861
## 2               -0.8297849               -0.4466436                -8.965658
##   special_conditions_at_site1 special_conditions_at_site2
## 1                   -8.379892                   -1.531607
## 2                   -1.086071                    1.007642
##   special_conditions_at_site3 special_conditions_at_site4
## 1                  -7.5745771                  0.60805518
## 2                   0.2977358                 -0.04888975
##   special_conditions_at_site5 special_conditions_at_site6
## 1                  -7.2552430                   -6.448164
## 2                  -0.4207747                   -1.003790
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   -5.341084           -7.8581690          -0.30150875
## 2                    1.270619            0.4732286           0.04209324
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1           -6.3922111            1.6207326            -6.862983
## 2            0.6919408           -0.4424418             0.574678
##   did_police_officer_attend_scene_of_collision1
## 1                                     2.7802828
## 2                                     0.8550327
#♥2. 2-tailed Z- statistic test
z <- summary(reduced_test)$coefficients/summary(reduced_test)$standard.errors
z
##   (Intercept) number_of_vehicles number_of_casualties speed_limit
## 1   -7.442808          -2.635403             2.929251    4.926118
## 2   -9.657756          -9.518278             1.659240    2.662436
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1        -2.651683       -0.3288002       -0.8766552        0.4597123
## 2        -4.433634       -1.2020809        0.5494862        0.6336528
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.8854484       -0.1342441         1.121848     -2.314185e+09
## 2       -2.0945557       -0.6177775        -2.456642     -2.456139e+00
##   junction_control2 junction_control3 pedestrian_crossing_human_control1
## 1        -0.7274581     -4.469004e+08                      -2.209751e+06
## 2        -3.4705689      1.014917e-01                      -1.297158e+00
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                      -4.492657e+12                               -0.2035525
## 2                      -1.197401e+00                               -1.8964865
##   pedestrian_crossing_physical_facilities4
## 1                                1.4234100
## 2                                0.2615176
##   pedestrian_crossing_physical_facilities5
## 1                               -1.1074860
## 2                                0.9084817
##   pedestrian_crossing_physical_facilities7
## 1                            -9.829356e+05
## 2                             1.631558e-02
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                 0.522902          5.152994          2.237439
## 2                                 1.073841          2.834480          2.353916
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.09447399          1.652132          -0.3418346       -1.180784e+06
## 2       -0.32986225         -1.575193          -0.6865170        3.813221e-01
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1          1.88699482         1.417958280       -1.510347e+04
## 2         -0.03434665         0.002765671       -1.066032e-01
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1       -4.755954e+05          -0.4630767               -0.4591094
## 2       -4.753742e-01           0.2542666               -2.4384432
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1            -504441.78681                -0.743508                  1.12888
## 2                 -1.25234                -2.030503             -84117.78011
##   special_conditions_at_site1 special_conditions_at_site2
## 1               -471376.86600                -403.7249154
## 2                    -2.02038                   0.7101829
##   special_conditions_at_site3 special_conditions_at_site4
## 1               -6.875296e+05                   0.8180663
## 2                5.762749e-01                  -0.2027574
##   special_conditions_at_site5 special_conditions_at_site6
## 1               -2.202957e+05                -9.92452e+04
## 2               -6.406746e-01                -9.33265e-01
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1               -83027.088631        -9.689915e+05           -0.2903356
## 2                    2.038346         1.026652e+00            0.1706717
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1        -61888.195185            1.5021190        -1.986794e+05
## 2             1.183745           -0.7842077         9.580485e-01
##   did_police_officer_attend_scene_of_collision1
## 1                                      2.760914
## 2                                      9.853916
pnorm(abs(z), 0, 1)       #Normal Distribution assumption
##   (Intercept) number_of_vehicles number_of_casualties speed_limit
## 1           1          0.9957981            0.9983011   0.9999996
## 2           1          1.0000000            0.9514662   0.9961211
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1        0.9959954        0.6288467        0.8096630        0.6771386
## 2        0.9999954        0.8853339        0.7086641        0.7368463
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.8120426        0.5533952        0.8690365         1.0000000
## 2        0.9818947        0.7316390        0.9929879         0.9929781
##   junction_control2 junction_control3 pedestrian_crossing_human_control1
## 1         0.7665273         1.0000000                          1.0000000
## 2         0.9997403         0.5404199                          0.9027116
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                          1.0000000                                0.5806484
## 2                          0.8844249                                0.9710521
##   pedestrian_crossing_physical_facilities4
## 1                                0.9226913
## 2                                0.6031533
##   pedestrian_crossing_physical_facilities5
## 1                                0.8659581
## 2                                0.8181881
##   pedestrian_crossing_physical_facilities7
## 1                                1.0000000
## 2                                0.5065087
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.6994788         0.9999999         0.9873712
## 2                                0.8585530         0.9977050         0.9907116
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1         0.5376337         0.9507462           0.6337623           1.0000000
## 2         0.6292480         0.9423940           0.7538064           0.6485179
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1           0.9704195           0.9218985           1.0000000
## 2           0.5136996           0.5011033           0.5424481
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1           1.0000000           0.6783453                0.6769222
## 2           0.6827399           0.6003552                0.9926247
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1                 1.000000                0.7714129                0.8705257
## 2                 0.894777                0.9788473                1.0000000
##   special_conditions_at_site1 special_conditions_at_site2
## 1                    1.000000                   1.0000000
## 2                    0.978328                   0.7612046
##   special_conditions_at_site3 special_conditions_at_site4
## 1                   1.0000000                   0.7933403
## 2                   0.7177853                   0.5803377
##   special_conditions_at_site5 special_conditions_at_site6
## 1                    1.000000                   1.0000000
## 2                    0.739133                   0.8246584
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   1.0000000            1.0000000            0.6142203
## 2                   0.9792423            0.8477078            0.5677590
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1            1.0000000            0.9334668            1.0000000
## 2            0.8817431            0.7835409            0.8309808
##   did_police_officer_attend_scene_of_collision1
## 1                                      0.997118
## 2                                      1.000000
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p
##   (Intercept) number_of_vehicles number_of_casualties  speed_limit
## 1 9.85878e-14        0.008403735           0.00339780 8.387937e-07
## 2 0.00000e+00        0.000000000           0.09706753 7.757729e-03
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1     8.009166e-03        0.7423067        0.3806740        0.6457228
## 2     9.265776e-06        0.2293322        0.5826718        0.5263074
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.3759149        0.8932096       0.26192693        0.00000000
## 2        0.0362105        0.5367220       0.01402423        0.01404389
##   junction_control2 junction_control3 pedestrian_crossing_human_control1
## 1      0.4669453779         0.0000000                          0.0000000
## 2      0.0005193571         0.9191602                          0.1945768
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                          0.0000000                               0.83870321
## 2                          0.2311501                               0.05789574
##   pedestrian_crossing_physical_facilities4
## 1                                0.1546173
## 2                                0.7936934
##   pedestrian_crossing_physical_facilities5
## 1                                0.2680839
## 2                                0.3636238
##   pedestrian_crossing_physical_facilities7
## 1                                0.0000000
## 2                                0.9869826
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.6010425      2.563607e-07        0.02525766
## 2                                0.2828939      4.590038e-03        0.01857683
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1         0.9247326        0.09850758           0.7324754           0.0000000
## 2         0.7415040        0.11521193           0.4923872           0.7029642
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1          0.05916102           0.1562029           0.0000000
## 2          0.97260072           0.9977933           0.9151038
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1           0.0000000           0.6433094               0.64615564
## 2           0.6345203           0.7992896               0.01475068
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1                 0.000000                0.4571742                0.2589486
## 2                 0.210446                0.0423054                0.0000000
##   special_conditions_at_site1 special_conditions_at_site2
## 1                  0.00000000                   0.0000000
## 2                  0.04334394                   0.4775907
##   special_conditions_at_site3 special_conditions_at_site4
## 1                   0.0000000                   0.4133193
## 2                   0.5644294                   0.8393247
##   special_conditions_at_site5 special_conditions_at_site6
## 1                   0.0000000                   0.0000000
## 2                   0.5217341                   0.3506832
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                  0.00000000            0.0000000            0.7715595
## 2                  0.04151533            0.3045843            0.8644819
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1            0.0000000            0.1330664            0.0000000
## 2            0.2365139            0.4329183            0.3380383
##   did_police_officer_attend_scene_of_collision1
## 1                                   0.005763984
## 2                                   0.000000000
summary(reduced_test)$coefficients
##   (Intercept) number_of_vehicles number_of_casualties speed_limit
## 1   -8.078260         -0.4660840           0.26447275 0.041477697
## 2   -1.288353         -0.4155048           0.05977593 0.006199458
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1       -1.2814101       -0.2417272      -0.58474797       0.13544816
## 2       -0.3918679       -0.1965509       0.09509609       0.04596641
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.4838749      -0.07098145        0.3234438       -15.7209642
## 2       -0.3469858      -0.07912671       -0.2040596        -0.5992423
##   junction_control2 junction_control3 pedestrian_crossing_human_control1
## 1        -0.2682920      -14.08467657                         -9.7133442
## 2        -0.3089527        0.02255284                         -0.4829515
##   pedestrian_crossing_human_control2 pedestrian_crossing_physical_facilities1
## 1                        -24.8529157                               -0.1079675
## 2                         -0.2194514                               -0.2291976
##   pedestrian_crossing_physical_facilities4
## 1                                0.5115622
## 2                                0.0258380
##   pedestrian_crossing_physical_facilities5
## 1                              -0.57336761
## 2                               0.09496456
##   pedestrian_crossing_physical_facilities7
## 1                              -7.85735237
## 2                               0.00837761
##   pedestrian_crossing_physical_facilities8 light_conditions4 light_conditions5
## 1                                0.2758907         1.1783276         1.7251576
## 2                                0.1406324         0.1704131         0.6815443
##   light_conditions6 light_conditions7 weather_conditions2 weather_conditions3
## 1       -0.05242388         1.2340997         -0.14154709           -8.982988
## 2       -0.05277091        -0.4871037         -0.07531591            0.161815
##   weather_conditions4 weather_conditions5 weather_conditions6
## 1         1.171154592        1.0017658540          -4.3837374
## 2        -0.008899186        0.0008380705          -0.1233909
##   weather_conditions7 weather_conditions8 road_surface_conditions2
## 1           -8.511244         -0.34336710               -0.1382315
## 2           -0.244166          0.04011264               -0.1952008
##   road_surface_conditions3 road_surface_conditions4 road_surface_conditions5
## 1               -4.9015342               -0.7732497                 1.539861
## 2               -0.8297849               -0.4466436                -8.965658
##   special_conditions_at_site1 special_conditions_at_site2
## 1                   -8.379892                   -1.531607
## 2                   -1.086071                    1.007642
##   special_conditions_at_site3 special_conditions_at_site4
## 1                  -7.5745771                  0.60805518
## 2                   0.2977358                 -0.04888975
##   special_conditions_at_site5 special_conditions_at_site6
## 1                  -7.2552430                   -6.448164
## 2                  -0.4207747                   -1.003790
##   special_conditions_at_site7 carriageway_hazards1 carriageway_hazards2
## 1                   -5.341084           -7.8581690          -0.30150875
## 2                    1.270619            0.4732286           0.04209324
##   carriageway_hazards3 carriageway_hazards6 carriageway_hazards7
## 1           -6.3922111            1.6207326            -6.862983
## 2            0.6919408           -0.4424418             0.574678
##   did_police_officer_attend_scene_of_collision1
## 1                                     2.7802828
## 2                                     0.8550327
#💚4. fit best model in stepwise regression  💜4
#💛4_1: Convert all category numeric variables to factors

# Convert y to a factor and relevel it
is.factor(data4$legacy_collision_severity)
## [1] TRUE
data4$legacy_collision_severity[1]    #Baseline is 3: Slight
## [1] 3
## Levels: 3 1 2
str(data4)  #1 response factor, 11 predictor factor, 9 numeric factor
## 'data.frame':    9550 obs. of  21 variables:
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : Factor w/ 3 levels "3","1","2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : Factor w/ 5 levels "1","2","3","6",..: 2 1 4 4 1 3 2 2 4 4 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : Factor w/ 8 levels "3","1","2","5",..: 8 2 7 5 2 5 1 5 8 1 ...
##  $ junction_control                            : Factor w/ 4 levels "4","1","2","3": 1 1 1 3 1 3 1 3 1 1 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : Factor w/ 3 levels "0","1","2": 3 1 1 1 1 1 1 1 1 1 ...
##  $ pedestrian_crossing_physical_facilities     : Factor w/ 6 levels "0","1","4","5",..: 4 1 1 1 1 4 1 3 1 1 ...
##  $ light_conditions                            : Factor w/ 5 levels "1","4","5","6",..: 2 2 2 2 2 2 4 2 2 1 ...
##  $ weather_conditions                          : Factor w/ 8 levels "1","2","3","4",..: 8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : Factor w/ 5 levels "1","2","3","4",..: 2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : Factor w/ 8 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ carriageway_hazards                         : Factor w/ 6 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ did_police_officer_attend_scene_of_collision: Factor w/ 2 levels "2","1": 2 2 2 2 2 2 2 2 2 2 ...
#💛4_2: fit Multinomial logit Best Reduced model (12 predictors) using stepwise regression  💜4
library(MASS)
## 
## Attaching package: 'MASS'
## 
## The following object is masked from 'package:dplyr':
## 
##     select
str(data4)
## 'data.frame':    9550 obs. of  21 variables:
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : Factor w/ 3 levels "3","1","2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : Factor w/ 5 levels "1","2","3","6",..: 2 1 4 4 1 3 2 2 4 4 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : Factor w/ 8 levels "3","1","2","5",..: 8 2 7 5 2 5 1 5 8 1 ...
##  $ junction_control                            : Factor w/ 4 levels "4","1","2","3": 1 1 1 3 1 3 1 3 1 1 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : Factor w/ 3 levels "0","1","2": 3 1 1 1 1 1 1 1 1 1 ...
##  $ pedestrian_crossing_physical_facilities     : Factor w/ 6 levels "0","1","4","5",..: 4 1 1 1 1 4 1 3 1 1 ...
##  $ light_conditions                            : Factor w/ 5 levels "1","4","5","6",..: 2 2 2 2 2 2 4 2 2 1 ...
##  $ weather_conditions                          : Factor w/ 8 levels "1","2","3","4",..: 8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : Factor w/ 5 levels "1","2","3","4",..: 2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : Factor w/ 8 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ carriageway_hazards                         : Factor w/ 6 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ did_police_officer_attend_scene_of_collision: Factor w/ 2 levels "2","1": 2 2 2 2 2 2 2 2 2 2 ...
step_test <- stepAIC(full_test, method = "backward")
## Start:  AIC=11358.18
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     road_type + speed_limit + junction_detail + junction_control + 
##     second_road_class + second_road_number + pedestrian_crossing_human_control + 
##     pedestrian_crossing_physical_facilities + light_conditions + 
##     weather_conditions + road_surface_conditions + special_conditions_at_site + 
##     carriageway_hazards + did_police_officer_attend_scene_of_collision
## 
## # weights:  177 (116 variable)
## initial  value 10491.747357 
## iter  10 value 6363.722528
## iter  20 value 6154.358730
## iter  30 value 5846.773297
## iter  40 value 5640.055095
## iter  50 value 5575.839417
## iter  60 value 5567.306002
## iter  70 value 5565.237143
## iter  80 value 5564.325085
## iter  90 value 5564.070935
## iter 100 value 5563.938519
## final  value 5563.938519 
## stopped after 100 iterations
## # weights:  177 (116 variable)
## initial  value 10491.747357 
## iter  10 value 6415.599719
## iter  20 value 6033.211056
## iter  30 value 5731.280473
## iter  40 value 5656.211241
## iter  50 value 5623.893034
## iter  60 value 5613.815968
## iter  70 value 5613.302107
## iter  80 value 5612.745762
## iter  90 value 5612.599936
## iter 100 value 5612.590494
## final  value 5612.590494 
## stopped after 100 iterations
## # weights:  177 (116 variable)
## initial  value 10491.747357 
## iter  10 value 6400.616651
## iter  20 value 5982.881352
## iter  30 value 5714.721221
## iter  40 value 5603.882620
## iter  50 value 5578.937588
## iter  60 value 5567.141747
## iter  70 value 5566.571405
## iter  80 value 5566.024207
## iter  90 value 5565.895371
## iter 100 value 5565.871348
## final  value 5565.871348 
## stopped after 100 iterations
## # weights:  177 (116 variable)
## initial  value 10491.747357 
## iter  10 value 6388.023525
## iter  20 value 5937.616942
## iter  30 value 5673.309080
## iter  40 value 5600.225951
## iter  50 value 5571.482694
## iter  60 value 5562.684760
## iter  70 value 5562.202251
## iter  80 value 5561.680188
## iter  90 value 5561.532094
## iter 100 value 5561.519803
## final  value 5561.519803 
## stopped after 100 iterations
## # weights:  177 (116 variable)
## initial  value 10491.747357 
## iter  10 value 6389.896134
## iter  20 value 5951.326137
## iter  30 value 5687.326120
## iter  40 value 5602.083775
## iter  50 value 5569.071537
## iter  60 value 5562.585428
## iter  70 value 5562.137379
## iter  80 value 5561.542602
## iter  90 value 5561.456665
## iter 100 value 5561.444434
## final  value 5561.444434 
## stopped after 100 iterations
## # weights:  177 (116 variable)
## initial  value 10491.747357 
## iter  10 value 6429.184234
## iter  20 value 6171.496468
## iter  30 value 5906.488293
## iter  40 value 5712.625359
## iter  50 value 5632.559021
## iter  60 value 5579.210874
## iter  70 value 5564.759520
## iter  80 value 5563.263507
## iter  90 value 5562.673631
## iter 100 value 5562.592476
## final  value 5562.592476 
## stopped after 100 iterations
## # weights:  168 (110 variable)
## initial  value 10491.747357 
## iter  10 value 6401.844651
## iter  20 value 5969.129511
## iter  30 value 5682.480297
## iter  40 value 5605.828810
## iter  50 value 5574.933669
## iter  60 value 5565.848850
## iter  70 value 5565.352486
## iter  80 value 5564.817713
## iter  90 value 5564.744318
## final  value 5564.740445 
## converged
## # weights:  177 (116 variable)
## initial  value 10491.747357 
## iter  10 value 6837.274132
## iter  20 value 6415.235511
## iter  30 value 5828.800046
## iter  40 value 5643.256028
## iter  50 value 5587.561867
## iter  60 value 5577.939392
## iter  70 value 5577.148321
## iter  80 value 5576.657126
## iter  90 value 5576.357846
## iter 100 value 5576.282121
## final  value 5576.282121 
## stopped after 100 iterations
## # weights:  159 (104 variable)
## initial  value 10491.747357 
## iter  10 value 6403.058969
## iter  20 value 5999.182345
## iter  30 value 5687.772942
## iter  40 value 5612.732726
## iter  50 value 5578.316163
## iter  60 value 5575.456148
## iter  70 value 5574.938308
## iter  80 value 5574.636344
## iter  90 value 5574.580843
## final  value 5574.578610 
## converged
## # weights:  171 (112 variable)
## initial  value 10491.747357 
## iter  10 value 6403.552003
## iter  20 value 5995.649555
## iter  30 value 5701.955387
## iter  40 value 5619.169270
## iter  50 value 5585.441962
## iter  60 value 5572.572897
## iter  70 value 5572.027747
## iter  80 value 5571.562777
## iter  90 value 5571.466132
## iter 100 value 5571.456023
## final  value 5571.456023 
## stopped after 100 iterations
## # weights:  177 (116 variable)
## initial  value 10491.747357 
## iter  10 value 6385.001249
## iter  20 value 5948.209664
## iter  30 value 5693.625705
## iter  40 value 5605.953663
## iter  50 value 5577.113378
## iter  60 value 5565.847493
## iter  70 value 5565.193652
## iter  80 value 5564.594151
## iter  90 value 5564.413099
## iter 100 value 5564.401062
## final  value 5564.401062 
## stopped after 100 iterations
## # weights:  177 (116 variable)
## initial  value 10491.747357 
## iter  10 value 6346.611381
## iter  20 value 6156.515733
## iter  30 value 5866.286493
## iter  40 value 5632.456090
## iter  50 value 5573.605411
## iter  60 value 5567.845317
## iter  70 value 5564.587027
## iter  80 value 5563.716724
## iter  90 value 5563.421753
## iter 100 value 5563.344067
## final  value 5563.344067 
## stopped after 100 iterations
## # weights:  174 (114 variable)
## initial  value 10491.747357 
## iter  10 value 6402.549439
## iter  20 value 5977.628457
## iter  30 value 5684.306736
## iter  40 value 5610.997360
## iter  50 value 5577.801091
## iter  60 value 5566.968577
## iter  70 value 5566.517059
## iter  80 value 5566.054273
## iter  90 value 5565.944113
## final  value 5565.943209 
## converged
## # weights:  165 (108 variable)
## initial  value 10491.747357 
## iter  10 value 6402.763627
## iter  20 value 5978.441874
## iter  30 value 5683.370944
## iter  40 value 5607.857166
## iter  50 value 5574.902474
## iter  60 value 5567.756393
## iter  70 value 5567.417176
## iter  80 value 5566.993435
## iter  90 value 5566.914639
## final  value 5566.911728 
## converged
## # weights:  168 (110 variable)
## initial  value 10491.747357 
## iter  10 value 6402.426506
## iter  20 value 5988.552946
## iter  30 value 5733.600536
## iter  40 value 5623.791612
## iter  50 value 5595.557833
## iter  60 value 5583.982646
## iter  70 value 5583.481214
## iter  80 value 5583.059150
## iter  90 value 5582.901923
## iter 100 value 5582.885600
## final  value 5582.885600 
## stopped after 100 iterations
## # weights:  159 (104 variable)
## initial  value 10491.747357 
## iter  10 value 6402.626400
## iter  20 value 5974.901605
## iter  30 value 5680.287201
## iter  40 value 5608.203180
## iter  50 value 5576.009588
## iter  60 value 5566.024649
## iter  70 value 5565.648229
## iter  80 value 5565.166413
## iter  90 value 5565.098983
## final  value 5565.095728 
## converged
## # weights:  168 (110 variable)
## initial  value 10491.747357 
## iter  10 value 6402.777829
## iter  20 value 5980.784593
## iter  30 value 5697.492612
## iter  40 value 5615.362706
## iter  50 value 5582.777628
## iter  60 value 5569.905002
## iter  70 value 5569.245929
## iter  80 value 5568.668359
## iter  90 value 5568.543016
## iter 100 value 5568.535128
## final  value 5568.535128 
## stopped after 100 iterations
## # weights:  159 (104 variable)
## initial  value 10491.747357 
## iter  10 value 6402.525983
## iter  20 value 5978.960239
## iter  30 value 5686.389889
## iter  40 value 5613.992941
## iter  50 value 5581.640792
## iter  60 value 5570.289948
## iter  70 value 5569.398938
## iter  80 value 5568.933604
## iter  90 value 5568.814556
## iter 100 value 5568.804917
## final  value 5568.804917 
## stopped after 100 iterations
## # weights:  165 (108 variable)
## initial  value 10491.747357 
## iter  10 value 6402.521710
## iter  20 value 5976.746623
## iter  30 value 5684.434257
## iter  40 value 5610.253751
## iter  50 value 5577.840914
## iter  60 value 5566.192700
## iter  70 value 5565.398202
## iter  80 value 5564.884686
## iter  90 value 5564.747584
## iter 100 value 5564.739831
## final  value 5564.739831 
## stopped after 100 iterations
## # weights:  177 (116 variable)
## initial  value 10491.747357 
## iter  10 value 6402.218956
## iter  20 value 6038.303229
## iter  30 value 5751.923932
## iter  40 value 5669.904257
## iter  50 value 5640.842229
## iter  60 value 5629.274691
## iter  70 value 5628.404492
## iter  80 value 5628.097235
## iter  90 value 5627.810913
## iter 100 value 5627.784334
## final  value 5627.784334 
## stopped after 100 iterations
##                                                Df   AIC
## - weather_conditions                           14 11338
## - carriageway_hazards                          10 11346
## - special_conditions_at_site                   14 11346
## - road_type                                     8 11350
## - pedestrian_crossing_physical_facilities      10 11350
## - first_road_class                              2 11355
## - day_of_week                                   2 11355
## - road_surface_conditions                       8 11357
## - junction_detail                              14 11357
## - first_road_number                             2 11357
## <none>                                            11358
## - second_road_number                            2 11359
## - police_force                                  2 11360
## - pedestrian_crossing_human_control             4 11360
## - second_road_class                             2 11361
## - number_of_casualties                          2 11364
## - junction_control                              6 11367
## - speed_limit                                   2 11385
## - light_conditions                              8 11386
## - number_of_vehicles                            2 11457
## - did_police_officer_attend_scene_of_collision  2 11488
## # weights:  159 (104 variable)
## initial  value 10491.747357 
## iter  10 value 6402.626400
## iter  20 value 5974.901605
## iter  30 value 5680.287201
## iter  40 value 5608.203180
## iter  50 value 5576.009588
## iter  60 value 5566.024649
## iter  70 value 5565.648229
## iter  80 value 5565.166413
## iter  90 value 5565.098983
## final  value 5565.095728 
## converged
## 
## Step:  AIC=11338.19
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     road_type + speed_limit + junction_detail + junction_control + 
##     second_road_class + second_road_number + pedestrian_crossing_human_control + 
##     pedestrian_crossing_physical_facilities + light_conditions + 
##     road_surface_conditions + special_conditions_at_site + carriageway_hazards + 
##     did_police_officer_attend_scene_of_collision
## 
## # weights:  156 (102 variable)
## initial  value 10491.747357 
## iter  10 value 6364.404784
## iter  20 value 6155.981586
## iter  30 value 5851.822917
## iter  40 value 5643.417647
## iter  50 value 5579.973344
## iter  60 value 5570.238114
## iter  70 value 5568.761642
## iter  80 value 5568.112719
## iter  90 value 5567.926665
## iter 100 value 5567.907479
## final  value 5567.907479 
## stopped after 100 iterations
## # weights:  156 (102 variable)
## initial  value 10491.747357 
## iter  10 value 6415.709856
## iter  20 value 6036.055351
## iter  30 value 5752.371489
## iter  40 value 5659.579084
## iter  50 value 5627.481089
## iter  60 value 5617.492492
## iter  70 value 5617.054029
## iter  80 value 5616.592969
## iter  90 value 5616.531726
## iter 100 value 5616.529277
## final  value 5616.529277 
## stopped after 100 iterations
## # weights:  156 (102 variable)
## initial  value 10491.747357 
## iter  10 value 6400.724242
## iter  20 value 6016.128410
## iter  30 value 5749.441221
## iter  40 value 5612.233020
## iter  50 value 5580.365796
## iter  60 value 5570.503491
## iter  70 value 5570.131201
## iter  80 value 5569.664587
## iter  90 value 5569.590598
## iter 100 value 5569.586222
## final  value 5569.586222 
## stopped after 100 iterations
## # weights:  156 (102 variable)
## initial  value 10491.747357 
## iter  10 value 6388.149357
## iter  20 value 5938.459867
## iter  30 value 5683.049267
## iter  40 value 5603.618750
## iter  50 value 5574.526963
## iter  60 value 5566.446911
## iter  70 value 5566.065817
## iter  80 value 5565.616861
## iter  90 value 5565.575308
## iter 100 value 5565.573037
## final  value 5565.573037 
## stopped after 100 iterations
## # weights:  156 (102 variable)
## initial  value 10491.747357 
## iter  10 value 6390.033215
## iter  20 value 5951.613361
## iter  30 value 5690.575209
## iter  40 value 5606.992742
## iter  50 value 5575.370035
## iter  60 value 5566.302529
## iter  70 value 5565.830912
## iter  80 value 5565.434339
## iter  90 value 5565.401432
## iter 100 value 5565.395297
## final  value 5565.395297 
## stopped after 100 iterations
## # weights:  156 (102 variable)
## initial  value 10491.747357 
## iter  10 value 6429.869567
## iter  20 value 6170.863686
## iter  30 value 5908.663178
## iter  40 value 5715.127897
## iter  50 value 5632.665450
## iter  60 value 5576.912540
## iter  70 value 5567.910880
## iter  80 value 5566.741930
## iter  90 value 5566.554892
## iter 100 value 5566.465314
## final  value 5566.465314 
## stopped after 100 iterations
## # weights:  147 (96 variable)
## initial  value 10491.747357 
## iter  10 value 6401.951172
## iter  20 value 5968.934397
## iter  30 value 5696.483691
## iter  40 value 5609.092630
## iter  50 value 5576.896496
## iter  60 value 5569.559509
## iter  70 value 5568.851191
## iter  80 value 5568.721887
## iter  90 value 5568.702839
## final  value 5568.701733 
## converged
## # weights:  156 (102 variable)
## initial  value 10491.747357 
## iter  10 value 6837.465945
## iter  20 value 6428.260720
## iter  30 value 5826.981169
## iter  40 value 5642.972881
## iter  50 value 5593.516186
## iter  60 value 5581.735788
## iter  70 value 5581.096590
## iter  80 value 5580.537460
## iter  90 value 5580.401257
## iter 100 value 5580.383954
## final  value 5580.383954 
## stopped after 100 iterations
## # weights:  138 (90 variable)
## initial  value 10491.747357 
## iter  10 value 6403.165232
## iter  20 value 5988.122370
## iter  30 value 5673.017561
## iter  40 value 5612.379125
## iter  50 value 5580.515280
## iter  60 value 5579.139384
## iter  70 value 5578.571543
## iter  80 value 5578.526092
## iter  90 value 5578.519387
## iter  90 value 5578.519337
## iter  90 value 5578.519337
## final  value 5578.519337 
## converged
## # weights:  150 (98 variable)
## initial  value 10491.747357 
## iter  10 value 6403.658510
## iter  20 value 5994.281862
## iter  30 value 5711.935616
## iter  40 value 5622.732928
## iter  50 value 5585.586634
## iter  60 value 5576.224061
## iter  70 value 5575.838291
## iter  80 value 5575.555006
## iter  90 value 5575.511459
## final  value 5575.509054 
## converged
## # weights:  156 (102 variable)
## initial  value 10491.747357 
## iter  10 value 6385.122732
## iter  20 value 5951.010265
## iter  30 value 5700.926559
## iter  40 value 5610.768955
## iter  50 value 5580.546102
## iter  60 value 5569.523922
## iter  70 value 5569.024361
## iter  80 value 5568.477892
## iter  90 value 5568.411975
## final  value 5568.408679 
## converged
## # weights:  156 (102 variable)
## initial  value 10491.747357 
## iter  10 value 6347.313571
## iter  20 value 6156.120442
## iter  30 value 5873.463532
## iter  40 value 5644.466743
## iter  50 value 5578.861374
## iter  60 value 5571.257331
## iter  70 value 5568.346061
## iter  80 value 5567.620583
## iter  90 value 5567.378892
## iter 100 value 5567.360125
## final  value 5567.360125 
## stopped after 100 iterations
## # weights:  153 (100 variable)
## initial  value 10491.747357 
## iter  10 value 6402.655627
## iter  20 value 5976.911268
## iter  30 value 5682.285316
## iter  40 value 5612.315655
## iter  50 value 5580.001031
## iter  60 value 5570.497415
## iter  70 value 5570.130735
## iter  80 value 5569.830611
## iter  90 value 5569.776831
## final  value 5569.773975 
## converged
## # weights:  144 (94 variable)
## initial  value 10491.747357 
## iter  10 value 6402.869987
## iter  20 value 5977.547095
## iter  30 value 5686.299798
## iter  40 value 5611.902361
## iter  50 value 5575.265231
## iter  60 value 5571.666433
## iter  70 value 5571.173049
## iter  80 value 5570.990700
## iter  90 value 5570.970071
## final  value 5570.969420 
## converged
## # weights:  147 (96 variable)
## initial  value 10491.747357 
## iter  10 value 6402.533020
## iter  20 value 5988.546822
## iter  30 value 5691.865031
## iter  40 value 5627.459949
## iter  50 value 5596.817735
## iter  60 value 5587.535060
## iter  70 value 5587.106375
## iter  80 value 5586.849711
## iter  90 value 5586.831195
## final  value 5586.826278 
## converged
## # weights:  147 (96 variable)
## initial  value 10491.747357 
## iter  10 value 6402.888011
## iter  20 value 5986.592484
## iter  30 value 5692.302170
## iter  40 value 5618.720643
## iter  50 value 5585.845264
## iter  60 value 5578.262935
## iter  70 value 5577.850560
## iter  80 value 5577.560313
## final  value 5577.516871 
## converged
## # weights:  138 (90 variable)
## initial  value 10491.747357 
## iter  10 value 6402.632163
## iter  20 value 5978.350089
## iter  30 value 5683.782280
## iter  40 value 5614.650908
## iter  50 value 5583.330963
## iter  60 value 5573.469582
## iter  70 value 5573.159087
## iter  80 value 5572.847534
## iter  90 value 5572.818231
## final  value 5572.817312 
## converged
## # weights:  144 (94 variable)
## initial  value 10491.747357 
## iter  10 value 6402.627890
## iter  20 value 5976.069140
## iter  30 value 5681.917522
## iter  40 value 5611.358135
## iter  50 value 5579.472912
## iter  60 value 5569.286064
## iter  70 value 5568.941546
## iter  80 value 5568.586667
## iter  90 value 5568.545187
## final  value 5568.543546 
## converged
## # weights:  156 (102 variable)
## initial  value 10491.747357 
## iter  10 value 6402.324701
## iter  20 value 6039.822393
## iter  30 value 5757.713864
## iter  40 value 5673.673580
## iter  50 value 5641.842997
## iter  60 value 5632.615273
## iter  70 value 5632.166221
## iter  80 value 5631.792278
## iter  90 value 5631.707443
## iter 100 value 5631.695898
## final  value 5631.695898 
## stopped after 100 iterations
##                                                Df   AIC
## - carriageway_hazards                          10 11325
## - special_conditions_at_site                   14 11326
## - road_type                                     8 11329
## - pedestrian_crossing_physical_facilities      10 11330
## - first_road_class                              2 11335
## - day_of_week                                   2 11335
## - first_road_number                             2 11337
## - junction_detail                              14 11337
## <none>                                            11338
## - second_road_number                            2 11339
## - pedestrian_crossing_human_control             4 11340
## - police_force                                  2 11340
## - second_road_class                             2 11341
## - number_of_casualties                          2 11343
## - junction_control                              6 11347
## - road_surface_conditions                       8 11347
## - speed_limit                                   2 11365
## - light_conditions                              8 11366
## - number_of_vehicles                            2 11437
## - did_police_officer_attend_scene_of_collision  2 11467
## # weights:  144 (94 variable)
## initial  value 10491.747357 
## iter  10 value 6402.627890
## iter  20 value 5976.069140
## iter  30 value 5681.917522
## iter  40 value 5611.358135
## iter  50 value 5579.472912
## iter  60 value 5569.286064
## iter  70 value 5568.941546
## iter  80 value 5568.586667
## iter  90 value 5568.545187
## final  value 5568.543546 
## converged
## 
## Step:  AIC=11325.09
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     road_type + speed_limit + junction_detail + junction_control + 
##     second_road_class + second_road_number + pedestrian_crossing_human_control + 
##     pedestrian_crossing_physical_facilities + light_conditions + 
##     road_surface_conditions + special_conditions_at_site + did_police_officer_attend_scene_of_collision
## 
## # weights:  141 (92 variable)
## initial  value 10491.747357 
## iter  10 value 6364.427101
## iter  20 value 6157.290537
## iter  30 value 5853.586233
## iter  40 value 5646.029576
## iter  50 value 5583.231209
## iter  60 value 5573.504888
## iter  70 value 5572.113933
## iter  80 value 5571.532919
## iter  90 value 5571.381563
## iter 100 value 5571.371625
## final  value 5571.371625 
## stopped after 100 iterations
## # weights:  141 (92 variable)
## initial  value 10491.747357 
## iter  10 value 6415.711323
## iter  20 value 6037.329490
## iter  30 value 5757.282978
## iter  40 value 5661.232650
## iter  50 value 5634.059218
## iter  60 value 5620.854940
## iter  70 value 5620.409934
## iter  80 value 5620.123451
## iter  90 value 5620.105439
## final  value 5620.104424 
## converged
## # weights:  141 (92 variable)
## initial  value 10491.747357 
## iter  10 value 6400.725734
## iter  20 value 6017.566807
## iter  30 value 5751.128001
## iter  40 value 5615.487188
## iter  50 value 5583.798543
## iter  60 value 5573.919112
## iter  70 value 5573.504067
## iter  80 value 5573.163383
## iter  90 value 5573.109803
## final  value 5573.106720 
## converged
## # weights:  141 (92 variable)
## initial  value 10491.747357 
## iter  10 value 6388.150863
## iter  20 value 5940.521960
## iter  30 value 5685.777577
## iter  40 value 5606.946318
## iter  50 value 5576.857319
## iter  60 value 5569.759325
## iter  70 value 5569.334534
## iter  80 value 5569.056031
## iter  90 value 5569.027546
## final  value 5569.026093 
## converged
## # weights:  141 (92 variable)
## initial  value 10491.747357 
## iter  10 value 6390.034806
## iter  20 value 5953.462125
## iter  30 value 5689.857567
## iter  40 value 5609.760807
## iter  50 value 5575.634936
## iter  60 value 5569.576665
## iter  70 value 5569.127703
## iter  80 value 5568.873897
## iter  90 value 5568.855004
## final  value 5568.853771 
## converged
## # weights:  141 (92 variable)
## initial  value 10491.747357 
## iter  10 value 6429.883851
## iter  20 value 6172.066673
## iter  30 value 5909.892918
## iter  40 value 5717.904943
## iter  50 value 5636.435255
## iter  60 value 5580.217118
## iter  70 value 5571.123273
## iter  80 value 5570.046952
## iter  90 value 5569.984391
## iter 100 value 5569.923719
## final  value 5569.923719 
## stopped after 100 iterations
## # weights:  132 (86 variable)
## initial  value 10491.747357 
## iter  10 value 6401.952664
## iter  20 value 5970.127087
## iter  30 value 5699.087711
## iter  40 value 5612.307826
## iter  50 value 5579.535595
## iter  60 value 5572.774443
## iter  70 value 5572.164623
## iter  80 value 5572.078917
## iter  90 value 5572.070932
## final  value 5572.070714 
## converged
## # weights:  141 (92 variable)
## initial  value 10491.747357 
## iter  10 value 6837.470345
## iter  20 value 6430.132568
## iter  30 value 5829.334601
## iter  40 value 5645.709155
## iter  50 value 5596.521259
## iter  60 value 5584.912019
## iter  70 value 5584.319931
## iter  80 value 5583.891668
## iter  90 value 5583.802733
## iter 100 value 5583.791435
## final  value 5583.791435 
## stopped after 100 iterations
## # weights:  123 (80 variable)
## initial  value 10491.747357 
## iter  10 value 6403.166720
## iter  20 value 5989.314923
## iter  30 value 5675.445707
## iter  40 value 5615.552950
## iter  50 value 5583.799456
## iter  60 value 5582.385816
## iter  70 value 5581.967994
## iter  80 value 5581.940454
## final  value 5581.938304 
## converged
## # weights:  135 (88 variable)
## initial  value 10491.747357 
## iter  10 value 6403.659998
## iter  20 value 5995.310119
## iter  30 value 5713.634131
## iter  40 value 5625.826341
## iter  50 value 5587.942256
## iter  60 value 5579.467908
## iter  70 value 5579.182153
## iter  80 value 5578.955337
## iter  90 value 5578.927579
## final  value 5578.926193 
## converged
## # weights:  141 (92 variable)
## initial  value 10491.747357 
## iter  10 value 6385.124137
## iter  20 value 5952.731166
## iter  30 value 5704.175895
## iter  40 value 5613.778847
## iter  50 value 5584.125311
## iter  60 value 5572.740698
## iter  70 value 5572.321256
## iter  80 value 5571.886239
## iter  90 value 5571.837129
## final  value 5571.834821 
## converged
## # weights:  141 (92 variable)
## initial  value 10491.747357 
## iter  10 value 6347.335556
## iter  20 value 6157.222344
## iter  30 value 5874.010266
## iter  40 value 5645.323487
## iter  50 value 5581.895101
## iter  60 value 5574.434708
## iter  70 value 5571.654443
## iter  80 value 5571.022610
## iter  90 value 5570.849485
## iter 100 value 5570.837870
## final  value 5570.837870 
## stopped after 100 iterations
## # weights:  138 (90 variable)
## initial  value 10491.747357 
## iter  10 value 6402.657118
## iter  20 value 5978.071474
## iter  30 value 5683.888365
## iter  40 value 5615.372340
## iter  50 value 5582.896036
## iter  60 value 5573.628713
## iter  70 value 5573.304981
## iter  80 value 5573.074871
## iter  90 value 5573.051486
## final  value 5573.050099 
## converged
## # weights:  129 (84 variable)
## initial  value 10491.747357 
## iter  10 value 6402.871478
## iter  20 value 5978.762853
## iter  30 value 5688.795206
## iter  40 value 5615.095462
## iter  50 value 5578.197002
## iter  60 value 5575.015521
## iter  70 value 5574.583195
## iter  80 value 5574.482097
## iter  90 value 5574.470996
## iter  90 value 5574.470965
## iter  90 value 5574.470965
## final  value 5574.470965 
## converged
## # weights:  132 (86 variable)
## initial  value 10491.747357 
## iter  10 value 6402.534509
## iter  20 value 5989.783666
## iter  30 value 5694.144234
## iter  40 value 5630.722695
## iter  50 value 5599.038709
## iter  60 value 5590.895013
## iter  70 value 5590.503034
## iter  80 value 5590.332511
## iter  90 value 5590.315678
## final  value 5590.314216 
## converged
## # weights:  132 (86 variable)
## initial  value 10491.747357 
## iter  10 value 6402.889501
## iter  20 value 5987.733997
## iter  30 value 5694.397411
## iter  40 value 5621.852921
## iter  50 value 5589.328746
## iter  60 value 5581.533227
## iter  70 value 5581.058526
## iter  80 value 5580.889298
## iter  90 value 5580.868879
## final  value 5580.868225 
## converged
## # weights:  123 (80 variable)
## initial  value 10491.747357 
## iter  10 value 6402.633653
## iter  20 value 5979.419616
## iter  30 value 5684.994152
## iter  40 value 5617.346726
## iter  50 value 5586.339241
## iter  60 value 5576.331803
## iter  70 value 5576.067160
## iter  80 value 5575.864097
## iter  90 value 5575.847018
## final  value 5575.846489 
## converged
## # weights:  141 (92 variable)
## initial  value 10491.747357 
## iter  10 value 6402.326189
## iter  20 value 6041.159210
## iter  30 value 5759.548440
## iter  40 value 5676.946226
## iter  50 value 5644.649944
## iter  60 value 5636.041435
## iter  70 value 5635.629150
## iter  80 value 5635.349443
## iter  90 value 5635.308275
## final  value 5635.303130 
## converged
##                                                Df   AIC
## - special_conditions_at_site                   14 11312
## - road_type                                     8 11316
## - pedestrian_crossing_physical_facilities      10 11317
## - first_road_class                              2 11322
## - day_of_week                                   2 11322
## - first_road_number                             2 11324
## - junction_detail                              14 11324
## <none>                                            11325
## - second_road_number                            2 11326
## - pedestrian_crossing_human_control             4 11326
## - police_force                                  2 11327
## - second_road_class                             2 11328
## - number_of_casualties                          2 11330
## - road_surface_conditions                       8 11334
## - junction_control                              6 11334
## - speed_limit                                   2 11352
## - light_conditions                              8 11353
## - number_of_vehicles                            2 11424
## - did_police_officer_attend_scene_of_collision  2 11455
## # weights:  123 (80 variable)
## initial  value 10491.747357 
## iter  10 value 6402.633653
## iter  20 value 5979.419616
## iter  30 value 5684.994152
## iter  40 value 5617.346726
## iter  50 value 5586.339241
## iter  60 value 5576.331803
## iter  70 value 5576.067160
## iter  80 value 5575.864097
## iter  90 value 5575.847018
## final  value 5575.846489 
## converged
## 
## Step:  AIC=11311.69
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     road_type + speed_limit + junction_detail + junction_control + 
##     second_road_class + second_road_number + pedestrian_crossing_human_control + 
##     pedestrian_crossing_physical_facilities + light_conditions + 
##     road_surface_conditions + did_police_officer_attend_scene_of_collision
## 
## # weights:  120 (78 variable)
## initial  value 10491.747357 
## iter  10 value 6364.511776
## iter  20 value 6160.854007
## iter  30 value 5856.208547
## iter  40 value 5651.747597
## iter  50 value 5590.210022
## iter  60 value 5580.331056
## iter  70 value 5579.061745
## iter  80 value 5578.742676
## iter  90 value 5578.653349
## final  value 5578.650988 
## converged
## # weights:  120 (78 variable)
## initial  value 10491.747357 
## iter  10 value 6415.717115
## iter  20 value 6040.836401
## iter  30 value 5760.692049
## iter  40 value 5670.444590
## iter  50 value 5638.590753
## iter  60 value 5628.196383
## iter  70 value 5627.823330
## iter  80 value 5627.607481
## iter  90 value 5627.583386
## final  value 5627.582947 
## converged
## # weights:  120 (78 variable)
## initial  value 10491.747357 
## iter  10 value 6400.731515
## iter  20 value 6021.151550
## iter  30 value 5752.823679
## iter  40 value 5622.054605
## iter  50 value 5589.996588
## iter  60 value 5580.895301
## iter  70 value 5580.633614
## iter  80 value 5580.430113
## iter  90 value 5580.398892
## final  value 5580.398403 
## converged
## # weights:  120 (78 variable)
## initial  value 10491.747357 
## iter  10 value 6388.157217
## iter  20 value 5945.474271
## iter  30 value 5690.245365
## iter  40 value 5613.304367
## iter  50 value 5583.261313
## iter  60 value 5576.803722
## iter  70 value 5576.467251
## iter  80 value 5576.322262
## iter  90 value 5576.307204
## final  value 5576.307064 
## converged
## # weights:  120 (78 variable)
## initial  value 10491.747357 
## iter  10 value 6390.041076
## iter  20 value 5957.952853
## iter  30 value 5689.312240
## iter  40 value 5615.632026
## iter  50 value 5581.706782
## iter  60 value 5576.522078
## iter  70 value 5576.261250
## iter  80 value 5576.110861
## iter  90 value 5576.105526
## final  value 5576.105339 
## converged
## # weights:  120 (78 variable)
## initial  value 10491.747357 
## iter  10 value 6429.941719
## iter  20 value 6175.185583
## iter  30 value 5913.797869
## iter  40 value 5723.489141
## iter  50 value 5644.870841
## iter  60 value 5587.874273
## iter  70 value 5578.610769
## iter  80 value 5577.269840
## iter  90 value 5577.235089
## iter 100 value 5577.208460
## final  value 5577.208460 
## stopped after 100 iterations
## # weights:  111 (72 variable)
## initial  value 10491.747357 
## iter  10 value 6401.958436
## iter  20 value 5973.606296
## iter  30 value 5705.238030
## iter  40 value 5617.911182
## iter  50 value 5585.508710
## iter  60 value 5579.834732
## iter  70 value 5579.458755
## iter  80 value 5579.411946
## final  value 5579.410537 
## converged
## # weights:  120 (78 variable)
## initial  value 10491.747357 
## iter  10 value 6837.498291
## iter  20 value 6433.981716
## iter  30 value 5834.831432
## iter  40 value 5651.128663
## iter  50 value 5598.758617
## iter  60 value 5591.665336
## iter  70 value 5591.182793
## iter  80 value 5590.932361
## iter  90 value 5590.874309
## final  value 5590.872629 
## converged
## # weights:  102 (66 variable)
## initial  value 10491.747357 
## iter  10 value 6403.172485
## iter  20 value 5992.668550
## iter  30 value 5680.763132
## iter  40 value 5620.903565
## iter  50 value 5590.537977
## iter  60 value 5589.487192
## iter  70 value 5589.229519
## iter  80 value 5589.210192
## final  value 5589.208832 
## converged
## # weights:  114 (74 variable)
## initial  value 10491.747357 
## iter  10 value 6403.665782
## iter  20 value 5998.478730
## iter  30 value 5717.767360
## iter  40 value 5632.890345
## iter  50 value 5599.506841
## iter  60 value 5586.804666
## iter  70 value 5586.598733
## iter  80 value 5586.483012
## iter  90 value 5586.471991
## final  value 5586.471859 
## converged
## # weights:  120 (78 variable)
## initial  value 10491.747357 
## iter  10 value 6385.129715
## iter  20 value 5957.020735
## iter  30 value 5710.412337
## iter  40 value 5620.050507
## iter  50 value 5592.126255
## iter  60 value 5579.696920
## iter  70 value 5579.244071
## iter  80 value 5579.050329
## iter  90 value 5579.031144
## final  value 5579.030999 
## converged
## # weights:  120 (78 variable)
## initial  value 10491.747357 
## iter  10 value 6347.420624
## iter  20 value 6160.658011
## iter  30 value 5873.781464
## iter  40 value 5643.103837
## iter  50 value 5587.889302
## iter  60 value 5581.071323
## iter  70 value 5578.597037
## iter  80 value 5578.157218
## iter  90 value 5578.040858
## final  value 5578.038011 
## converged
## # weights:  117 (76 variable)
## initial  value 10491.747357 
## iter  10 value 6402.662881
## iter  20 value 5981.475815
## iter  30 value 5686.850802
## iter  40 value 5621.579021
## iter  50 value 5589.387456
## iter  60 value 5580.749452
## iter  70 value 5580.515764
## iter  80 value 5580.416670
## iter  90 value 5580.403577
## final  value 5580.403454 
## converged
## # weights:  108 (70 variable)
## initial  value 10491.747357 
## iter  10 value 6402.877247
## iter  20 value 5982.108231
## iter  30 value 5693.715500
## iter  40 value 5620.984998
## iter  50 value 5584.075663
## iter  60 value 5581.989653
## iter  70 value 5581.727508
## iter  80 value 5581.691724
## final  value 5581.688127 
## converged
## # weights:  111 (72 variable)
## initial  value 10491.747357 
## iter  10 value 6402.540276
## iter  20 value 5993.128084
## iter  30 value 5698.634035
## iter  40 value 5636.963596
## iter  50 value 5603.810079
## iter  60 value 5597.775260
## iter  70 value 5597.548793
## iter  80 value 5597.459948
## iter  90 value 5597.448706
## final  value 5597.448576 
## converged
## # weights:  111 (72 variable)
## initial  value 10491.747357 
## iter  10 value 6402.895263
## iter  20 value 5990.975821
## iter  30 value 5697.955903
## iter  40 value 5628.668663
## iter  50 value 5598.928725
## iter  60 value 5588.488632
## iter  70 value 5588.204035
## iter  80 value 5588.120884
## iter  90 value 5588.110203
## iter  90 value 5588.110160
## iter  90 value 5588.110160
## final  value 5588.110160 
## converged
## # weights:  120 (78 variable)
## initial  value 10491.747357 
## iter  10 value 6402.331940
## iter  20 value 6044.093664
## iter  30 value 5761.916826
## iter  40 value 5682.763846
## iter  50 value 5650.718857
## iter  60 value 5642.399015
## iter  70 value 5642.012978
## iter  80 value 5641.861403
## iter  90 value 5641.839508
## final  value 5641.838479 
## converged
##                                                Df   AIC
## - road_type                                     8 11303
## - pedestrian_crossing_physical_facilities      10 11303
## - first_road_class                              2 11308
## - day_of_week                                   2 11309
## - first_road_number                             2 11310
## - junction_detail                              14 11310
## <none>                                            11312
## - second_road_number                            2 11312
## - pedestrian_crossing_human_control             4 11313
## - police_force                                  2 11313
## - second_road_class                             2 11314
## - number_of_casualties                          2 11317
## - road_surface_conditions                       8 11320
## - junction_control                              6 11321
## - speed_limit                                   2 11338
## - light_conditions                              8 11339
## - number_of_vehicles                            2 11411
## - did_police_officer_attend_scene_of_collision  2 11440
## # weights:  111 (72 variable)
## initial  value 10491.747357 
## iter  10 value 6401.958436
## iter  20 value 5973.606296
## iter  30 value 5705.238030
## iter  40 value 5617.911182
## iter  50 value 5585.508710
## iter  60 value 5579.834732
## iter  70 value 5579.458755
## iter  80 value 5579.411946
## final  value 5579.410537 
## converged
## 
## Step:  AIC=11302.82
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     speed_limit + junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     pedestrian_crossing_physical_facilities + light_conditions + 
##     road_surface_conditions + did_police_officer_attend_scene_of_collision
## 
## # weights:  108 (70 variable)
## initial  value 10491.747357 
## iter  10 value 6368.535764
## iter  20 value 6146.346772
## iter  30 value 5843.670139
## iter  40 value 5644.681858
## iter  50 value 5588.265484
## iter  60 value 5583.177125
## iter  70 value 5582.078573
## iter  80 value 5581.954230
## iter  90 value 5581.931101
## final  value 5581.931000 
## converged
## # weights:  108 (70 variable)
## initial  value 10491.747357 
## iter  10 value 6415.119867
## iter  20 value 6035.006514
## iter  30 value 5743.522799
## iter  40 value 5665.408818
## iter  50 value 5634.129844
## iter  60 value 5631.053633
## iter  70 value 5630.749560
## iter  80 value 5630.712069
## final  value 5630.709164 
## converged
## # weights:  108 (70 variable)
## initial  value 10491.747357 
## iter  10 value 6400.062680
## iter  20 value 5998.196305
## iter  30 value 5704.961837
## iter  40 value 5618.759797
## iter  50 value 5587.500088
## iter  60 value 5584.238800
## iter  70 value 5583.953463
## iter  80 value 5583.905371
## final  value 5583.904201 
## converged
## # weights:  108 (70 variable)
## initial  value 10491.747357 
## iter  10 value 6387.626666
## iter  20 value 5947.359080
## iter  30 value 5694.909079
## iter  40 value 5618.216213
## iter  50 value 5585.381200
## iter  60 value 5580.278657
## iter  70 value 5579.910593
## iter  80 value 5579.876741
## final  value 5579.875803 
## converged
## # weights:  108 (70 variable)
## initial  value 10491.747357 
## iter  10 value 6389.913591
## iter  20 value 5978.504025
## iter  30 value 5687.331283
## iter  40 value 5618.456854
## iter  50 value 5582.738932
## iter  60 value 5580.012818
## iter  70 value 5579.685210
## iter  80 value 5579.663368
## final  value 5579.662678 
## converged
## # weights:  108 (70 variable)
## initial  value 10491.747357 
## iter  10 value 6433.094427
## iter  20 value 6175.184353
## iter  30 value 5904.405655
## iter  40 value 5717.000606
## iter  50 value 5629.809415
## iter  60 value 5583.932804
## iter  70 value 5581.309866
## iter  80 value 5580.859656
## iter  90 value 5580.835235
## iter 100 value 5580.829646
## final  value 5580.829646 
## stopped after 100 iterations
## # weights:  108 (70 variable)
## initial  value 10491.747357 
## iter  10 value 6826.528507
## iter  20 value 6357.220336
## iter  30 value 5836.007037
## iter  40 value 5648.636524
## iter  50 value 5600.400014
## iter  60 value 5595.146042
## iter  70 value 5594.504869
## iter  80 value 5594.402048
## final  value 5594.393634 
## converged
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6402.494229
## iter  20 value 6003.311434
## iter  30 value 5689.448726
## iter  40 value 5613.926466
## iter  50 value 5597.374381
## iter  60 value 5596.980329
## iter  70 value 5596.930818
## final  value 5596.929858 
## converged
## # weights:  102 (66 variable)
## initial  value 10491.747357 
## iter  10 value 6402.993622
## iter  20 value 5995.784791
## iter  30 value 5738.648259
## iter  40 value 5632.191352
## iter  50 value 5593.467030
## iter  60 value 5590.688475
## iter  70 value 5590.495279
## iter  80 value 5590.470458
## final  value 5590.469280 
## converged
## # weights:  108 (70 variable)
## initial  value 10491.747357 
## iter  10 value 6384.883988
## iter  20 value 5958.671715
## iter  30 value 5707.385065
## iter  40 value 5620.435170
## iter  50 value 5587.563214
## iter  60 value 5583.065000
## iter  70 value 5582.676398
## iter  80 value 5582.591167
## final  value 5582.588458 
## converged
## # weights:  108 (70 variable)
## initial  value 10491.747357 
## iter  10 value 6351.117976
## iter  20 value 6159.987796
## iter  30 value 5844.486949
## iter  40 value 5631.346945
## iter  50 value 5588.684656
## iter  60 value 5583.326613
## iter  70 value 5581.776414
## iter  80 value 5581.626740
## final  value 5581.618813 
## converged
## # weights:  105 (68 variable)
## initial  value 10491.747357 
## iter  10 value 6401.987760
## iter  20 value 5975.622821
## iter  30 value 5708.887105
## iter  40 value 5622.995691
## iter  50 value 5589.593140
## iter  60 value 5584.232294
## iter  70 value 5584.008559
## iter  80 value 5583.963051
## final  value 5583.960807 
## converged
## # weights:  96 (62 variable)
## initial  value 10491.747357 
## iter  10 value 6402.203678
## iter  20 value 5976.434265
## iter  30 value 5686.248276
## iter  40 value 5609.224183
## iter  50 value 5587.006200
## iter  60 value 5585.613447
## iter  70 value 5585.427273
## iter  80 value 5585.409812
## final  value 5585.409703 
## converged
## # weights:  99 (64 variable)
## initial  value 10491.747357 
## iter  10 value 6401.865048
## iter  20 value 5993.779283
## iter  30 value 5750.178113
## iter  40 value 5639.495346
## iter  50 value 5603.070464
## iter  60 value 5600.819060
## iter  70 value 5600.597214
## iter  80 value 5600.557459
## final  value 5600.555692 
## converged
## # weights:  99 (64 variable)
## initial  value 10491.747357 
## iter  10 value 6402.221138
## iter  20 value 5982.829573
## iter  30 value 5685.533215
## iter  40 value 5624.625009
## iter  50 value 5593.513222
## iter  60 value 5591.841768
## iter  70 value 5591.644137
## iter  80 value 5591.622115
## final  value 5591.621449 
## converged
## # weights:  108 (70 variable)
## initial  value 10491.747357 
## iter  10 value 6401.652434
## iter  20 value 6036.999487
## iter  30 value 5763.119228
## iter  40 value 5681.129291
## iter  50 value 5649.362759
## iter  60 value 5645.145748
## iter  70 value 5644.930858
## iter  80 value 5644.844507
## final  value 5644.837931 
## converged
##                                                Df   AIC
## - pedestrian_crossing_physical_facilities      10 11295
## - first_road_class                              2 11299
## - day_of_week                                   2 11300
## - first_road_number                             2 11302
## <none>                                            11303
## - second_road_number                            2 11303
## - police_force                                  2 11304
## - pedestrian_crossing_human_control             4 11304
## - second_road_class                             2 11305
## - number_of_casualties                          2 11308
## - junction_detail                              14 11310
## - road_surface_conditions                       8 11311
## - junction_control                              6 11313
## - speed_limit                                   2 11329
## - light_conditions                              8 11329
## - number_of_vehicles                            2 11401
## - did_police_officer_attend_scene_of_collision  2 11430
## # weights:  96 (62 variable)
## initial  value 10491.747357 
## iter  10 value 6402.203678
## iter  20 value 5976.434265
## iter  30 value 5686.248276
## iter  40 value 5609.224183
## iter  50 value 5587.006200
## iter  60 value 5585.613447
## iter  70 value 5585.427273
## iter  80 value 5585.409812
## final  value 5585.409703 
## converged
## 
## Step:  AIC=11294.82
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     speed_limit + junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision
## 
## # weights:  93 (60 variable)
## initial  value 10491.747357 
## iter  10 value 6370.304399
## iter  20 value 6147.800257
## iter  30 value 5817.393621
## iter  40 value 5624.171567
## iter  50 value 5590.639254
## iter  60 value 5587.945462
## iter  70 value 5587.644469
## iter  80 value 5587.579833
## final  value 5587.578852 
## converged
## # weights:  93 (60 variable)
## initial  value 10491.747357 
## iter  10 value 6415.384189
## iter  20 value 6049.841219
## iter  30 value 5736.879582
## iter  40 value 5662.980062
## iter  50 value 5637.904153
## iter  60 value 5637.034473
## iter  70 value 5636.886902
## iter  80 value 5636.877538
## final  value 5636.877418 
## converged
## # weights:  93 (60 variable)
## initial  value 10491.747357 
## iter  10 value 6400.311988
## iter  20 value 5980.654131
## iter  30 value 5719.234599
## iter  40 value 5613.322548
## iter  50 value 5591.040248
## iter  60 value 5590.086847
## iter  70 value 5589.962298
## final  value 5589.956413 
## converged
## # weights:  93 (60 variable)
## initial  value 10491.747357 
## iter  10 value 6387.955659
## iter  20 value 5949.923363
## iter  30 value 5671.550657
## iter  40 value 5606.388355
## iter  50 value 5587.097067
## iter  60 value 5586.072309
## iter  70 value 5585.862591
## iter  80 value 5585.849224
## iter  80 value 5585.849174
## iter  80 value 5585.849174
## final  value 5585.849174 
## converged
## # weights:  93 (60 variable)
## initial  value 10491.747357 
## iter  10 value 6390.231937
## iter  20 value 5983.182023
## iter  30 value 5684.018624
## iter  40 value 5606.697200
## iter  50 value 5586.140568
## iter  60 value 5585.722438
## iter  70 value 5585.619044
## final  value 5585.615037 
## converged
## # weights:  93 (60 variable)
## initial  value 10491.747357 
## iter  10 value 6436.246240
## iter  20 value 6178.456359
## iter  30 value 5890.825648
## iter  40 value 5708.297362
## iter  50 value 5611.970091
## iter  60 value 5587.347110
## iter  70 value 5586.842022
## iter  80 value 5586.824948
## iter  90 value 5586.811174
## final  value 5586.810230 
## converged
## # weights:  93 (60 variable)
## initial  value 10491.747357 
## iter  10 value 6826.909794
## iter  20 value 6357.259454
## iter  30 value 5765.933282
## iter  40 value 5631.417545
## iter  50 value 5601.654612
## iter  60 value 5600.862924
## iter  70 value 5600.688576
## iter  80 value 5600.680444
## final  value 5600.680337 
## converged
## # weights:  75 (48 variable)
## initial  value 10491.747357 
## iter  10 value 6402.739951
## iter  20 value 5991.626328
## iter  30 value 5662.438330
## iter  40 value 5608.567770
## iter  50 value 5603.326483
## iter  60 value 5603.103748
## iter  70 value 5603.098432
## final  value 5603.098251 
## converged
## # weights:  87 (56 variable)
## initial  value 10491.747357 
## iter  10 value 6403.246860
## iter  20 value 6003.844132
## iter  30 value 5692.546326
## iter  40 value 5619.743921
## iter  50 value 5596.854301
## iter  60 value 5596.398832
## iter  70 value 5596.346541
## final  value 5596.346411 
## converged
## # weights:  93 (60 variable)
## initial  value 10491.747357 
## iter  10 value 6385.195547
## iter  20 value 5962.255424
## iter  30 value 5699.243972
## iter  40 value 5613.697613
## iter  50 value 5589.919309
## iter  60 value 5588.726295
## iter  70 value 5588.559703
## final  value 5588.554701 
## converged
## # weights:  93 (60 variable)
## initial  value 10491.747357 
## iter  10 value 6353.224671
## iter  20 value 6161.604520
## iter  30 value 5805.731743
## iter  40 value 5615.656854
## iter  50 value 5591.690262
## iter  60 value 5588.090507
## iter  70 value 5587.776491
## iter  80 value 5587.731679
## final  value 5587.730881 
## converged
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6402.233184
## iter  20 value 5978.498002
## iter  30 value 5714.533511
## iter  40 value 5626.546816
## iter  50 value 5590.859491
## iter  60 value 5590.103233
## iter  70 value 5589.989617
## final  value 5589.985417 
## converged
## # weights:  84 (54 variable)
## initial  value 10491.747357 
## iter  10 value 6402.110868
## iter  20 value 5989.973810
## iter  30 value 5720.006544
## iter  40 value 5625.836768
## iter  50 value 5607.192370
## iter  60 value 5606.694123
## iter  70 value 5606.618228
## final  value 5606.614273 
## converged
## # weights:  84 (54 variable)
## initial  value 10491.747357 
## iter  10 value 6402.466807
## iter  20 value 5979.393553
## iter  30 value 5696.112238
## iter  40 value 5622.975644
## iter  50 value 5598.102806
## iter  60 value 5597.643357
## iter  70 value 5597.565290
## final  value 5597.561329 
## converged
## # weights:  93 (60 variable)
## initial  value 10491.747357 
## iter  10 value 6401.896438
## iter  20 value 6034.910621
## iter  30 value 5747.070104
## iter  40 value 5675.110446
## iter  50 value 5651.616736
## iter  60 value 5650.643812
## iter  70 value 5650.527297
## iter  80 value 5650.516381
## final  value 5650.516124 
## converged
##                                                Df   AIC
## - first_road_class                              2 11291
## - day_of_week                                   2 11292
## - first_road_number                             2 11294
## <none>                                            11295
## - police_force                                  2 11295
## - second_road_number                            2 11296
## - pedestrian_crossing_human_control             4 11296
## - second_road_class                             2 11297
## - number_of_casualties                          2 11300
## - junction_detail                              14 11302
## - road_surface_conditions                       8 11303
## - junction_control                              6 11305
## - light_conditions                              8 11321
## - speed_limit                                   2 11321
## - number_of_vehicles                            2 11394
## - did_police_officer_attend_scene_of_collision  2 11421
## # weights:  93 (60 variable)
## initial  value 10491.747357 
## iter  10 value 6390.231937
## iter  20 value 5983.182023
## iter  30 value 5684.018624
## iter  40 value 5606.697200
## iter  50 value 5586.140568
## iter  60 value 5585.722438
## iter  70 value 5585.619044
## final  value 5585.615037 
## converged
## 
## Step:  AIC=11291.23
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_number + 
##     speed_limit + junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision
## 
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6516.466578
## iter  20 value 6174.759791
## iter  30 value 5828.651606
## iter  40 value 5657.391951
## iter  50 value 5590.916074
## iter  60 value 5588.206265
## iter  70 value 5587.969913
## iter  80 value 5587.920403
## final  value 5587.917573 
## converged
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6379.578861
## iter  20 value 6015.020284
## iter  30 value 5717.310041
## iter  40 value 5676.940082
## iter  50 value 5637.890216
## iter  60 value 5637.208285
## iter  70 value 5637.133027
## final  value 5637.128901 
## converged
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6389.270659
## iter  20 value 5921.801336
## iter  30 value 5657.244387
## iter  40 value 5607.291863
## iter  50 value 5590.524555
## iter  60 value 5590.193392
## iter  70 value 5590.145130
## final  value 5590.142313 
## converged
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6357.585504
## iter  20 value 5928.943080
## iter  30 value 5666.084333
## iter  40 value 5603.339370
## iter  50 value 5586.687013
## iter  60 value 5586.142516
## iter  70 value 5586.054932
## final  value 5586.053706 
## converged
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6581.210978
## iter  20 value 6177.860989
## iter  30 value 5857.714920
## iter  40 value 5689.948380
## iter  50 value 5601.511367
## iter  60 value 5588.046155
## iter  70 value 5587.094422
## iter  80 value 5587.068378
## iter  90 value 5587.050474
## final  value 5587.049997 
## converged
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6501.372498
## iter  20 value 6027.770826
## iter  30 value 5743.879638
## iter  40 value 5651.774239
## iter  50 value 5602.081333
## iter  60 value 5601.322739
## iter  70 value 5601.180108
## iter  80 value 5601.143397
## final  value 5601.143029 
## converged
## # weights:  72 (46 variable)
## initial  value 10491.747357 
## iter  10 value 6390.833620
## iter  20 value 5997.762294
## iter  30 value 5689.499059
## iter  40 value 5606.080109
## iter  50 value 5603.627977
## iter  60 value 5603.455992
## iter  70 value 5603.441798
## iter  70 value 5603.441759
## iter  70 value 5603.441759
## final  value 5603.441759 
## converged
## # weights:  84 (54 variable)
## initial  value 10491.747357 
## iter  10 value 6391.341399
## iter  20 value 5973.351471
## iter  30 value 5670.564248
## iter  40 value 5610.339161
## iter  50 value 5596.912683
## iter  60 value 5596.786870
## iter  70 value 5596.747907
## final  value 5596.746847 
## converged
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6406.885324
## iter  20 value 5941.706207
## iter  30 value 5698.005762
## iter  40 value 5613.624799
## iter  50 value 5589.654570
## iter  60 value 5588.963999
## iter  70 value 5588.864084
## final  value 5588.861380 
## converged
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6421.106171
## iter  20 value 6150.095594
## iter  30 value 5743.182678
## iter  40 value 5608.503719
## iter  50 value 5591.137196
## iter  60 value 5588.099183
## iter  70 value 5587.956830
## iter  80 value 5587.921205
## final  value 5587.920379 
## converged
## # weights:  87 (56 variable)
## initial  value 10491.747357 
## iter  10 value 6390.266526
## iter  20 value 5985.531206
## iter  30 value 5691.442295
## iter  40 value 5615.503185
## iter  50 value 5590.675146
## iter  60 value 5590.287183
## iter  70 value 5590.216056
## final  value 5590.212606 
## converged
## # weights:  81 (52 variable)
## initial  value 10491.747357 
## iter  10 value 6390.188520
## iter  20 value 6000.419402
## iter  30 value 5694.384315
## iter  40 value 5621.318536
## iter  50 value 5607.142078
## iter  60 value 5606.851235
## iter  70 value 5606.776601
## final  value 5606.773174 
## converged
## # weights:  81 (52 variable)
## initial  value 10491.747357 
## iter  10 value 6390.594428
## iter  20 value 5989.263749
## iter  30 value 5700.265439
## iter  40 value 5619.502429
## iter  50 value 5598.272350
## iter  60 value 5597.859388
## iter  70 value 5597.807943
## final  value 5597.807316 
## converged
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6389.818628
## iter  20 value 6011.770283
## iter  30 value 5732.088125
## iter  40 value 5671.280729
## iter  50 value 5652.256690
## iter  60 value 5651.737821
## iter  70 value 5651.622803
## iter  80 value 5651.614862
## iter  80 value 5651.614836
## iter  80 value 5651.614836
## final  value 5651.614836 
## converged
##                                                Df   AIC
## - day_of_week                                   2 11288
## - first_road_number                             2 11290
## <none>                                            11291
## - police_force                                  2 11292
## - second_road_number                            2 11292
## - pedestrian_crossing_human_control             4 11292
## - second_road_class                             2 11294
## - number_of_casualties                          2 11296
## - junction_detail                              14 11299
## - road_surface_conditions                       8 11300
## - junction_control                              6 11302
## - light_conditions                              8 11318
## - speed_limit                                   2 11318
## - number_of_vehicles                            2 11390
## - did_police_officer_attend_scene_of_collision  2 11419
## # weights:  90 (58 variable)
## initial  value 10491.747357 
## iter  10 value 6357.585504
## iter  20 value 5928.943080
## iter  30 value 5666.084333
## iter  40 value 5603.339370
## iter  50 value 5586.687013
## iter  60 value 5586.142516
## iter  70 value 5586.054932
## final  value 5586.053706 
## converged
## 
## Step:  AIC=11288.11
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + first_road_number + speed_limit + 
##     junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision
## 
## # weights:  87 (56 variable)
## initial  value 10491.747357 
## iter  10 value 6547.966992
## iter  20 value 6110.224302
## iter  30 value 5756.078357
## iter  40 value 5614.960955
## iter  50 value 5590.695658
## iter  60 value 5588.567212
## iter  70 value 5588.378007
## iter  80 value 5588.359239
## final  value 5588.358451 
## converged
## # weights:  87 (56 variable)
## initial  value 10491.747357 
## iter  10 value 6377.353639
## iter  20 value 5932.461528
## iter  30 value 5703.728345
## iter  40 value 5648.587873
## iter  50 value 5637.949317
## iter  60 value 5637.584892
## iter  70 value 5637.545619
## final  value 5637.545040 
## converged
## # weights:  87 (56 variable)
## initial  value 10491.747357 
## iter  10 value 6356.979886
## iter  20 value 5903.191536
## iter  30 value 5667.618944
## iter  40 value 5601.152529
## iter  50 value 5591.094096
## iter  60 value 5590.692632
## iter  70 value 5590.584013
## final  value 5590.582766 
## converged
## # weights:  87 (56 variable)
## initial  value 10491.747357 
## iter  10 value 6390.688672
## iter  20 value 6068.171327
## iter  30 value 5802.662006
## iter  40 value 5667.165113
## iter  50 value 5596.384046
## iter  60 value 5587.756537
## iter  70 value 5587.528297
## iter  80 value 5587.506653
## iter  90 value 5587.504043
## iter  90 value 5587.504009
## iter  90 value 5587.504008
## final  value 5587.504008 
## converged
## # weights:  87 (56 variable)
## initial  value 10491.747357 
## iter  10 value 7066.287343
## iter  20 value 6269.625351
## iter  30 value 5697.698290
## iter  40 value 5624.344922
## iter  50 value 5606.777059
## iter  60 value 5601.648456
## iter  70 value 5601.562266
## iter  80 value 5601.548264
## iter  80 value 5601.548226
## iter  80 value 5601.548226
## final  value 5601.548226 
## converged
## # weights:  69 (44 variable)
## initial  value 10491.747357 
## iter  10 value 6358.193800
## iter  20 value 5914.432842
## iter  30 value 5648.483421
## iter  40 value 5604.986196
## iter  50 value 5603.964143
## iter  60 value 5603.898781
## final  value 5603.897476 
## converged
## # weights:  81 (52 variable)
## initial  value 10491.747357 
## iter  10 value 6358.757229
## iter  20 value 5939.340374
## iter  30 value 5679.696900
## iter  40 value 5607.805666
## iter  50 value 5597.419294
## iter  60 value 5597.233522
## iter  70 value 5597.180362
## final  value 5597.180230 
## converged
## # weights:  87 (56 variable)
## initial  value 10491.747357 
## iter  10 value 6453.846005
## iter  20 value 5918.323938
## iter  30 value 5673.707266
## iter  40 value 5601.387608
## iter  50 value 5589.788986
## iter  60 value 5589.324284
## iter  70 value 5589.277193
## final  value 5589.276303 
## converged
## # weights:  87 (56 variable)
## initial  value 10491.747357 
## iter  10 value 6420.185127
## iter  20 value 6097.372743
## iter  30 value 5718.712092
## iter  40 value 5606.422422
## iter  50 value 5590.972820
## iter  60 value 5588.474239
## iter  70 value 5588.349849
## iter  80 value 5588.335701
## iter  80 value 5588.335651
## iter  80 value 5588.335651
## final  value 5588.335651 
## converged
## # weights:  84 (54 variable)
## initial  value 10491.747357 
## iter  10 value 6357.620095
## iter  20 value 5929.361116
## iter  30 value 5671.464189
## iter  40 value 5603.175668
## iter  50 value 5591.022632
## iter  60 value 5590.680746
## iter  70 value 5590.653579
## final  value 5590.652780 
## converged
## # weights:  78 (50 variable)
## initial  value 10491.747357 
## iter  10 value 6357.587564
## iter  20 value 5917.347875
## iter  30 value 5681.946094
## iter  40 value 5614.811766
## iter  50 value 5607.572545
## iter  60 value 5607.315368
## iter  70 value 5607.300412
## final  value 5607.300178 
## converged
## # weights:  78 (50 variable)
## initial  value 10491.747357 
## iter  10 value 6357.953050
## iter  20 value 5938.722170
## iter  30 value 5666.630024
## iter  40 value 5609.360730
## iter  50 value 5598.586875
## iter  60 value 5598.303726
## iter  70 value 5598.264211
## iter  70 value 5598.264166
## iter  70 value 5598.264165
## final  value 5598.264165 
## converged
## # weights:  87 (56 variable)
## initial  value 10491.747357 
## iter  10 value 6357.054471
## iter  20 value 5957.684313
## iter  30 value 5720.369318
## iter  40 value 5665.746422
## iter  50 value 5652.311829
## iter  60 value 5652.039537
## iter  70 value 5651.968478
## final  value 5651.967091 
## converged
##                                                Df   AIC
## - first_road_number                             2 11287
## <none>                                            11288
## - second_road_number                            2 11289
## - police_force                                  2 11289
## - pedestrian_crossing_human_control             4 11289
## - second_road_class                             2 11291
## - number_of_casualties                          2 11293
## - junction_detail                              14 11296
## - road_surface_conditions                       8 11296
## - junction_control                              6 11298
## - light_conditions                              8 11315
## - speed_limit                                   2 11315
## - number_of_vehicles                            2 11387
## - did_police_officer_attend_scene_of_collision  2 11416
## # weights:  87 (56 variable)
## initial  value 10491.747357 
## iter  10 value 6390.688672
## iter  20 value 6068.171327
## iter  30 value 5802.662006
## iter  40 value 5667.165113
## iter  50 value 5596.384046
## iter  60 value 5587.756537
## iter  70 value 5587.528297
## iter  80 value 5587.506653
## iter  90 value 5587.504043
## iter  90 value 5587.504009
## iter  90 value 5587.504008
## final  value 5587.504008 
## converged
## 
## Step:  AIC=11287.01
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + speed_limit + junction_detail + junction_control + 
##     second_road_class + second_road_number + pedestrian_crossing_human_control + 
##     light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision
## 
## # weights:  84 (54 variable)
## initial  value 10491.747357 
## iter  10 value 5953.914906
## iter  20 value 5811.024622
## iter  30 value 5652.849176
## iter  40 value 5600.414578
## iter  50 value 5590.460034
## iter  60 value 5589.831672
## iter  70 value 5589.759182
## final  value 5589.757975 
## converged
## # weights:  84 (54 variable)
## initial  value 10491.747357 
## iter  10 value 6451.715078
## iter  20 value 6051.227069
## iter  30 value 5810.906967
## iter  40 value 5701.492811
## iter  50 value 5643.049354
## iter  60 value 5639.368765
## iter  70 value 5638.945415
## iter  80 value 5638.923745
## final  value 5638.921699 
## converged
## # weights:  84 (54 variable)
## initial  value 10491.747357 
## iter  10 value 6392.763635
## iter  20 value 6030.387581
## iter  30 value 5768.530747
## iter  40 value 5660.946082
## iter  50 value 5594.307743
## iter  60 value 5592.345575
## iter  70 value 5592.154034
## iter  80 value 5592.133282
## final  value 5592.132045 
## converged
## # weights:  84 (54 variable)
## initial  value 10491.747357 
## iter  10 value 6302.509778
## iter  20 value 5880.468479
## iter  30 value 5655.105719
## iter  40 value 5609.862794
## iter  50 value 5605.952157
## iter  60 value 5603.007325
## iter  70 value 5602.992203
## final  value 5602.990537 
## converged
## # weights:  66 (42 variable)
## initial  value 10491.747357 
## iter  10 value 6406.167728
## iter  20 value 6090.912183
## iter  30 value 5748.114085
## iter  40 value 5620.439934
## iter  50 value 5605.315885
## iter  60 value 5605.177391
## iter  70 value 5605.156867
## final  value 5605.153808 
## converged
## # weights:  78 (50 variable)
## initial  value 10491.747357 
## iter  10 value 6407.604800
## iter  20 value 6012.384017
## iter  30 value 5786.186612
## iter  40 value 5673.622530
## iter  50 value 5602.032339
## iter  60 value 5598.667680
## iter  70 value 5598.420696
## iter  80 value 5598.400169
## final  value 5598.399813 
## converged
## # weights:  84 (54 variable)
## initial  value 10491.747357 
## iter  10 value 6385.459651
## iter  20 value 6059.494095
## iter  30 value 5771.259273
## iter  40 value 5664.413337
## iter  50 value 5600.848834
## iter  60 value 5591.470851
## iter  70 value 5591.216058
## iter  80 value 5591.196343
## final  value 5591.195233 
## converged
## # weights:  84 (54 variable)
## initial  value 10491.747357 
## iter  10 value 6002.317473
## iter  20 value 5855.383091
## iter  30 value 5655.738739
## iter  40 value 5601.979971
## iter  50 value 5591.019132
## iter  60 value 5590.435063
## iter  70 value 5590.352834
## final  value 5590.351245 
## converged
## # weights:  81 (52 variable)
## initial  value 10491.747357 
## iter  10 value 6391.218077
## iter  20 value 6068.922486
## iter  30 value 5805.512068
## iter  40 value 5684.065040
## iter  50 value 5596.318434
## iter  60 value 5592.311459
## iter  70 value 5592.073008
## iter  80 value 5592.059325
## iter  90 value 5592.057158
## final  value 5592.056939 
## converged
## # weights:  75 (48 variable)
## initial  value 10491.747357 
## iter  10 value 6391.693858
## iter  20 value 6066.763549
## iter  30 value 5783.711013
## iter  40 value 5657.944042
## iter  50 value 5610.189338
## iter  60 value 5608.895856
## iter  70 value 5608.792732
## iter  80 value 5608.775660
## final  value 5608.774622 
## converged
## # weights:  75 (48 variable)
## initial  value 10491.747357 
## iter  10 value 6394.902103
## iter  20 value 6065.213409
## iter  30 value 5804.032654
## iter  40 value 5670.408334
## iter  50 value 5602.740709
## iter  60 value 5599.710142
## iter  70 value 5599.580962
## iter  80 value 5599.571763
## final  value 5599.570883 
## converged
## # weights:  84 (54 variable)
## initial  value 10491.747357 
## iter  10 value 6392.062914
## iter  20 value 6110.556163
## iter  30 value 5847.116338
## iter  40 value 5728.610634
## iter  50 value 5658.491611
## iter  60 value 5653.374831
## iter  70 value 5653.350031
## iter  80 value 5653.336638
## final  value 5653.335809 
## converged
##                                                Df   AIC
## <none>                                            11287
## - police_force                                  2 11288
## - pedestrian_crossing_human_control             4 11288
## - second_road_number                            2 11289
## - second_road_class                             2 11290
## - number_of_casualties                          2 11292
## - junction_detail                              14 11294
## - road_surface_conditions                       8 11295
## - junction_control                              6 11297
## - light_conditions                              8 11314
## - speed_limit                                   2 11314
## - number_of_vehicles                            2 11386
## - did_police_officer_attend_scene_of_collision  2 11415
summary(step_test)  ##Residual Deviance: 11175.01 AIC: 11287.01
## Call:
## multinom(formula = legacy_collision_severity ~ police_force + 
##     number_of_vehicles + number_of_casualties + speed_limit + 
##     junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision, 
##     data = data4)
## 
## Coefficients:
##   (Intercept)  police_force number_of_vehicles number_of_casualties speed_limit
## 1   -9.442147  0.0003092832         -0.4529742           0.26178422  0.04148386
## 2   -1.623928 -0.0029140357         -0.4178323           0.06324246  0.00851386
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1       -0.9917024       -0.2201158       -0.3020790       0.08135917
## 2       -0.3519316       -0.1786110        0.1011727       0.03786262
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.4833014      -0.14867867        0.3204084       -10.6982581
## 2       -0.3475981      -0.08173265       -0.2206055        -0.5546216
##   junction_control2 junction_control3 second_road_class second_road_number
## 1        -0.2925639      -10.19036182        0.24119581       7.942130e-05
## 2        -0.2479221        0.02370078        0.05539577       5.433642e-05
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                        -24.3708361                         -9.4014438
## 2                         -0.5296658                         -0.2438371
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1         1.1818027         1.7133780       -0.09737516         1.1120524
## 2         0.1669279         0.6908065       -0.03320217        -0.4843814
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1               -0.1563564              -24.3928676               -0.8678382
## 2               -0.2224119               -0.7145325               -0.4523797
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1                 1.710754                                     2.7837857
## 2               -24.023772                                     0.8572225
## 
## Std. Errors:
##   (Intercept) police_force number_of_vehicles number_of_casualties speed_limit
## 1 0.005796409  0.005457743         0.01649447           0.07954138 0.007232952
## 2 0.016247182  0.001371113         0.04138959           0.03568908 0.002184144
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1     0.0009313294      0.000311626      0.001798214       0.00210335
## 2     0.0853045114      0.016225520      0.014865426       0.06890990
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1     0.0006280668       0.00223136      0.002584508      4.087865e-09
## 2     0.0183769679       0.12485069      0.080619841      1.364578e-03
##   junction_control2 junction_control3 second_road_class second_road_number
## 1       0.002216504      6.091331e-09        0.04242003       9.052596e-05
## 2       0.069561852      3.105755e-03        0.01702285       2.148846e-05
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                       2.466634e-15                       2.989700e-08
## 2                       6.175203e-04                       4.240239e-03
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1       0.005313224       0.000234287      0.0007741689      0.0005836393
## 2       0.058778444       0.001619227      0.0075320036      0.0010781867
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1              0.002512534             1.750303e-15             0.0001735918
## 2              0.061684801             3.065412e-04             0.0018807475
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1             1.191014e-04                                   0.005684965
## 2             1.058180e-14                                   0.078907654
## 
## Residual Deviance: 11175.01 
## AIC: 11287.01
coef(step_test) #coefficient matrix whose y Baseline:3; also the values of Log Odds Ratio
##   (Intercept)  police_force number_of_vehicles number_of_casualties speed_limit
## 1   -9.442147  0.0003092832         -0.4529742           0.26178422  0.04148386
## 2   -1.623928 -0.0029140357         -0.4178323           0.06324246  0.00851386
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1       -0.9917024       -0.2201158       -0.3020790       0.08135917
## 2       -0.3519316       -0.1786110        0.1011727       0.03786262
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.4833014      -0.14867867        0.3204084       -10.6982581
## 2       -0.3475981      -0.08173265       -0.2206055        -0.5546216
##   junction_control2 junction_control3 second_road_class second_road_number
## 1        -0.2925639      -10.19036182        0.24119581       7.942130e-05
## 2        -0.2479221        0.02370078        0.05539577       5.433642e-05
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                        -24.3708361                         -9.4014438
## 2                         -0.5296658                         -0.2438371
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1         1.1818027         1.7133780       -0.09737516         1.1120524
## 2         0.1669279         0.6908065       -0.03320217        -0.4843814
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1               -0.1563564              -24.3928676               -0.8678382
## 2               -0.2224119               -0.7145325               -0.4523797
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1                 1.710754                                     2.7837857
## 2               -24.023772                                     0.8572225
#Among💜1~💜4, 💜4 stepwise model has smallest AIC, hence it is the best model.

#12 significant predictors in best model 💜4:
#police_force + number_of_vehicles + number_of_casualties + speed_limit + junction_detail + junction_control + second_road_class + second_road_number + pedestrian_crossing_human_control + light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision

#For example, the -0.4530 suggests that for one unit increase in ‘number_of_vehicles’, the logit coefficient for ‘1: Serious’ relative to ‘3: Slight’ will go down by that amount, 0.4530. 

#If 1,2,3 respectively represents severity of #1: Fatal   #2: Serious  #3: Slight
#The equation of step_test is: 💜4 
#ln(P(severity= 1)/P(severity = 3)) = -9.4421 + 0.0003*police_force  - 0.4530*number_of_vehicles + 0.2618*number_of_casualties + 0.0415*speed_limit - 0.9917*junction_detail(1) - 0.2201*junction_detail(2)- 0.3021*junction_detail(5) +  0.0814*junction_detail(6) + 0.4833*junction_detail(7)- 0.1487*junction_detail(8) +  0.3204*junction_detail(9) - 10.6983*junction_control(1) - 0.2926*junction_control(2) - 10.1904*junction_control(3) + 0.2412*second_road_class + 7.942130e-05*second_road_number - 24.3708*pedestrian_crossing_human_control(1)  -9.4014*pedestrian_crossing_human_control(2) + 1.1818*light_conditions(4)  + 1.7134*light_conditions(5) - 0.0974*light_conditions(6) + 1.1121*light_conditions(7) - 0.1564*road_surface_conditions(2) - 24.3929*road_surface_conditions(3) - 0.8678*road_surface_conditions(4) + 1.7108*road_surface_conditions(5) + 2.7838*did_police_officer_attend_scene_of_collision(1) 

#ln(P(severity= 2)/P(severity = 3)) = -1.6239 - 0.0029*police_force  - 0.4178*number_of_vehicles + 0.0632*number_of_casualties + 0.0085*speed_limit - 0.3519*junction_detail(1) - 0.1786*junction_detail(2)+ 0.1012*junction_detail(5) +  0.0378*junction_detail(6) - 0.3476*junction_detail(7)- 0.0817*junction_detail(8) -  0.2206*junction_detail(9) - 0.5546*junction_control(1) - 0.2479*junction_control(2) + 0.0237*junction_control(3) + 0.0554*second_road_class + 5.433642e-05*second_road_number - 0.5297*pedestrian_crossing_human_control(1)  -0.2438*pedestrian_crossing_human_control(2) + 0.1669*light_conditions(4)  + 0.6908*light_conditions(5) - 0.0332*light_conditions(6) - 0.4844*light_conditions(7) - 0.2224*road_surface_conditions(2) - 0.7145*road_surface_conditions(3) - 0.4524*road_surface_conditions(4) - 24.0238*road_surface_conditions(5) + 0.8572*did_police_officer_attend_scene_of_collision(1) 

#🍑2. 2-tailed Z- statistic test
z <- summary(step_test)$coefficients/summary(step_test)$standard.errors
z
##   (Intercept) police_force number_of_vehicles number_of_casualties speed_limit
## 1 -1628.96493   0.05666869          -27.46219             3.291170    5.735399
## 2   -99.95139  -2.12530733          -10.09511             1.772039    3.898030
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1     -1064.824582       -706.34608      -167.988339       38.6807581
## 2        -4.125591        -11.00803         6.805909        0.5494511
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        769.50640      -66.6314124       123.972680     -2.617077e+09
## 2        -18.91488       -0.6546431        -2.736368     -4.064417e+02
##   junction_control2 junction_control3 second_road_class second_road_number
## 1       -131.993398     -1.672928e+09          5.685895          0.8773318
## 2         -3.564052      7.631244e+00          3.254201          2.5286330
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                      -9.880201e+15                      -3.144611e+08
## 2                      -8.577301e+02                      -5.750550e+01
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1        222.426660         7313.1584       -125.780256         1905.3761
## 2          2.839951          426.6273         -4.408146         -449.2556
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1               -62.230542            -1.393637e+16               -4999.3031
## 2                -3.605619            -2.330951e+03                -240.5319
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1             1.436384e+04                                     489.67506
## 2            -2.270292e+15                                      10.86362
pnorm(abs(z), 0, 1)       #Normal Distribution assumption
##   (Intercept) police_force number_of_vehicles number_of_casualties speed_limit
## 1           1    0.5225954                  1            0.9995011   1.0000000
## 2           1    0.9832195                  1            0.9618060   0.9999515
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1        1.0000000                1                1         1.000000
## 2        0.9999815                1                1         0.708652
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1                1        1.0000000        1.0000000                 1
## 2                1        0.7436512        0.9968939                 1
##   junction_control2 junction_control3 second_road_class second_road_number
## 1         1.0000000                 1         1.0000000          0.8098468
## 2         0.9998174                 1         0.9994314          0.9942746
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                                  1                                  1
## 2                                  1                                  1
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1          1.000000                 1         1.0000000                 1
## 2          0.997744                 1         0.9999948                 1
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1                1.0000000                        1                        1
## 2                0.9998443                        1                        1
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1                        1                                             1
## 2                        1                                             1
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p
##   (Intercept) police_force number_of_vehicles number_of_casualties  speed_limit
## 1           0   0.95480912                  0          0.000997716 9.728323e-09
## 2           0   0.03356098                  0          0.076388058 9.697851e-05
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1     0.000000e+00                0      0.00000e+00        0.0000000
## 2     3.697834e-05                0      1.00413e-11        0.5826959
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1                0        0.0000000      0.000000000                 0
## 2                0        0.5126975      0.006212155                 0
##   junction_control2 junction_control3 second_road_class second_road_number
## 1      0.0000000000      0.000000e+00      1.301297e-08         0.38030644
## 2      0.0003651735      2.331468e-14      1.137120e-03         0.01145077
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                                  0                                  0
## 2                                  0                                  0
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1       0.000000000                 0      0.000000e+00                 0
## 2       0.004512044                 0      1.042593e-05                 0
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1             0.0000000000                        0                        0
## 2             0.0003114099                        0                        0
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1                        0                                             0
## 2                        0                                             0
summary(step_test)$coefficients
##   (Intercept)  police_force number_of_vehicles number_of_casualties speed_limit
## 1   -9.442147  0.0003092832         -0.4529742           0.26178422  0.04148386
## 2   -1.623928 -0.0029140357         -0.4178323           0.06324246  0.00851386
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1       -0.9917024       -0.2201158       -0.3020790       0.08135917
## 2       -0.3519316       -0.1786110        0.1011727       0.03786262
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.4833014      -0.14867867        0.3204084       -10.6982581
## 2       -0.3475981      -0.08173265       -0.2206055        -0.5546216
##   junction_control2 junction_control3 second_road_class second_road_number
## 1        -0.2925639      -10.19036182        0.24119581       7.942130e-05
## 2        -0.2479221        0.02370078        0.05539577       5.433642e-05
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                        -24.3708361                         -9.4014438
## 2                         -0.5296658                         -0.2438371
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1         1.1818027         1.7133780       -0.09737516         1.1120524
## 2         0.1669279         0.6908065       -0.03320217        -0.4843814
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1               -0.1563564              -24.3928676               -0.8678382
## 2               -0.2224119               -0.7145325               -0.4523797
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1                 1.710754                                     2.7837857
## 2               -24.023772                                     0.8572225
#
deviance(step_test)
## [1] 11175.01
deviance(full_test)
## [1] 11122.18
full_test$edf
## [1] 118
step_test$edf
## [1] 56
####
#Model Evaluation

#💛4_3: Devirance test
#Between full_test/shorted_test/reduced_test and best model

deviance(step_test)
## [1] 11175.01
deviance(full_test)
## [1] 11122.18
full_test$edf
## [1] 118
step_test$edf
## [1] 56
deviance(step_test) > deviance(full_test)
## [1] TRUE
pchisq(deviance(step_test)-deviance(full_test),full_test$edf-step_test$edf,lower=F)
## [1] 0.790379
pchisq(deviance(full_test)-deviance(step_test),full_test$edf-step_test$edf,lower=F)
## [1] 1
pchisq(deviance(step_test)-deviance(shorted_test),shorted_test$edf-step_test$edf,lower=F)
## [1] 0.7596963
pchisq(deviance(step_test)-deviance(reduced_test),reduced_test$edf-step_test$edf,lower=F)
## [1] 0.9742975
#p > alpha, Not reject H0, so compared with full_test/shorted_test/reduced_test, step_test is better.
cat("Best mutinomial model is stepwise model.")
## Best mutinomial model is stepwise model.
#💛4_4: Root Mean Squared Error (RMSE)
#It evaluates how well the predicted probabilities from the model match the observed data. RMSE measures the average error of the model.
# Predicted probabilities for the best model
predicted_probs <- predict(step_test, type = "probs")

# Create a matrix of true labels (one-hot encoded for each severity category)
true_labels <- model.matrix(~ legacy_collision_severity - 1, data = data4)

# Calculate the RMSE for each severity category (1: Fatal, 2: Serious, 3: Slight)
rmse_fatal <- sqrt(mean((true_labels[, 1] - predicted_probs[, 1])^2))

rmse_serious <- sqrt(mean((true_labels[, 2] - predicted_probs[, 2])^2))
rmse_slight <- sqrt(mean((true_labels[, 3] - predicted_probs[, 3])^2))

# Average RMSE for the overall model
rmse_total <- sqrt(mean((true_labels - predicted_probs)^2))

# Print RMSE values
rmse_fatal
## [1] 0.4252239
rmse_serious
## [1] 0.1030828
rmse_slight
## [1] 0.41988
rmse_total
## [1] 0.3501146
cat("RMSE values:\n")
## RMSE values:
cat("Fatal:", rmse_fatal, "\n")
## Fatal: 0.4252239
cat("Serious:", rmse_serious, "\n")
## Serious: 0.1030828
cat("Slight:", rmse_slight, "\n")
## Slight: 0.41988
cat("Overall RMSE:", rmse_total, "\n")
## Overall RMSE: 0.3501146
####

####Next, carry analysis for Best model: step_test in 💚5 ~ 💚10

#💚5. Relative Risk Ratio and  Output tables

#💛5_1: Relative Risk Ratio
rr_ratio <- exp(coef(step_test))  #explonentiate the logit coefficient 
rr_ratio
##    (Intercept) police_force number_of_vehicles number_of_casualties speed_limit
## 1 7.930992e-05    1.0003093          0.6357345             1.299246    1.042356
## 2 1.971228e-01    0.9970902          0.6584726             1.065285    1.008550
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1        0.3709446        0.8024259        0.7392797         1.084760
## 2        0.7033283        0.8364312        1.1064677         1.038589
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        1.6214185        0.8618460         1.377690      2.258424e-05
## 2        0.7063827        0.9215183         0.802033      5.742895e-01
##   junction_control2 junction_control3 second_road_class second_road_number
## 1         0.7463475      0.0000375303          1.272770           1.000079
## 2         0.7804208      1.0239838710          1.056959           1.000054
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                       2.605436e-11                       8.260471e-05
## 2                       5.888017e-01                       7.836153e-01
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1          3.260246          5.547670         0.9072156         3.0405924
## 2          1.181669          1.995324         0.9673430         0.6160782
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1                0.8552544             2.548662e-11                0.4198582
## 2                0.8005855             4.894209e-01                0.6361126
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1             5.533131e+00                                     16.180159
## 2             3.686452e-11                                      2.356606
#The relative risk ratio for a one-unit increase in the variable "number_of_casualties" is 1.2992 for being in "severity = 1" vs. "severity = 3".
cbind(Estimate = coef(step_test),  OR = exp(coef(step_test)))
##   (Intercept)  police_force number_of_vehicles number_of_casualties speed_limit
## 1   -9.442147  0.0003092832         -0.4529742           0.26178422  0.04148386
## 2   -1.623928 -0.0029140357         -0.4178323           0.06324246  0.00851386
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1       -0.9917024       -0.2201158       -0.3020790       0.08135917
## 2       -0.3519316       -0.1786110        0.1011727       0.03786262
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        0.4833014      -0.14867867        0.3204084       -10.6982581
## 2       -0.3475981      -0.08173265       -0.2206055        -0.5546216
##   junction_control2 junction_control3 second_road_class second_road_number
## 1        -0.2925639      -10.19036182        0.24119581       7.942130e-05
## 2        -0.2479221        0.02370078        0.05539577       5.433642e-05
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                        -24.3708361                         -9.4014438
## 2                         -0.5296658                         -0.2438371
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1         1.1818027         1.7133780       -0.09737516         1.1120524
## 2         0.1669279         0.6908065       -0.03320217        -0.4843814
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1               -0.1563564              -24.3928676               -0.8678382
## 2               -0.2224119               -0.7145325               -0.4523797
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1                 1.710754                                     2.7837857
## 2               -24.023772                                     0.8572225
##    (Intercept) police_force number_of_vehicles number_of_casualties speed_limit
## 1 7.930992e-05    1.0003093          0.6357345             1.299246    1.042356
## 2 1.971228e-01    0.9970902          0.6584726             1.065285    1.008550
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1        0.3709446        0.8024259        0.7392797         1.084760
## 2        0.7033283        0.8364312        1.1064677         1.038589
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        1.6214185        0.8618460         1.377690      2.258424e-05
## 2        0.7063827        0.9215183         0.802033      5.742895e-01
##   junction_control2 junction_control3 second_road_class second_road_number
## 1         0.7463475      0.0000375303          1.272770           1.000079
## 2         0.7804208      1.0239838710          1.056959           1.000054
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                       2.605436e-11                       8.260471e-05
## 2                       5.888017e-01                       7.836153e-01
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1          3.260246          5.547670         0.9072156         3.0405924
## 2          1.181669          1.995324         0.9673430         0.6160782
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1                0.8552544             2.548662e-11                0.4198582
## 2                0.8005855             4.894209e-01                0.6361126
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1             5.533131e+00                                     16.180159
## 2             3.686452e-11                                      2.356606
round(cbind(Estimate = coef(step_test),  OR = exp(coef(step_test))),4)
##   (Intercept) police_force number_of_vehicles number_of_casualties speed_limit
## 1     -9.4421       0.0003            -0.4530               0.2618      0.0415
## 2     -1.6239      -0.0029            -0.4178               0.0632      0.0085
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1          -0.9917          -0.2201          -0.3021           0.0814
## 2          -0.3519          -0.1786           0.1012           0.0379
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1           0.4833          -0.1487           0.3204          -10.6983
## 2          -0.3476          -0.0817          -0.2206           -0.5546
##   junction_control2 junction_control3 second_road_class second_road_number
## 1           -0.2926          -10.1904            0.2412              1e-04
## 2           -0.2479            0.0237            0.0554              1e-04
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                           -24.3708                            -9.4014
## 2                            -0.5297                            -0.2438
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1            1.1818            1.7134           -0.0974            1.1121
## 2            0.1669            0.6908           -0.0332           -0.4844
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1                  -0.1564                 -24.3929                  -0.8678
## 2                  -0.2224                  -0.7145                  -0.4524
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1                   1.7108                                        2.7838
## 2                 -24.0238                                        0.8572
##   (Intercept) police_force number_of_vehicles number_of_casualties speed_limit
## 1      0.0001       1.0003             0.6357               1.2992      1.0424
## 2      0.1971       0.9971             0.6585               1.0653      1.0086
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1           0.3709           0.8024           0.7393           1.0848
## 2           0.7033           0.8364           1.1065           1.0386
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1           1.6214           0.8618           1.3777            0.0000
## 2           0.7064           0.9215           0.8020            0.5743
##   junction_control2 junction_control3 second_road_class second_road_number
## 1            0.7463             0.000            1.2728             1.0001
## 2            0.7804             1.024            1.0570             1.0001
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                             0.0000                             0.0001
## 2                             0.5888                             0.7836
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1            3.2602            5.5477            0.9072            3.0406
## 2            1.1817            1.9953            0.9673            0.6161
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1                   0.8553                   0.0000                   0.4199
## 2                   0.8006                   0.4894                   0.6361
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1                   5.5331                                       16.1802
## 2                   0.0000                                        2.3566
#💛5_2: Output tables
#The multinom() function  Modeling never provides p-values of the coefficients, which can get using the stargazer() function.

#...for the raw estimations of logit coefficients (Log relative risk ratio) 
library(stargazer)
## 
## Please cite as: 
## 
##  Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.
##  R package version 5.2.3. https://CRAN.R-project.org/package=stargazer
table1 <- stargazer(step_test, type="text", out="logit.htm")   
## 
## ==========================================================================
##                                                   Dependent variable:     
##                                               ----------------------------
##                                                     1              2      
##                                                    (1)            (2)     
## --------------------------------------------------------------------------
## police_force                                      0.0003       -0.003**   
##                                                  (0.005)        (0.001)   
##                                                                           
## number_of_vehicles                              -0.453***      -0.418***  
##                                                  (0.016)        (0.041)   
##                                                                           
## number_of_casualties                             0.262***       0.063*    
##                                                  (0.080)        (0.036)   
##                                                                           
## speed_limit                                      0.041***      0.009***   
##                                                  (0.007)        (0.002)   
##                                                                           
## junction_detail1                                -0.992***      -0.352***  
##                                                  (0.001)        (0.085)   
##                                                                           
## junction_detail2                                -0.220***      -0.179***  
##                                                  (0.0003)       (0.016)   
##                                                                           
## junction_detail5                                -0.302***      0.101***   
##                                                  (0.002)        (0.015)   
##                                                                           
## junction_detail6                                 0.081***        0.038    
##                                                  (0.002)        (0.069)   
##                                                                           
## junction_detail7                                 0.483***      -0.348***  
##                                                  (0.001)        (0.018)   
##                                                                           
## junction_detail8                                -0.149***       -0.082    
##                                                  (0.002)        (0.125)   
##                                                                           
## junction_detail9                                 0.320***      -0.221***  
##                                                  (0.003)        (0.081)   
##                                                                           
## junction_control1                               -10.698***     -0.555***  
##                                                  (0.000)        (0.001)   
##                                                                           
## junction_control2                               -0.293***      -0.248***  
##                                                  (0.002)        (0.070)   
##                                                                           
## junction_control3                               -10.190***     0.024***   
##                                                  (0.000)        (0.003)   
##                                                                           
## second_road_class                                0.241***      0.055***   
##                                                  (0.042)        (0.017)   
##                                                                           
## second_road_number                                0.0001       0.0001**   
##                                                  (0.0001)      (0.00002)  
##                                                                           
## pedestrian_crossing_human_control1              -24.371***     -0.530***  
##                                                  (0.000)        (0.001)   
##                                                                           
## pedestrian_crossing_human_control2              -9.401***      -0.244***  
##                                                 (0.00000)       (0.004)   
##                                                                           
## light_conditions4                                1.182***      0.167***   
##                                                  (0.005)        (0.059)   
##                                                                           
## light_conditions5                                1.713***      0.691***   
##                                                  (0.0002)       (0.002)   
##                                                                           
## light_conditions6                               -0.097***      -0.033***  
##                                                  (0.001)        (0.008)   
##                                                                           
## light_conditions7                                1.112***      -0.484***  
##                                                  (0.001)        (0.001)   
##                                                                           
## road_surface_conditions2                        -0.156***      -0.222***  
##                                                  (0.003)        (0.062)   
##                                                                           
## road_surface_conditions3                        -24.393***     -0.715***  
##                                                  (0.000)       (0.0003)   
##                                                                           
## road_surface_conditions4                        -0.868***      -0.452***  
##                                                  (0.0002)       (0.002)   
##                                                                           
## road_surface_conditions5                         1.711***     -24.024***  
##                                                  (0.0001)       (0.000)   
##                                                                           
## did_police_officer_attend_scene_of_collision1    2.784***      0.857***   
##                                                  (0.006)        (0.079)   
##                                                                           
## Constant                                        -9.442***      -1.624***  
##                                                  (0.006)        (0.016)   
##                                                                           
## --------------------------------------------------------------------------
## Akaike Inf. Crit.                               11,287.010    11,287.010  
## ==========================================================================
## Note:                                          *p<0.1; **p<0.05; ***p<0.01
table1  
##  [1] ""                                                                          
##  [2] "=========================================================================="
##  [3] "                                                  Dependent variable:     "
##  [4] "                                              ----------------------------"
##  [5] "                                                    1              2      "
##  [6] "                                                   (1)            (2)     "
##  [7] "--------------------------------------------------------------------------"
##  [8] "police_force                                      0.0003       -0.003**   "
##  [9] "                                                 (0.005)        (0.001)   "
## [10] "                                                                          "
## [11] "number_of_vehicles                              -0.453***      -0.418***  "
## [12] "                                                 (0.016)        (0.041)   "
## [13] "                                                                          "
## [14] "number_of_casualties                             0.262***       0.063*    "
## [15] "                                                 (0.080)        (0.036)   "
## [16] "                                                                          "
## [17] "speed_limit                                      0.041***      0.009***   "
## [18] "                                                 (0.007)        (0.002)   "
## [19] "                                                                          "
## [20] "junction_detail1                                -0.992***      -0.352***  "
## [21] "                                                 (0.001)        (0.085)   "
## [22] "                                                                          "
## [23] "junction_detail2                                -0.220***      -0.179***  "
## [24] "                                                 (0.0003)       (0.016)   "
## [25] "                                                                          "
## [26] "junction_detail5                                -0.302***      0.101***   "
## [27] "                                                 (0.002)        (0.015)   "
## [28] "                                                                          "
## [29] "junction_detail6                                 0.081***        0.038    "
## [30] "                                                 (0.002)        (0.069)   "
## [31] "                                                                          "
## [32] "junction_detail7                                 0.483***      -0.348***  "
## [33] "                                                 (0.001)        (0.018)   "
## [34] "                                                                          "
## [35] "junction_detail8                                -0.149***       -0.082    "
## [36] "                                                 (0.002)        (0.125)   "
## [37] "                                                                          "
## [38] "junction_detail9                                 0.320***      -0.221***  "
## [39] "                                                 (0.003)        (0.081)   "
## [40] "                                                                          "
## [41] "junction_control1                               -10.698***     -0.555***  "
## [42] "                                                 (0.000)        (0.001)   "
## [43] "                                                                          "
## [44] "junction_control2                               -0.293***      -0.248***  "
## [45] "                                                 (0.002)        (0.070)   "
## [46] "                                                                          "
## [47] "junction_control3                               -10.190***     0.024***   "
## [48] "                                                 (0.000)        (0.003)   "
## [49] "                                                                          "
## [50] "second_road_class                                0.241***      0.055***   "
## [51] "                                                 (0.042)        (0.017)   "
## [52] "                                                                          "
## [53] "second_road_number                                0.0001       0.0001**   "
## [54] "                                                 (0.0001)      (0.00002)  "
## [55] "                                                                          "
## [56] "pedestrian_crossing_human_control1              -24.371***     -0.530***  "
## [57] "                                                 (0.000)        (0.001)   "
## [58] "                                                                          "
## [59] "pedestrian_crossing_human_control2              -9.401***      -0.244***  "
## [60] "                                                (0.00000)       (0.004)   "
## [61] "                                                                          "
## [62] "light_conditions4                                1.182***      0.167***   "
## [63] "                                                 (0.005)        (0.059)   "
## [64] "                                                                          "
## [65] "light_conditions5                                1.713***      0.691***   "
## [66] "                                                 (0.0002)       (0.002)   "
## [67] "                                                                          "
## [68] "light_conditions6                               -0.097***      -0.033***  "
## [69] "                                                 (0.001)        (0.008)   "
## [70] "                                                                          "
## [71] "light_conditions7                                1.112***      -0.484***  "
## [72] "                                                 (0.001)        (0.001)   "
## [73] "                                                                          "
## [74] "road_surface_conditions2                        -0.156***      -0.222***  "
## [75] "                                                 (0.003)        (0.062)   "
## [76] "                                                                          "
## [77] "road_surface_conditions3                        -24.393***     -0.715***  "
## [78] "                                                 (0.000)       (0.0003)   "
## [79] "                                                                          "
## [80] "road_surface_conditions4                        -0.868***      -0.452***  "
## [81] "                                                 (0.0002)       (0.002)   "
## [82] "                                                                          "
## [83] "road_surface_conditions5                         1.711***     -24.024***  "
## [84] "                                                 (0.0001)       (0.000)   "
## [85] "                                                                          "
## [86] "did_police_officer_attend_scene_of_collision1    2.784***      0.857***   "
## [87] "                                                 (0.006)        (0.079)   "
## [88] "                                                                          "
## [89] "Constant                                        -9.442***      -1.624***  "
## [90] "                                                 (0.006)        (0.016)   "
## [91] "                                                                          "
## [92] "--------------------------------------------------------------------------"
## [93] "Akaike Inf. Crit.                               11,287.010    11,287.010  "
## [94] "=========================================================================="
## [95] "Note:                                          *p<0.1; **p<0.05; ***p<0.01"
#We might prefer to print an output table2 of relative risk  rather than log relative risk in table1.

#Output tables of Relative Risk Ratio
rr_ratio #Matrix of Relative Risk Ratio
##    (Intercept) police_force number_of_vehicles number_of_casualties speed_limit
## 1 7.930992e-05    1.0003093          0.6357345             1.299246    1.042356
## 2 1.971228e-01    0.9970902          0.6584726             1.065285    1.008550
##   junction_detail1 junction_detail2 junction_detail5 junction_detail6
## 1        0.3709446        0.8024259        0.7392797         1.084760
## 2        0.7033283        0.8364312        1.1064677         1.038589
##   junction_detail7 junction_detail8 junction_detail9 junction_control1
## 1        1.6214185        0.8618460         1.377690      2.258424e-05
## 2        0.7063827        0.9215183         0.802033      5.742895e-01
##   junction_control2 junction_control3 second_road_class second_road_number
## 1         0.7463475      0.0000375303          1.272770           1.000079
## 2         0.7804208      1.0239838710          1.056959           1.000054
##   pedestrian_crossing_human_control1 pedestrian_crossing_human_control2
## 1                       2.605436e-11                       8.260471e-05
## 2                       5.888017e-01                       7.836153e-01
##   light_conditions4 light_conditions5 light_conditions6 light_conditions7
## 1          3.260246          5.547670         0.9072156         3.0405924
## 2          1.181669          1.995324         0.9673430         0.6160782
##   road_surface_conditions2 road_surface_conditions3 road_surface_conditions4
## 1                0.8552544             2.548662e-11                0.4198582
## 2                0.8005855             4.894209e-01                0.6361126
##   road_surface_conditions5 did_police_officer_attend_scene_of_collision1
## 1             5.533131e+00                                     16.180159
## 2             3.686452e-11                                      2.356606
#Create using the stargazer() function
table2 <- stargazer(step_test, type="text", coef=list(rr_ratio), p.auto=FALSE, out="rr_ratio.htm")
## 
## ==========================================================================
##                                                   Dependent variable:     
##                                               ----------------------------
##                                                     1              2      
##                                                    (1)            (2)     
## --------------------------------------------------------------------------
## police_force                                      1.000         0.997**   
##                                                  (0.005)        (0.001)   
##                                                                           
## number_of_vehicles                               0.636***      0.658***   
##                                                  (0.016)        (0.041)   
##                                                                           
## number_of_casualties                             1.299***       1.065*    
##                                                  (0.080)        (0.036)   
##                                                                           
## speed_limit                                      1.042***      1.009***   
##                                                  (0.007)        (0.002)   
##                                                                           
## junction_detail1                                 0.371***      0.703***   
##                                                  (0.001)        (0.085)   
##                                                                           
## junction_detail2                                 0.802***      0.836***   
##                                                  (0.0003)       (0.016)   
##                                                                           
## junction_detail5                                 0.739***      1.106***   
##                                                  (0.002)        (0.015)   
##                                                                           
## junction_detail6                                 1.085***        1.039    
##                                                  (0.002)        (0.069)   
##                                                                           
## junction_detail7                                 1.621***      0.706***   
##                                                  (0.001)        (0.018)   
##                                                                           
## junction_detail8                                 0.862***        0.922    
##                                                  (0.002)        (0.125)   
##                                                                           
## junction_detail9                                 1.378***      0.802***   
##                                                  (0.003)        (0.081)   
##                                                                           
## junction_control1                               0.00002***     0.574***   
##                                                  (0.000)        (0.001)   
##                                                                           
## junction_control2                                0.746***      0.780***   
##                                                  (0.002)        (0.070)   
##                                                                           
## junction_control3                               0.00004***     1.024***   
##                                                  (0.000)        (0.003)   
##                                                                           
## second_road_class                                1.273***      1.057***   
##                                                  (0.042)        (0.017)   
##                                                                           
## second_road_number                                1.000         1.000**   
##                                                  (0.0001)      (0.00002)  
##                                                                           
## pedestrian_crossing_human_control1               0.000***      0.589***   
##                                                  (0.000)        (0.001)   
##                                                                           
## pedestrian_crossing_human_control2              0.0001***      0.784***   
##                                                 (0.00000)       (0.004)   
##                                                                           
## light_conditions4                                3.260***      1.182***   
##                                                  (0.005)        (0.059)   
##                                                                           
## light_conditions5                                5.548***      1.995***   
##                                                  (0.0002)       (0.002)   
##                                                                           
## light_conditions6                                0.907***      0.967***   
##                                                  (0.001)        (0.008)   
##                                                                           
## light_conditions7                                3.041***      0.616***   
##                                                  (0.001)        (0.001)   
##                                                                           
## road_surface_conditions2                         0.855***      0.801***   
##                                                  (0.003)        (0.062)   
##                                                                           
## road_surface_conditions3                         0.000***      0.489***   
##                                                  (0.000)       (0.0003)   
##                                                                           
## road_surface_conditions4                         0.420***      0.636***   
##                                                  (0.0002)       (0.002)   
##                                                                           
## road_surface_conditions5                         5.533***      0.000***   
##                                                  (0.0001)       (0.000)   
##                                                                           
## did_police_officer_attend_scene_of_collision1   16.180***      2.357***   
##                                                  (0.006)        (0.079)   
##                                                                           
## Constant                                        0.0001***      0.197***   
##                                                  (0.006)        (0.016)   
##                                                                           
## --------------------------------------------------------------------------
## Akaike Inf. Crit.                               11,287.010    11,287.010  
## ==========================================================================
## Note:                                          *p<0.1; **p<0.05; ***p<0.01
table2
##  [1] ""                                                                          
##  [2] "=========================================================================="
##  [3] "                                                  Dependent variable:     "
##  [4] "                                              ----------------------------"
##  [5] "                                                    1              2      "
##  [6] "                                                   (1)            (2)     "
##  [7] "--------------------------------------------------------------------------"
##  [8] "police_force                                      1.000         0.997**   "
##  [9] "                                                 (0.005)        (0.001)   "
## [10] "                                                                          "
## [11] "number_of_vehicles                               0.636***      0.658***   "
## [12] "                                                 (0.016)        (0.041)   "
## [13] "                                                                          "
## [14] "number_of_casualties                             1.299***       1.065*    "
## [15] "                                                 (0.080)        (0.036)   "
## [16] "                                                                          "
## [17] "speed_limit                                      1.042***      1.009***   "
## [18] "                                                 (0.007)        (0.002)   "
## [19] "                                                                          "
## [20] "junction_detail1                                 0.371***      0.703***   "
## [21] "                                                 (0.001)        (0.085)   "
## [22] "                                                                          "
## [23] "junction_detail2                                 0.802***      0.836***   "
## [24] "                                                 (0.0003)       (0.016)   "
## [25] "                                                                          "
## [26] "junction_detail5                                 0.739***      1.106***   "
## [27] "                                                 (0.002)        (0.015)   "
## [28] "                                                                          "
## [29] "junction_detail6                                 1.085***        1.039    "
## [30] "                                                 (0.002)        (0.069)   "
## [31] "                                                                          "
## [32] "junction_detail7                                 1.621***      0.706***   "
## [33] "                                                 (0.001)        (0.018)   "
## [34] "                                                                          "
## [35] "junction_detail8                                 0.862***        0.922    "
## [36] "                                                 (0.002)        (0.125)   "
## [37] "                                                                          "
## [38] "junction_detail9                                 1.378***      0.802***   "
## [39] "                                                 (0.003)        (0.081)   "
## [40] "                                                                          "
## [41] "junction_control1                               0.00002***     0.574***   "
## [42] "                                                 (0.000)        (0.001)   "
## [43] "                                                                          "
## [44] "junction_control2                                0.746***      0.780***   "
## [45] "                                                 (0.002)        (0.070)   "
## [46] "                                                                          "
## [47] "junction_control3                               0.00004***     1.024***   "
## [48] "                                                 (0.000)        (0.003)   "
## [49] "                                                                          "
## [50] "second_road_class                                1.273***      1.057***   "
## [51] "                                                 (0.042)        (0.017)   "
## [52] "                                                                          "
## [53] "second_road_number                                1.000         1.000**   "
## [54] "                                                 (0.0001)      (0.00002)  "
## [55] "                                                                          "
## [56] "pedestrian_crossing_human_control1               0.000***      0.589***   "
## [57] "                                                 (0.000)        (0.001)   "
## [58] "                                                                          "
## [59] "pedestrian_crossing_human_control2              0.0001***      0.784***   "
## [60] "                                                (0.00000)       (0.004)   "
## [61] "                                                                          "
## [62] "light_conditions4                                3.260***      1.182***   "
## [63] "                                                 (0.005)        (0.059)   "
## [64] "                                                                          "
## [65] "light_conditions5                                5.548***      1.995***   "
## [66] "                                                 (0.0002)       (0.002)   "
## [67] "                                                                          "
## [68] "light_conditions6                                0.907***      0.967***   "
## [69] "                                                 (0.001)        (0.008)   "
## [70] "                                                                          "
## [71] "light_conditions7                                3.041***      0.616***   "
## [72] "                                                 (0.001)        (0.001)   "
## [73] "                                                                          "
## [74] "road_surface_conditions2                         0.855***      0.801***   "
## [75] "                                                 (0.003)        (0.062)   "
## [76] "                                                                          "
## [77] "road_surface_conditions3                         0.000***      0.489***   "
## [78] "                                                 (0.000)       (0.0003)   "
## [79] "                                                                          "
## [80] "road_surface_conditions4                         0.420***      0.636***   "
## [81] "                                                 (0.0002)       (0.002)   "
## [82] "                                                                          "
## [83] "road_surface_conditions5                         5.533***      0.000***   "
## [84] "                                                 (0.0001)       (0.000)   "
## [85] "                                                                          "
## [86] "did_police_officer_attend_scene_of_collision1   16.180***      2.357***   "
## [87] "                                                 (0.006)        (0.079)   "
## [88] "                                                                          "
## [89] "Constant                                        0.0001***      0.197***   "
## [90] "                                                 (0.006)        (0.016)   "
## [91] "                                                                          "
## [92] "--------------------------------------------------------------------------"
## [93] "Akaike Inf. Crit.                               11,287.010    11,287.010  "
## [94] "=========================================================================="
## [95] "Note:                                          *p<0.1; **p<0.05; ***p<0.01"
cat("the value '0.636' in table2 means that keeping all other variables constant, if number_of_vehicles increases one unit, you are 0.636 times more likely to stay in the 1:Fatal severity as compared to 3:Slight severity. The coefficient is  significant.")
## the value '0.636' in table2 means that keeping all other variables constant, if number_of_vehicles increases one unit, you are 0.636 times more likely to stay in the 1:Fatal severity as compared to 3:Slight severity. The coefficient is  significant.
cat("RRR is 0.739 for Fatal crashes relative to Slight crashes.
Interpretation: A crash at a junction type coded as 5 (compared to the baseline junction type 3 - T or staggered junction) is 26.1% less likely to result in a Fatal crash compared to a Slight crash.")
## RRR is 0.739 for Fatal crashes relative to Slight crashes.
## Interpretation: A crash at a junction type coded as 5 (compared to the baseline junction type 3 - T or staggered junction) is 26.1% less likely to result in a Fatal crash compared to a Slight crash.
cat("RRR = 1: No effect of the predictor on the odds of being in a specific outcome category versus the baseline.
RRR > 1: The predictor increases the odds of being in the specific outcome category compared to the baseline.
RRR < 1: The predictor decreases the odds of being in the specific outcome category compared to the baseline.")
## RRR = 1: No effect of the predictor on the odds of being in a specific outcome category versus the baseline.
## RRR > 1: The predictor increases the odds of being in the specific outcome category compared to the baseline.
## RRR < 1: The predictor decreases the odds of being in the specific outcome category compared to the baseline.
#💚6. predicted probabilities by fitting best model

pp <- fitted(step_test) 
view(pp)  #caculate "predicted probabilities" for each Severity levels :c(3,1,2)
head(pp)
##           3            1         2
## 1 0.7679678 1.978478e-06 0.2320302
## 2 0.7507021 9.030279e-03 0.2402676
## 3 0.6909440 1.931065e-02 0.2897453
## 4 0.7796731 7.231680e-03 0.2130952
## 5 0.7821548 8.971030e-03 0.2088741
## 6 0.7146779 1.234528e-02 0.2729769
dim(pp)
## [1] 9550    3
#12 significant predictors in best model 💜4:
#police_force + number_of_vehicles + number_of_casualties + speed_limit + junction_detail + junction_control + second_road_class + second_road_number + pedestrian_crossing_human_control + light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision

#💚7.  Predict Probability of another dataset using best model

#Method 2:
#calculate the mean probabilities within each level of "pedestrian_crossing_human_control"
summary(data4$police_force)  ##1,63 is min & max
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     1.0     4.0    20.0    22.7    43.0    63.0
summary( data4$number_of_vehicles)##1,8
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00    1.00    2.00    1.84    2.00    8.00
summary( data4$number_of_casualties) ##1,17
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   1.000   1.000   1.292   1.000  17.000
summary( data4$speed_limit) ##20,70 (1-70)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   20.00   30.00   30.00   33.02   30.00   70.00
summary(data4$junction_detail) ##1:3&5:9 (8 numbers)
##    3    1    2    5    6    7    8    9 
## 4679 1089  242  185 1642  275  370 1068
summary(data4$junction_control) ##1,4
##    4    1    2    3 
## 7546  125 1767  112
summary(data4$second_road_class) ##1,6
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   5.000   6.000   5.318   6.000   6.000
summary(data4$second_road_number) ##0,6547
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     0.0     0.0     0.0   397.6     0.0  6547.0
summary(data4$light_conditions)  ##1,4,5,6,7 (5 numbers)
##    1    4    5    6    7 
## 6963 2208   57  235   87
summary(data4$road_surface_conditions)  ##1:5
##    1    2    3    4    5 
## 7330 2035   30  151    4
summary(data4$did_police_officer_attend_scene_of_collision)  ##1,2
##    2    1 
## 1314 8236
summary(data4$pedestrian_crossing_human_control)  #0:2 (3)
##    0    1    2 
## 9289   53  208
str(data4) 
## 'data.frame':    9550 obs. of  21 variables:
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : Factor w/ 3 levels "3","1","2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : Factor w/ 5 levels "1","2","3","6",..: 2 1 4 4 1 3 2 2 4 4 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : Factor w/ 8 levels "3","1","2","5",..: 8 2 7 5 2 5 1 5 8 1 ...
##  $ junction_control                            : Factor w/ 4 levels "4","1","2","3": 1 1 1 3 1 3 1 3 1 1 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : Factor w/ 3 levels "0","1","2": 3 1 1 1 1 1 1 1 1 1 ...
##  $ pedestrian_crossing_physical_facilities     : Factor w/ 6 levels "0","1","4","5",..: 4 1 1 1 1 4 1 3 1 1 ...
##  $ light_conditions                            : Factor w/ 5 levels "1","4","5","6",..: 2 2 2 2 2 2 4 2 2 1 ...
##  $ weather_conditions                          : Factor w/ 8 levels "1","2","3","4",..: 8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : Factor w/ 5 levels "1","2","3","4",..: 2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : Factor w/ 8 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ carriageway_hazards                         : Factor w/ 6 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ did_police_officer_attend_scene_of_collision: Factor w/ 2 levels "2","1": 2 2 2 2 2 2 2 2 2 2 ...
data4$pedestrian_crossing_human_control[1]
## [1] 2
## Levels: 0 1 2
dwrite1 <- data.frame(pedestrian_crossing_human_control = rep(c(0:2), each = 2800),police_force = rep(1:70, 120), number_of_vehicles = rep(1:10,840), number_of_casualties = rep(1:20,420), speed_limit = rep(1:70,120), junction_detail = rep(c(1:3,5:9),1050), junction_control = rep(c(1:4),2100), second_road_class = rep(c(1:10),840), second_road_number = rep(c(1:8400),1), light_conditions = rep(c(1,4,5,6,7),1680), road_surface_conditions = rep(c(1:5),1680), did_police_officer_attend_scene_of_collision = rep(c(1:2),4200))  #8400 is least common multiple of 2,3,4,5,6+4,8, 8+2,17+3,63+7,70, 6547+1853 
#Among 12 significant predictors in step_test, 6 are factors, and the rest are numbers(according to comparion table for Stats19)
dwrite1$pedestrian_crossing_human_control <- as.factor(dwrite1$pedestrian_crossing_human_control)
dwrite1$junction_detail <- as.factor(dwrite1$junction_detail)
dwrite1$junction_control <- as.factor(dwrite1$junction_control)
dwrite1$light_conditions <- as.factor(dwrite1$light_conditions)
dwrite1$road_surface_conditions <- as.factor(dwrite1$road_surface_conditions)
dwrite1$did_police_officer_attend_scene_of_collision <- as.factor(dwrite1$did_police_officer_attend_scene_of_collision)
#relevel 6 predictors
dwrite1$junction_detail <- relevel(dwrite1$junction_detail, ref = "3")
dwrite1$junction_detail[1]  #Baseline: 3 (T or staggered junction)
## [1] 1
## Levels: 3 1 2 5 6 7 8 9
dwrite1$junction_control <- relevel(dwrite1$junction_control, ref = "4")
dwrite1$junction_control[1] #Baseline: 4 (Give way or uncontrolled)
## [1] 1
## Levels: 4 1 2 3
dwrite1$did_police_officer_attend_scene_of_collision <- relevel(dwrite1$did_police_officer_attend_scene_of_collision, ref = "2")
dwrite1$did_police_officer_attend_scene_of_collision[1]#Baseline: 2 (No)
## [1] 1
## Levels: 2 1
library(fpp3)
view(dwrite1)  
str(dwrite1)  # 6 factors, 6 numeric
## 'data.frame':    8400 obs. of  12 variables:
##  $ pedestrian_crossing_human_control           : Factor w/ 3 levels "0","1","2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ police_force                                : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ number_of_vehicles                          : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ number_of_casualties                        : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ speed_limit                                 : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ junction_detail                             : Factor w/ 8 levels "3","1","2","5",..: 2 3 1 4 5 6 7 8 2 3 ...
##  $ junction_control                            : Factor w/ 4 levels "4","1","2","3": 2 3 4 1 2 3 4 1 2 3 ...
##  $ second_road_class                           : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ second_road_number                          : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ light_conditions                            : Factor w/ 5 levels "1","4","5","6",..: 1 2 3 4 5 1 2 3 4 5 ...
##  $ road_surface_conditions                     : Factor w/ 5 levels "1","2","3","4",..: 1 2 3 4 5 1 2 3 4 5 ...
##  $ did_police_officer_attend_scene_of_collision: Factor w/ 2 levels "2","1": 2 1 2 1 2 1 2 1 2 1 ...
dim(dwrite1)
## [1] 8400   12
dim(predict(step_test, newdata = dwrite1, type = "probs", se = TRUE))
## [1] 8400    3
dim(pp)
## [1] 9550    3
## store the predicted probabilities into new dataset
view(predict(step_test, newdata = dwrite1, type = "probs", se = TRUE))
pp.write1 <- cbind(dwrite1, predict(step_test, newdata = dwrite1, type = "probs", se = TRUE))
view(pp.write1)
head(pp.write1)
##   pedestrian_crossing_human_control police_force number_of_vehicles
## 1                                 0            1                  1
## 2                                 0            2                  2
## 3                                 0            3                  3
## 4                                 0            4                  4
## 5                                 0            5                  5
## 6                                 0            6                  6
##   number_of_casualties speed_limit junction_detail junction_control
## 1                    1           1               1                1
## 2                    2           2               2                2
## 3                    3           3               3                3
## 4                    4           4               5                4
## 5                    5           5               6                1
## 6                    6           6               7                2
##   second_road_class second_road_number light_conditions road_surface_conditions
## 1                 1                  1                1                       1
## 2                 2                  2                4                       2
## 3                 3                  3                5                       3
## 4                 4                  4                6                       4
## 5                 5                  5                7                       5
## 6                 6                  6                1                       1
##   did_police_officer_attend_scene_of_collision         3            1
## 1                                            1 0.8772669 1.033853e-08
## 2                                            2 0.9364742 1.490457e-04
## 3                                            1 0.8385327 7.522150e-18
## 4                                            2 0.9601405 3.096658e-05
## 5                                            1 0.9999992 8.373167e-07
## 6                                            2 0.9815090 1.634826e-04
##              2
## 1 1.227331e-01
## 2 6.337673e-02
## 3 1.614673e-01
## 4 3.982849e-02
## 5 1.450202e-12
## 6 1.832751e-02
dim(pp.write1)
## [1] 8400   15
## calculate the mean probabilities within each level of pedestrian_

##View the average predicted probability for different values of severity within each level of pedestrian_crossing_human_control/junction_detail/light_conditons/road_surface_conditions/did
by(pp.write1[, 13:15], pp.write1$pedestrian_crossing_human_control, colMeans)
## pp.write1$pedestrian_crossing_human_control: 0
##          3          1          2 
## 0.90335566 0.01169309 0.08495125 
## ------------------------------------------------------------ 
## pp.write1$pedestrian_crossing_human_control: 1
##            3            1            2 
## 9.370883e-01 5.114906e-13 6.291172e-02 
## ------------------------------------------------------------ 
## pp.write1$pedestrian_crossing_human_control: 2
##            3            1            2 
## 9.107483e-01 2.014414e-06 8.924966e-02
by(pp.write1[, 13:15], pp.write1$junction_detail, colMeans)
## pp.write1$junction_detail: 3
##            3            1            2 
## 8.548769e-01 6.820260e-06 1.451163e-01 
## ------------------------------------------------------------ 
## pp.write1$junction_detail: 1
##            3            1            2 
## 9.317388e-01 3.781050e-07 6.826084e-02 
## ------------------------------------------------------------ 
## pp.write1$junction_detail: 2
##            3            1            2 
## 0.9638733476 0.0009181833 0.0352084691 
## ------------------------------------------------------------ 
## pp.write1$junction_detail: 5
##          3          1          2 
## 0.91992736 0.01080842 0.06926422 
## ------------------------------------------------------------ 
## pp.write1$junction_detail: 6
##            3            1            2 
## 9.050125e-01 1.087991e-06 9.498642e-02 
## ------------------------------------------------------------ 
## pp.write1$junction_detail: 7
##           3           1           2 
## 0.968185072 0.001831831 0.029983097 
## ------------------------------------------------------------ 
## pp.write1$junction_detail: 8
##            3            1            2 
## 8.627065e-01 5.859182e-06 1.372877e-01 
## ------------------------------------------------------------ 
## pp.write1$junction_detail: 9
##          3          1          2 
## 0.93019228 0.01761436 0.05219336
by(pp.write1[, 13:15], pp.write1$junction_control, colMeans)
## pp.write1$junction_control: 4
##          3          1          2 
## 0.92505982 0.01421139 0.06072879 
## ------------------------------------------------------------ 
## pp.write1$junction_control: 1
##            3            1            2 
## 9.183756e-01 7.330481e-07 8.162363e-02 
## ------------------------------------------------------------ 
## pp.write1$junction_control: 2
##           3           1           2 
## 0.966029210 0.001375007 0.032595783 
## ------------------------------------------------------------ 
## pp.write1$junction_control: 3
##            3            1            2 
## 8.587917e-01 6.339721e-06 1.412020e-01
by(pp.write1[, 13:15], pp.write1$light_conditions, colMeans)
## pp.write1$light_conditions: 1
##            3            1            2 
## 0.8285958083 0.0008789727 0.1705252191 
## ------------------------------------------------------------ 
## pp.write1$light_conditions: 4
##           3           1           2 
## 0.907400405 0.001466661 0.091132934 
## ------------------------------------------------------------ 
## pp.write1$light_conditions: 5
##            3            1            2 
## 9.019792e-01 1.391305e-13 9.802083e-02 
## ------------------------------------------------------------ 
## pp.write1$light_conditions: 6
##            3            1            2 
## 0.9642401524 0.0002511038 0.0355087438 
## ------------------------------------------------------------ 
## pp.write1$light_conditions: 7
##            3            1            2 
## 9.831049e-01 1.689510e-02 1.842256e-12
by(pp.write1[, 13:15], pp.write1$road_surface_conditions, colMeans)
## pp.write1$road_surface_conditions: 1
##            3            1            2 
## 0.8285958083 0.0008789727 0.1705252191 
## ------------------------------------------------------------ 
## pp.write1$road_surface_conditions: 2
##           3           1           2 
## 0.907400405 0.001466661 0.091132934 
## ------------------------------------------------------------ 
## pp.write1$road_surface_conditions: 3
##            3            1            2 
## 9.019792e-01 1.391305e-13 9.802083e-02 
## ------------------------------------------------------------ 
## pp.write1$road_surface_conditions: 4
##            3            1            2 
## 0.9642401524 0.0002511038 0.0355087438 
## ------------------------------------------------------------ 
## pp.write1$road_surface_conditions: 5
##            3            1            2 
## 9.831049e-01 1.689510e-02 1.842256e-12
by(pp.write1[, 13:15], pp.write1$did_police_officer_attend_scene_of_collision, colMeans)
## pp.write1$did_police_officer_attend_scene_of_collision: 2
##           3           1           2 
## 0.945544515 0.007793198 0.046662287 
## ------------------------------------------------------------ 
## pp.write1$did_police_officer_attend_scene_of_collision: 1
##            3            1            2 
## 8.885837e-01 3.536385e-06 1.114128e-01
##保留4位有效数字
# Combine all tables into one large table with rounded values
library(dplyr)
# Function to process each variable group with rounding
process_group <- function(variable, group_col) {
  result <- by(
    pp.write1[, 13:15],
    pp.write1[[group_col]],
    function(x) round(colMeans(x), 4)
  )
  
  # Convert to a data frame for better combination
  df <- do.call(rbind, result)
  df <- as.data.frame(df)
  df$Group <- rownames(df)
  df$Variable <- variable
  rownames(df) <- NULL
  return(df)
}

# Process each variable group
pedestrian_table <- process_group("pedestrian_crossing_human_control", "pedestrian_crossing_human_control")
junction_detail_table <- process_group("junction_detail", "junction_detail")
junction_control_table <- process_group("junction_control", "junction_control")
light_conditions_table <- process_group("light_conditions", "light_conditions")
road_surface_conditions_table <- process_group("road_surface_conditions", "road_surface_conditions")
police_attend_table <- process_group("did_police_officer_attend_scene_of_collision", "did_police_officer_attend_scene_of_collision")

# Combine all tables
Table4_7 <- bind_rows(
  pedestrian_table,
  junction_detail_table,
  junction_control_table,
  light_conditions_table,
  road_surface_conditions_table,
  police_attend_table
)

Table4_7
##         3      1      2 Group                                     Variable
## 1  0.9034 0.0117 0.0850     0            pedestrian_crossing_human_control
## 2  0.9371 0.0000 0.0629     1            pedestrian_crossing_human_control
## 3  0.9107 0.0000 0.0892     2            pedestrian_crossing_human_control
## 4  0.8549 0.0000 0.1451     3                              junction_detail
## 5  0.9317 0.0000 0.0683     1                              junction_detail
## 6  0.9639 0.0009 0.0352     2                              junction_detail
## 7  0.9199 0.0108 0.0693     5                              junction_detail
## 8  0.9050 0.0000 0.0950     6                              junction_detail
## 9  0.9682 0.0018 0.0300     7                              junction_detail
## 10 0.8627 0.0000 0.1373     8                              junction_detail
## 11 0.9302 0.0176 0.0522     9                              junction_detail
## 12 0.9251 0.0142 0.0607     4                             junction_control
## 13 0.9184 0.0000 0.0816     1                             junction_control
## 14 0.9660 0.0014 0.0326     2                             junction_control
## 15 0.8588 0.0000 0.1412     3                             junction_control
## 16 0.8286 0.0009 0.1705     1                             light_conditions
## 17 0.9074 0.0015 0.0911     4                             light_conditions
## 18 0.9020 0.0000 0.0980     5                             light_conditions
## 19 0.9642 0.0003 0.0355     6                             light_conditions
## 20 0.9831 0.0169 0.0000     7                             light_conditions
## 21 0.8286 0.0009 0.1705     1                      road_surface_conditions
## 22 0.9074 0.0015 0.0911     2                      road_surface_conditions
## 23 0.9020 0.0000 0.0980     3                      road_surface_conditions
## 24 0.9642 0.0003 0.0355     4                      road_surface_conditions
## 25 0.9831 0.0169 0.0000     5                      road_surface_conditions
## 26 0.9455 0.0078 0.0467     2 did_police_officer_attend_scene_of_collision
## 27 0.8886 0.0000 0.1114     1 did_police_officer_attend_scene_of_collision
view(Table4_7)


####🙅CAN BE DELETED!

#For another model with only 2 predictors, plot the Predicted Probabilities against number_of_vehicles by the Level of pedestrian_crossing_human_control for 3 Severity levels: 1,2,3. 
str(data4) 
## 'data.frame':    9550 obs. of  21 variables:
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : Factor w/ 3 levels "3","1","2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : Factor w/ 5 levels "1","2","3","6",..: 2 1 4 4 1 3 2 2 4 4 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : Factor w/ 8 levels "3","1","2","5",..: 8 2 7 5 2 5 1 5 8 1 ...
##  $ junction_control                            : Factor w/ 4 levels "4","1","2","3": 1 1 1 3 1 3 1 3 1 1 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : Factor w/ 3 levels "0","1","2": 3 1 1 1 1 1 1 1 1 1 ...
##  $ pedestrian_crossing_physical_facilities     : Factor w/ 6 levels "0","1","4","5",..: 4 1 1 1 1 4 1 3 1 1 ...
##  $ light_conditions                            : Factor w/ 5 levels "1","4","5","6",..: 2 2 2 2 2 2 4 2 2 1 ...
##  $ weather_conditions                          : Factor w/ 8 levels "1","2","3","4",..: 8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : Factor w/ 5 levels "1","2","3","4",..: 2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : Factor w/ 8 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ carriageway_hazards                         : Factor w/ 6 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ did_police_officer_attend_scene_of_collision: Factor w/ 2 levels "2","1": 2 2 2 2 2 2 2 2 2 2 ...
test1 <- multinom(legacy_collision_severity ~ pedestrian_crossing_human_control + did_police_officer_attend_scene_of_collision + number_of_vehicles, data = data4)
## # weights:  18 (10 variable)
## initial  value 10491.747357 
## iter  10 value 5689.796127
## iter  20 value 5676.336770
## final  value 5676.336599 
## converged
summary(test1)
## Call:
## multinom(formula = legacy_collision_severity ~ pedestrian_crossing_human_control + 
##     did_police_officer_attend_scene_of_collision + number_of_vehicles, 
##     data = data4)
## 
## Coefficients:
##   (Intercept) pedestrian_crossing_human_control1
## 1   -6.455208                         -5.8439375
## 2   -1.222027                         -0.5490931
##   pedestrian_crossing_human_control2
## 1                         -9.0554303
## 2                         -0.3823266
##   did_police_officer_attend_scene_of_collision1 number_of_vehicles
## 1                                     3.0094071         -0.3228061
## 2                                     0.8679758         -0.3777217
## 
## Std. Errors:
##   (Intercept) pedestrian_crossing_human_control1
## 1   1.0396943                         21.8278595
## 2   0.1086562                          0.3690732
##   pedestrian_crossing_human_control2
## 1                         54.3363861
## 2                          0.1773201
##   did_police_officer_attend_scene_of_collision1 number_of_vehicles
## 1                                    1.00389121         0.16804613
## 2                                    0.08571158         0.04177891
## 
## Residual Deviance: 11352.67 
## AIC: 11372.67
#8.  Method 2:
## calculate the mean probabilities within each level of severity
summary(data4$number_of_vehicles)  #continuous; 1~8
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00    1.00    2.00    1.84    2.00    8.00
dwrite11 <- data.frame(pedestrian_crossing_human_control =rep(c("0", "1", "2"), each = 6), did_police_officer_attend_scene_of_collision = rep(c("1", "2"), each = 9), number_of_vehicles = rep(c(1:9),2))    #3,9 has least common :9
view(dwrite11) 
## store the predicted probabilities into new dataset
view(predict(test1, newdata = dwrite11, type = "probs", se = TRUE))
pp.write2 <- cbind(dwrite11, predict(test1, newdata = dwrite11, type = "probs", se = TRUE))
library(fpp3)
view(pp.write2)
##View the average predicted probability for different values of severity within each level of chosen predictor.
by(pp.write2[, 4:6], pp.write2$pedestrian_crossing_human_control, colMeans)
## pp.write2$pedestrian_crossing_human_control: 0
##           3           1           2 
## 0.816935010 0.009173384 0.173891606 
## ------------------------------------------------------------ 
## pp.write2$pedestrian_crossing_human_control: 1
##            3            1            2 
## 9.514770e-01 4.668808e-06 4.851831e-02 
## ------------------------------------------------------------ 
## pp.write2$pedestrian_crossing_human_control: 2
##            3            1            2 
## 9.795224e-01 2.538917e-08 2.047756e-02
by(pp.write2[, 4:6], pp.write2$number_of_vehicles, colMeans)
## pp.write2$number_of_vehicles: 1
##           3           1           2 
## 0.780194856 0.007675034 0.212130110 
## ------------------------------------------------------------ 
## pp.write2$number_of_vehicles: 2
##           3           1           2 
## 0.834339847 0.006208432 0.159451720 
## ------------------------------------------------------------ 
## pp.write2$number_of_vehicles: 3
##           3           1           2 
## 0.877871137 0.004888937 0.117239926 
## ------------------------------------------------------------ 
## pp.write2$number_of_vehicles: 4
##           3           1           2 
## 0.908433378 0.003765988 0.087800634 
## ------------------------------------------------------------ 
## pp.write2$number_of_vehicles: 5
##           3           1           2 
## 0.934672567 0.002852379 0.062475054 
## ------------------------------------------------------------ 
## pp.write2$number_of_vehicles: 6
##           3           1           2 
## 0.953883503 0.002132838 0.043983659 
## ------------------------------------------------------------ 
## pp.write2$number_of_vehicles: 7
##            3            1            2 
## 9.789532e-01 4.695427e-06 2.104214e-02 
## ------------------------------------------------------------ 
## pp.write2$number_of_vehicles: 8
##            3            1            2 
## 9.854671e-01 3.430217e-06 1.452950e-02 
## ------------------------------------------------------------ 
## pp.write2$number_of_vehicles: 9
##            3            1            2 
## 9.899878e-01 2.499080e-06 1.000967e-02
#9. plot the Predicted Probabilities against the "number_of_vehicles" by the Level of "pedestrian_crossing_human_control" for 3 Severity levels: 1,2,3

## melt data set to long for ggplot2
library(reshape2)
library(ggplot2)
lpp2 <- melt(pp.write2, id.vars = c("pedestrian_crossing_human_control","did_police_officer_attend_scene_of_collision", "number_of_vehicles"), value.name = "probability")
view(lpp2)
tail(lpp2)
##    pedestrian_crossing_human_control
## 49                                 2
## 50                                 2
## 51                                 2
## 52                                 2
## 53                                 2
## 54                                 2
##    did_police_officer_attend_scene_of_collision number_of_vehicles variable
## 49                                            2                  4        2
## 50                                            2                  5        2
## 51                                            2                  6        2
## 52                                            2                  7        2
## 53                                            2                  8        2
## 54                                            2                  9        2
##    probability
## 49 0.042482966
## 50 0.029513148
## 51 0.020418508
## 52 0.014085755
## 53 0.009697646
## 54 0.006667312
## plot Predicted Probabilities across "number_of_vehicles" values for each level of "ped...."
## facetted by program type: prog

ggplot(lpp2, aes(x = number_of_vehicles, y = probability, colour = pedestrian_crossing_human_control)) + geom_line()+ facet_grid(variable ~
    ., scales = "free") +
  theme(legend.position = "top")  # Place legend at the top

ggplot(lpp2, aes(x = number_of_vehicles, y = probability, colour = did_police_officer_attend_scene_of_collision)) + geom_line()+ facet_grid(variable ~
    ., scales = "free") +
  theme(legend.position = "top")  # Place legend at the top

####repeat 2
test2 <- multinom(legacy_collision_severity ~  speed_limit + junction_detail + junction_control, data = data4)
## # weights:  39 (24 variable)
## initial  value 10491.747357 
## iter  10 value 6208.964317
## iter  20 value 5901.220564
## iter  30 value 5762.256659
## iter  40 value 5746.445066
## final  value 5746.444197 
## converged
summary(data4$speed_limit)  #20-70;
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   20.00   30.00   30.00   33.02   30.00   70.00
dwrite_2 <- data.frame(junction_control =rep(c(1:4), each = 20), junction_detail = rep(c(1:3,5:9), each = 10), speed_limit = rep(c(0:79),1))    #4,8,51+29 has least common :80
dwrite_2$junction_detail <- as.factor(dwrite_2$junction_detail)
dwrite_2$junction_control <- as.factor(dwrite_2$junction_control)
dwrite_2$junction_detail <- relevel(dwrite_2$junction_detail, ref = "3")
dwrite_2$junction_detail[1]  #Baseline: 3 (T or staggered junction)
## [1] 1
## Levels: 3 1 2 5 6 7 8 9
dwrite_2$junction_control <- relevel(dwrite_2$junction_control, ref = "4")

pp.write_2 <- cbind(dwrite_2, predict(test2, newdata = dwrite_2, type = "probs", se = TRUE))
lpp2 <- melt(pp.write_2, id.vars = c("junction_detail", "junction_control", "speed_limit"), value.name = "probability")
ggplot(lpp2, aes(x = speed_limit, y = probability, colour = junction_detail)) + geom_line()+ facet_grid(variable ~
    ., scales = "free") +
  theme(legend.position = "top")  # Place legend at the top

ggplot(lpp2, aes(x = speed_limit, y = probability, colour = junction_control)) + geom_line()+ facet_grid(variable ~
    ., scales = "free")+
  theme(legend.position = "top")  # Place legend at the top

####repeat 3
test3 <- multinom(legacy_collision_severity ~  police_force + light_conditions + road_surface_conditions, data = data4)
## # weights:  33 (20 variable)
## initial  value 10491.747357 
## iter  10 value 6107.121236
## iter  20 value 5767.676481
## iter  30 value 5764.231927
## iter  40 value 5764.192863
## final  value 5764.192736 
## converged
summary(data4$police_force)  #1-63
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     1.0     4.0    20.0    22.7    43.0    63.0
dwrite_3 <- data.frame(light_conditions =rep(c(1,4,5,6,7), each = 13), road_surface_conditions = rep(c(1:5), each = 13), police_force = rep(c(1:65),1))    #5,63+2 has least common :65
dwrite_3$light_conditions <- as.factor(dwrite_3$light_conditions)
dwrite_3$road_surface_conditions <- as.factor(dwrite_3$road_surface_conditions)
dwrite_3$light_conditions <- relevel(dwrite_3$light_conditions, ref = "1")
dwrite_3$road_surface_conditions <- relevel(dwrite_3$road_surface_conditions, ref = "1")

pp.write_3 <- cbind(dwrite_3, predict(test3, newdata = dwrite_3, type = "probs", se = TRUE))
lpp3 <- melt(pp.write_3, id.vars = c("light_conditions", "road_surface_conditions", "police_force"), value.name = "probability")
ggplot(lpp3, aes(x = police_force, y = probability, colour = light_conditions)) + geom_line()+ facet_grid(variable ~
    ., scales = "free") +
  theme(legend.position = "top")  # Place legend at the top

ggplot(lpp3, aes(x = police_force, y = probability, colour = road_surface_conditions)) + geom_line()+ facet_grid(variable ~
    ., scales = "free") +
  theme(legend.position = "top")  # Place legend at the top

####



#💚8 Table 2
#extracts parameter estimates and goodness-of-fit measures from the multinomial model (step_test) and generates a table with the results.
library(broom) #For tidying model output
## Warning: package 'broom' was built under R version 4.3.3
library(AER)  # For goodness-of-fit measures
## Loading required package: car
## Loading required package: carData
## 
## Attaching package: 'car'
## 
## The following object is masked from 'package:dplyr':
## 
##     recode
## 
## Loading required package: lmtest
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## 
## The following object is masked from 'package:tsibble':
## 
##     index
## 
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## 
## Loading required package: sandwich
## Loading required package: survival
#💛8_1: parameter estimates (including estimates, standard errors, p-values)

#💙8_1_1 Extract parameter estimates for 1:Fatal and 2:Serious severity, given 3: Slight is chosen baseline
library(broom) #原本❌ exponentiate = TRUE ,oddsratio=exp(estimate),求出的Table4_2不对(是exp(exp(estimate))了,model_summary里的estimate先求了指数exp(estimate)
model_summary <- tidy(step_test, exponentiate = FALSE, conf.int = TRUE, conf.level = 0.95)  
model_summary          
## # A tibble: 56 × 8
##    y.level term        estimate std.error statistic   p.value conf.low conf.high
##    <chr>   <chr>          <dbl>     <dbl>     <dbl>     <dbl>    <dbl>     <dbl>
##  1 1       (Intercept) -9.44e+0  0.00580   -1.63e+3 0          -9.45     -9.43  
##  2 1       police_for…  3.09e-4  0.00546    5.67e-2 9.55e-  1  -0.0104    0.0110
##  3 1       number_of_… -4.53e-1  0.0165    -2.75e+1 4.97e-166  -0.485    -0.421 
##  4 1       number_of_…  2.62e-1  0.0795     3.29e+0 9.98e-  4   0.106     0.418 
##  5 1       speed_limit  4.15e-2  0.00723    5.74e+0 9.73e-  9   0.0273    0.0557
##  6 1       junction_d… -9.92e-1  0.000931  -1.06e+3 0          -0.994    -0.990 
##  7 1       junction_d… -2.20e-1  0.000312  -7.06e+2 0          -0.221    -0.220 
##  8 1       junction_d… -3.02e-1  0.00180   -1.68e+2 0          -0.306    -0.299 
##  9 1       junction_d…  8.14e-2  0.00210    3.87e+1 0           0.0772    0.0855
## 10 1       junction_d…  4.83e-1  0.000628   7.70e+2 0           0.482     0.485 
## # ℹ 46 more rows
view(model_summary)
serious_summary <- model_summary[model_summary$y.level == "2", ]
serious_summary
## # A tibble: 28 × 8
##    y.level term         estimate std.error statistic  p.value conf.low conf.high
##    <chr>   <chr>           <dbl>     <dbl>     <dbl>    <dbl>    <dbl>     <dbl>
##  1 2       (Intercept)  -1.62      0.0162   -100.    0        -1.66    -1.59    
##  2 2       police_force -0.00291   0.00137    -2.13  3.36e- 2 -0.00560 -0.000227
##  3 2       number_of_v… -0.418     0.0414    -10.1   5.81e-24 -0.499   -0.337   
##  4 2       number_of_c…  0.0632    0.0357      1.77  7.64e- 2 -0.00671  0.133   
##  5 2       speed_limit   0.00851   0.00218     3.90  9.70e- 5  0.00423  0.0128  
##  6 2       junction_de… -0.352     0.0853     -4.13  3.70e- 5 -0.519   -0.185   
##  7 2       junction_de… -0.179     0.0162    -11.0   3.50e-28 -0.210   -0.147   
##  8 2       junction_de…  0.101     0.0149      6.81  1.00e-11  0.0720   0.130   
##  9 2       junction_de…  0.0379    0.0689      0.549 5.83e- 1 -0.0972   0.173   
## 10 2       junction_de… -0.348     0.0184    -18.9   8.60e-80 -0.384   -0.312   
## # ℹ 18 more rows
view(serious_summary)
fatal_summary <- model_summary[model_summary$y.level == "1", ]
fatal_summary
## # A tibble: 28 × 8
##    y.level term        estimate std.error statistic   p.value conf.low conf.high
##    <chr>   <chr>          <dbl>     <dbl>     <dbl>     <dbl>    <dbl>     <dbl>
##  1 1       (Intercept) -9.44e+0  0.00580   -1.63e+3 0          -9.45     -9.43  
##  2 1       police_for…  3.09e-4  0.00546    5.67e-2 9.55e-  1  -0.0104    0.0110
##  3 1       number_of_… -4.53e-1  0.0165    -2.75e+1 4.97e-166  -0.485    -0.421 
##  4 1       number_of_…  2.62e-1  0.0795     3.29e+0 9.98e-  4   0.106     0.418 
##  5 1       speed_limit  4.15e-2  0.00723    5.74e+0 9.73e-  9   0.0273    0.0557
##  6 1       junction_d… -9.92e-1  0.000931  -1.06e+3 0          -0.994    -0.990 
##  7 1       junction_d… -2.20e-1  0.000312  -7.06e+2 0          -0.221    -0.220 
##  8 1       junction_d… -3.02e-1  0.00180   -1.68e+2 0          -0.306    -0.299 
##  9 1       junction_d…  8.14e-2  0.00210    3.87e+1 0           0.0772    0.0855
## 10 1       junction_d…  4.83e-1  0.000628   7.70e+2 0           0.482     0.485 
## # ℹ 18 more rows
view(fatal_summary)
#💙8_1_2 Extract Odds Ratio for Fatal and Serious

fatal_summary$OR <- exp(fatal_summary$estimate)
view(fatal_summary$OR)
view(fatal_summary)
serious_summary$OR <- exp(serious_summary$estimate)
view(serious_summary$OR)
view(serious_summary)

fatal_summary_ <- fatal_summary[,c(1,2,3,9,4,6)]
view(fatal_summary_)
serious_summary_ <- serious_summary[,c(1,2,3,9,4,6)]
view(serious_summary_)
table2_ <- rbind(fatal_summary_, serious_summary_)
table2_
## # A tibble: 56 × 6
##    y.level term                  estimate        OR std.error   p.value
##    <chr>   <chr>                    <dbl>     <dbl>     <dbl>     <dbl>
##  1 1       (Intercept)          -9.44     0.0000793  0.00580  0        
##  2 1       police_force          0.000309 1.00       0.00546  9.55e-  1
##  3 1       number_of_vehicles   -0.453    0.636      0.0165   4.97e-166
##  4 1       number_of_casualties  0.262    1.30       0.0795   9.98e-  4
##  5 1       speed_limit           0.0415   1.04       0.00723  9.73e-  9
##  6 1       junction_detail1     -0.992    0.371      0.000931 0        
##  7 1       junction_detail2     -0.220    0.802      0.000312 0        
##  8 1       junction_detail5     -0.302    0.739      0.00180  0        
##  9 1       junction_detail6      0.0814   1.08       0.00210  0        
## 10 1       junction_detail7      0.483    1.62       0.000628 0        
## # ℹ 46 more rows
view(table2_)
#P.S. table2_$estimate is exactly the estimate in step_test. Verify:
a <- cbind( t(exp(coef(step_test))[1,]), t(exp(coef(step_test))[2,]) )
dim(a)
## [1]  1 56
t(a)  #transform of matrix 
##                                                       [,1]
## (Intercept)                                   7.930992e-05
## police_force                                  1.000309e+00
## number_of_vehicles                            6.357345e-01
## number_of_casualties                          1.299246e+00
## speed_limit                                   1.042356e+00
## junction_detail1                              3.709446e-01
## junction_detail2                              8.024259e-01
## junction_detail5                              7.392797e-01
## junction_detail6                              1.084760e+00
## junction_detail7                              1.621419e+00
## junction_detail8                              8.618460e-01
## junction_detail9                              1.377690e+00
## junction_control1                             2.258424e-05
## junction_control2                             7.463475e-01
## junction_control3                             3.753030e-05
## second_road_class                             1.272770e+00
## second_road_number                            1.000079e+00
## pedestrian_crossing_human_control1            2.605436e-11
## pedestrian_crossing_human_control2            8.260471e-05
## light_conditions4                             3.260246e+00
## light_conditions5                             5.547670e+00
## light_conditions6                             9.072156e-01
## light_conditions7                             3.040592e+00
## road_surface_conditions2                      8.552544e-01
## road_surface_conditions3                      2.548662e-11
## road_surface_conditions4                      4.198582e-01
## road_surface_conditions5                      5.533131e+00
## did_police_officer_attend_scene_of_collision1 1.618016e+01
## (Intercept)                                   1.971228e-01
## police_force                                  9.970902e-01
## number_of_vehicles                            6.584726e-01
## number_of_casualties                          1.065285e+00
## speed_limit                                   1.008550e+00
## junction_detail1                              7.033283e-01
## junction_detail2                              8.364312e-01
## junction_detail5                              1.106468e+00
## junction_detail6                              1.038589e+00
## junction_detail7                              7.063827e-01
## junction_detail8                              9.215183e-01
## junction_detail9                              8.020330e-01
## junction_control1                             5.742895e-01
## junction_control2                             7.804208e-01
## junction_control3                             1.023984e+00
## second_road_class                             1.056959e+00
## second_road_number                            1.000054e+00
## pedestrian_crossing_human_control1            5.888017e-01
## pedestrian_crossing_human_control2            7.836153e-01
## light_conditions4                             1.181669e+00
## light_conditions5                             1.995324e+00
## light_conditions6                             9.673430e-01
## light_conditions7                             6.160782e-01
## road_surface_conditions2                      8.005855e-01
## road_surface_conditions3                      4.894209e-01
## road_surface_conditions4                      6.361126e-01
## road_surface_conditions5                      3.686452e-11
## did_police_officer_attend_scene_of_collision1 2.356606e+00
t(a) == table2_$estimate
##                                                [,1]
## (Intercept)                                   FALSE
## police_force                                  FALSE
## number_of_vehicles                            FALSE
## number_of_casualties                          FALSE
## speed_limit                                   FALSE
## junction_detail1                              FALSE
## junction_detail2                              FALSE
## junction_detail5                              FALSE
## junction_detail6                              FALSE
## junction_detail7                              FALSE
## junction_detail8                              FALSE
## junction_detail9                              FALSE
## junction_control1                             FALSE
## junction_control2                             FALSE
## junction_control3                             FALSE
## second_road_class                             FALSE
## second_road_number                            FALSE
## pedestrian_crossing_human_control1            FALSE
## pedestrian_crossing_human_control2            FALSE
## light_conditions4                             FALSE
## light_conditions5                             FALSE
## light_conditions6                             FALSE
## light_conditions7                             FALSE
## road_surface_conditions2                      FALSE
## road_surface_conditions3                      FALSE
## road_surface_conditions4                      FALSE
## road_surface_conditions5                      FALSE
## did_police_officer_attend_scene_of_collision1 FALSE
## (Intercept)                                   FALSE
## police_force                                  FALSE
## number_of_vehicles                            FALSE
## number_of_casualties                          FALSE
## speed_limit                                   FALSE
## junction_detail1                              FALSE
## junction_detail2                              FALSE
## junction_detail5                              FALSE
## junction_detail6                              FALSE
## junction_detail7                              FALSE
## junction_detail8                              FALSE
## junction_detail9                              FALSE
## junction_control1                             FALSE
## junction_control2                             FALSE
## junction_control3                             FALSE
## second_road_class                             FALSE
## second_road_number                            FALSE
## pedestrian_crossing_human_control1            FALSE
## pedestrian_crossing_human_control2            FALSE
## light_conditions4                             FALSE
## light_conditions5                             FALSE
## light_conditions6                             FALSE
## light_conditions7                             FALSE
## road_surface_conditions2                      FALSE
## road_surface_conditions3                      FALSE
## road_surface_conditions4                      FALSE
## road_surface_conditions5                      FALSE
## did_police_officer_attend_scene_of_collision1 FALSE
#💛8_2: Extract goodness-of-fit measures
library(AER)  
#💙8_2_1 Log likelihood Null&Full model

#Log likelihood Null model
null_model <- update(step_test, .~1)  # Null model
## # weights:  6 (2 variable)
## initial  value 10491.747357 
## iter  10 value 5793.892932
## final  value 5793.892874 
## converged
logLik_null <- logLik(null_model)
logLik_null
## 'log Lik.' -5793.893 (df=2)
#Log likelihood Full model
logLik_full <- logLik(step_test)      # Full model
logLik_full
## 'log Lik.' -5587.504 (df=56)
#💙8_2_2 McFadden's R2
R2McFadden <- 1 - as.numeric(logLik_full / logLik_null)
R2McFadden
## [1] 0.0356218
#💙8_2_3 AIC and BIC
AIC_value <- AIC(step_test)
BIC_value <- BIC(step_test)
AIC_value
## [1] 11287.01
BIC_value
## [1] 11688.21
table2_$Loglikelihood_null_model <- logLik_null
table2_$Loglikelihood_full_model <- logLik_full
table2_$R2McFadden <- R2McFadden
table2_$AIC_value  <- AIC_value
table2_$BIC_value   <- BIC_value
table2 <- table2_
view(table2)
table2
## # A tibble: 56 × 11
##    y.level term      estimate      OR std.error   p.value Loglikelihood_null_m…¹
##    <chr>   <chr>        <dbl>   <dbl>     <dbl>     <dbl> <logLik>              
##  1 1       (Interce… -9.44e+0 7.93e-5  0.00580  0         -5793.893             
##  2 1       police_f…  3.09e-4 1.00e+0  0.00546  9.55e-  1 -5793.893             
##  3 1       number_o… -4.53e-1 6.36e-1  0.0165   4.97e-166 -5793.893             
##  4 1       number_o…  2.62e-1 1.30e+0  0.0795   9.98e-  4 -5793.893             
##  5 1       speed_li…  4.15e-2 1.04e+0  0.00723  9.73e-  9 -5793.893             
##  6 1       junction… -9.92e-1 3.71e-1  0.000931 0         -5793.893             
##  7 1       junction… -2.20e-1 8.02e-1  0.000312 0         -5793.893             
##  8 1       junction… -3.02e-1 7.39e-1  0.00180  0         -5793.893             
##  9 1       junction…  8.14e-2 1.08e+0  0.00210  0         -5793.893             
## 10 1       junction…  4.83e-1 1.62e+0  0.000628 0         -5793.893             
## # ℹ 46 more rows
## # ℹ abbreviated name: ¹​Loglikelihood_null_model
## # ℹ 4 more variables: Loglikelihood_full_model <logLik>, R2McFadden <dbl>,
## #   AIC_value <dbl>, BIC_value <dbl>
str(table2)
## tibble [56 × 11] (S3: tbl_df/tbl/data.frame)
##  $ y.level                 : chr [1:56] "1" "1" "1" "1" ...
##  $ term                    : chr [1:56] "(Intercept)" "police_force" "number_of_vehicles" "number_of_casualties" ...
##  $ estimate                : num [1:56] -9.442147 0.000309 -0.452974 0.261784 0.041484 ...
##  $ OR                      : num [1:56] 7.93e-05 1.00 6.36e-01 1.30 1.04 ...
##  $ std.error               : num [1:56] 0.0058 0.00546 0.01649 0.07954 0.00723 ...
##  $ p.value                 : num [1:56] 0.00 9.55e-01 4.97e-166 9.98e-04 9.73e-09 ...
##  $ Loglikelihood_null_model:Class 'logLik' : -5794, -5794, -5794, -5794, ... (df=2)
##  $ Loglikelihood_full_model:Class 'logLik' : -5588, -5588, -5588, -5588, ... (df=56)
##  $ R2McFadden              : num [1:56] 0.0356 0.0356 0.0356 0.0356 0.0356 ...
##  $ AIC_value               : num [1:56] 11287 11287 11287 11287 11287 ...
##  $ BIC_value               : num [1:56] 11688 11688 11688 11688 11688 ...
#This is Table 2 in article https://www.mdpi.com/2071-1050/14/6/3188 
#Another display method of Table 2 is below:
# Organize the parameter estimates
results <- data.frame(
  Variable = c(fatal_summary$term, serious_summary$term),
  Estimate_Fatal = c(fatal_summary$estimate),
  OR_Fatal = c(exp(fatal_summary$estimate)),  # Odds Ratio for Fatal
  Std_Err_Fatal = c(fatal_summary$std.error),
  P_value_Fatal = c(fatal_summary$p.value),
  Estimate_Serious = c(serious_summary$estimate),
  OR_Serious = c(exp(serious_summary$estimate)),  # Odds Ratio for Serious
  Std_Err_Serious = c(serious_summary$std.error),
  P_value_Serious = c(serious_summary$p.value)
)

# Organize the goodness-of-fit results
goodness_of_fit <- data.frame(
  Metric = c("Log likelihood null model", "Log likelihood full model", "R2McFadden", "AIC", "BIC"),
  Value = c(as.numeric(logLik_null), as.numeric(logLik_full), R2McFadden, AIC_value, BIC_value)
)

# Print the tables : Table4_2
print(results)
##                                         Variable Estimate_Fatal     OR_Fatal
## 1                                    (Intercept)  -9.442147e+00 7.930992e-05
## 2                                   police_force   3.092832e-04 1.000309e+00
## 3                             number_of_vehicles  -4.529742e-01 6.357345e-01
## 4                           number_of_casualties   2.617842e-01 1.299246e+00
## 5                                    speed_limit   4.148386e-02 1.042356e+00
## 6                               junction_detail1  -9.917024e-01 3.709446e-01
## 7                               junction_detail2  -2.201158e-01 8.024259e-01
## 8                               junction_detail5  -3.020790e-01 7.392797e-01
## 9                               junction_detail6   8.135917e-02 1.084760e+00
## 10                              junction_detail7   4.833014e-01 1.621419e+00
## 11                              junction_detail8  -1.486787e-01 8.618460e-01
## 12                              junction_detail9   3.204084e-01 1.377690e+00
## 13                             junction_control1  -1.069826e+01 2.258424e-05
## 14                             junction_control2  -2.925639e-01 7.463475e-01
## 15                             junction_control3  -1.019036e+01 3.753030e-05
## 16                             second_road_class   2.411958e-01 1.272770e+00
## 17                            second_road_number   7.942130e-05 1.000079e+00
## 18            pedestrian_crossing_human_control1  -2.437084e+01 2.605436e-11
## 19            pedestrian_crossing_human_control2  -9.401444e+00 8.260471e-05
## 20                             light_conditions4   1.181803e+00 3.260246e+00
## 21                             light_conditions5   1.713378e+00 5.547670e+00
## 22                             light_conditions6  -9.737516e-02 9.072156e-01
## 23                             light_conditions7   1.112052e+00 3.040592e+00
## 24                      road_surface_conditions2  -1.563564e-01 8.552544e-01
## 25                      road_surface_conditions3  -2.439287e+01 2.548662e-11
## 26                      road_surface_conditions4  -8.678382e-01 4.198582e-01
## 27                      road_surface_conditions5   1.710754e+00 5.533131e+00
## 28 did_police_officer_attend_scene_of_collision1   2.783786e+00 1.618016e+01
## 29                                   (Intercept)  -9.442147e+00 7.930992e-05
## 30                                  police_force   3.092832e-04 1.000309e+00
## 31                            number_of_vehicles  -4.529742e-01 6.357345e-01
## 32                          number_of_casualties   2.617842e-01 1.299246e+00
## 33                                   speed_limit   4.148386e-02 1.042356e+00
## 34                              junction_detail1  -9.917024e-01 3.709446e-01
## 35                              junction_detail2  -2.201158e-01 8.024259e-01
## 36                              junction_detail5  -3.020790e-01 7.392797e-01
## 37                              junction_detail6   8.135917e-02 1.084760e+00
## 38                              junction_detail7   4.833014e-01 1.621419e+00
## 39                              junction_detail8  -1.486787e-01 8.618460e-01
## 40                              junction_detail9   3.204084e-01 1.377690e+00
## 41                             junction_control1  -1.069826e+01 2.258424e-05
## 42                             junction_control2  -2.925639e-01 7.463475e-01
## 43                             junction_control3  -1.019036e+01 3.753030e-05
## 44                             second_road_class   2.411958e-01 1.272770e+00
## 45                            second_road_number   7.942130e-05 1.000079e+00
## 46            pedestrian_crossing_human_control1  -2.437084e+01 2.605436e-11
## 47            pedestrian_crossing_human_control2  -9.401444e+00 8.260471e-05
## 48                             light_conditions4   1.181803e+00 3.260246e+00
## 49                             light_conditions5   1.713378e+00 5.547670e+00
## 50                             light_conditions6  -9.737516e-02 9.072156e-01
## 51                             light_conditions7   1.112052e+00 3.040592e+00
## 52                      road_surface_conditions2  -1.563564e-01 8.552544e-01
## 53                      road_surface_conditions3  -2.439287e+01 2.548662e-11
## 54                      road_surface_conditions4  -8.678382e-01 4.198582e-01
## 55                      road_surface_conditions5   1.710754e+00 5.533131e+00
## 56 did_police_officer_attend_scene_of_collision1   2.783786e+00 1.618016e+01
##    Std_Err_Fatal P_value_Fatal Estimate_Serious   OR_Serious Std_Err_Serious
## 1   5.796409e-03  0.000000e+00    -1.623928e+00 1.971228e-01    1.624718e-02
## 2   5.457743e-03  9.548091e-01    -2.914036e-03 9.970902e-01    1.371113e-03
## 3   1.649447e-02 4.969198e-166    -4.178323e-01 6.584726e-01    4.138959e-02
## 4   7.954138e-02  9.977160e-04     6.324246e-02 1.065285e+00    3.568908e-02
## 5   7.232952e-03  9.728323e-09     8.513860e-03 1.008550e+00    2.184144e-03
## 6   9.313294e-04  0.000000e+00    -3.519316e-01 7.033283e-01    8.530451e-02
## 7   3.116260e-04  0.000000e+00    -1.786110e-01 8.364312e-01    1.622552e-02
## 8   1.798214e-03  0.000000e+00     1.011727e-01 1.106468e+00    1.486543e-02
## 9   2.103350e-03  0.000000e+00     3.786262e-02 1.038589e+00    6.890990e-02
## 10  6.280668e-04  0.000000e+00    -3.475981e-01 7.063827e-01    1.837697e-02
## 11  2.231360e-03  0.000000e+00    -8.173265e-02 9.215183e-01    1.248507e-01
## 12  2.584508e-03  0.000000e+00    -2.206055e-01 8.020330e-01    8.061984e-02
## 13  4.087865e-09  0.000000e+00    -5.546216e-01 5.742895e-01    1.364578e-03
## 14  2.216504e-03  0.000000e+00    -2.479221e-01 7.804208e-01    6.956185e-02
## 15  6.091331e-09  0.000000e+00     2.370078e-02 1.023984e+00    3.105755e-03
## 16  4.242003e-02  1.301297e-08     5.539577e-02 1.056959e+00    1.702285e-02
## 17  9.052596e-05  3.803064e-01     5.433642e-05 1.000054e+00    2.148846e-05
## 18  2.466634e-15  0.000000e+00    -5.296658e-01 5.888017e-01    6.175203e-04
## 19  2.989700e-08  0.000000e+00    -2.438371e-01 7.836153e-01    4.240239e-03
## 20  5.313224e-03  0.000000e+00     1.669279e-01 1.181669e+00    5.877844e-02
## 21  2.342870e-04  0.000000e+00     6.908065e-01 1.995324e+00    1.619227e-03
## 22  7.741689e-04  0.000000e+00    -3.320217e-02 9.673430e-01    7.532004e-03
## 23  5.836393e-04  0.000000e+00    -4.843814e-01 6.160782e-01    1.078187e-03
## 24  2.512534e-03  0.000000e+00    -2.224119e-01 8.005855e-01    6.168480e-02
## 25  1.750303e-15  0.000000e+00    -7.145325e-01 4.894209e-01    3.065412e-04
## 26  1.735918e-04  0.000000e+00    -4.523797e-01 6.361126e-01    1.880748e-03
## 27  1.191014e-04  0.000000e+00    -2.402377e+01 3.686452e-11    1.058180e-14
## 28  5.684965e-03  0.000000e+00     8.572225e-01 2.356606e+00    7.890765e-02
## 29  5.796409e-03  0.000000e+00    -1.623928e+00 1.971228e-01    1.624718e-02
## 30  5.457743e-03  9.548091e-01    -2.914036e-03 9.970902e-01    1.371113e-03
## 31  1.649447e-02 4.969198e-166    -4.178323e-01 6.584726e-01    4.138959e-02
## 32  7.954138e-02  9.977160e-04     6.324246e-02 1.065285e+00    3.568908e-02
## 33  7.232952e-03  9.728323e-09     8.513860e-03 1.008550e+00    2.184144e-03
## 34  9.313294e-04  0.000000e+00    -3.519316e-01 7.033283e-01    8.530451e-02
## 35  3.116260e-04  0.000000e+00    -1.786110e-01 8.364312e-01    1.622552e-02
## 36  1.798214e-03  0.000000e+00     1.011727e-01 1.106468e+00    1.486543e-02
## 37  2.103350e-03  0.000000e+00     3.786262e-02 1.038589e+00    6.890990e-02
## 38  6.280668e-04  0.000000e+00    -3.475981e-01 7.063827e-01    1.837697e-02
## 39  2.231360e-03  0.000000e+00    -8.173265e-02 9.215183e-01    1.248507e-01
## 40  2.584508e-03  0.000000e+00    -2.206055e-01 8.020330e-01    8.061984e-02
## 41  4.087865e-09  0.000000e+00    -5.546216e-01 5.742895e-01    1.364578e-03
## 42  2.216504e-03  0.000000e+00    -2.479221e-01 7.804208e-01    6.956185e-02
## 43  6.091331e-09  0.000000e+00     2.370078e-02 1.023984e+00    3.105755e-03
## 44  4.242003e-02  1.301297e-08     5.539577e-02 1.056959e+00    1.702285e-02
## 45  9.052596e-05  3.803064e-01     5.433642e-05 1.000054e+00    2.148846e-05
## 46  2.466634e-15  0.000000e+00    -5.296658e-01 5.888017e-01    6.175203e-04
## 47  2.989700e-08  0.000000e+00    -2.438371e-01 7.836153e-01    4.240239e-03
## 48  5.313224e-03  0.000000e+00     1.669279e-01 1.181669e+00    5.877844e-02
## 49  2.342870e-04  0.000000e+00     6.908065e-01 1.995324e+00    1.619227e-03
## 50  7.741689e-04  0.000000e+00    -3.320217e-02 9.673430e-01    7.532004e-03
## 51  5.836393e-04  0.000000e+00    -4.843814e-01 6.160782e-01    1.078187e-03
## 52  2.512534e-03  0.000000e+00    -2.224119e-01 8.005855e-01    6.168480e-02
## 53  1.750303e-15  0.000000e+00    -7.145325e-01 4.894209e-01    3.065412e-04
## 54  1.735918e-04  0.000000e+00    -4.523797e-01 6.361126e-01    1.880748e-03
## 55  1.191014e-04  0.000000e+00    -2.402377e+01 3.686452e-11    1.058180e-14
## 56  5.684965e-03  0.000000e+00     8.572225e-01 2.356606e+00    7.890765e-02
##    P_value_Serious
## 1     0.000000e+00
## 2     3.356098e-02
## 3     5.806754e-24
## 4     7.638806e-02
## 5     9.697851e-05
## 6     3.697834e-05
## 7     3.495680e-28
## 8     1.004133e-11
## 9     5.826959e-01
## 10    8.601815e-80
## 11    5.126975e-01
## 12    6.212155e-03
## 13    0.000000e+00
## 14    3.651735e-04
## 15    2.324996e-14
## 16    1.137120e-03
## 17    1.145077e-02
## 18    0.000000e+00
## 19    0.000000e+00
## 20    4.512044e-03
## 21    0.000000e+00
## 22    1.042593e-05
## 23    0.000000e+00
## 24    3.114099e-04
## 25    0.000000e+00
## 26    0.000000e+00
## 27    0.000000e+00
## 28    1.718080e-27
## 29    0.000000e+00
## 30    3.356098e-02
## 31    5.806754e-24
## 32    7.638806e-02
## 33    9.697851e-05
## 34    3.697834e-05
## 35    3.495680e-28
## 36    1.004133e-11
## 37    5.826959e-01
## 38    8.601815e-80
## 39    5.126975e-01
## 40    6.212155e-03
## 41    0.000000e+00
## 42    3.651735e-04
## 43    2.324996e-14
## 44    1.137120e-03
## 45    1.145077e-02
## 46    0.000000e+00
## 47    0.000000e+00
## 48    4.512044e-03
## 49    0.000000e+00
## 50    1.042593e-05
## 51    0.000000e+00
## 52    3.114099e-04
## 53    0.000000e+00
## 54    0.000000e+00
## 55    0.000000e+00
## 56    1.718080e-27
print(goodness_of_fit)
##                      Metric         Value
## 1 Log likelihood null model -5793.8928741
## 2 Log likelihood full model -5587.5040085
## 3                R2McFadden     0.0356218
## 4                       AIC 11287.0080170
## 5                       BIC 11688.2086173
Table4_2 <- results
#Apply rounding from the second column onward, skipping the first column (variable names)
Table4_2[, 2:ncol(Table4_2)] <- round(Table4_2[, 2:ncol(Table4_2)], 3)
Table4_2
##                                         Variable Estimate_Fatal OR_Fatal
## 1                                    (Intercept)         -9.442    0.000
## 2                                   police_force          0.000    1.000
## 3                             number_of_vehicles         -0.453    0.636
## 4                           number_of_casualties          0.262    1.299
## 5                                    speed_limit          0.041    1.042
## 6                               junction_detail1         -0.992    0.371
## 7                               junction_detail2         -0.220    0.802
## 8                               junction_detail5         -0.302    0.739
## 9                               junction_detail6          0.081    1.085
## 10                              junction_detail7          0.483    1.621
## 11                              junction_detail8         -0.149    0.862
## 12                              junction_detail9          0.320    1.378
## 13                             junction_control1        -10.698    0.000
## 14                             junction_control2         -0.293    0.746
## 15                             junction_control3        -10.190    0.000
## 16                             second_road_class          0.241    1.273
## 17                            second_road_number          0.000    1.000
## 18            pedestrian_crossing_human_control1        -24.371    0.000
## 19            pedestrian_crossing_human_control2         -9.401    0.000
## 20                             light_conditions4          1.182    3.260
## 21                             light_conditions5          1.713    5.548
## 22                             light_conditions6         -0.097    0.907
## 23                             light_conditions7          1.112    3.041
## 24                      road_surface_conditions2         -0.156    0.855
## 25                      road_surface_conditions3        -24.393    0.000
## 26                      road_surface_conditions4         -0.868    0.420
## 27                      road_surface_conditions5          1.711    5.533
## 28 did_police_officer_attend_scene_of_collision1          2.784   16.180
## 29                                   (Intercept)         -9.442    0.000
## 30                                  police_force          0.000    1.000
## 31                            number_of_vehicles         -0.453    0.636
## 32                          number_of_casualties          0.262    1.299
## 33                                   speed_limit          0.041    1.042
## 34                              junction_detail1         -0.992    0.371
## 35                              junction_detail2         -0.220    0.802
## 36                              junction_detail5         -0.302    0.739
## 37                              junction_detail6          0.081    1.085
## 38                              junction_detail7          0.483    1.621
## 39                              junction_detail8         -0.149    0.862
## 40                              junction_detail9          0.320    1.378
## 41                             junction_control1        -10.698    0.000
## 42                             junction_control2         -0.293    0.746
## 43                             junction_control3        -10.190    0.000
## 44                             second_road_class          0.241    1.273
## 45                            second_road_number          0.000    1.000
## 46            pedestrian_crossing_human_control1        -24.371    0.000
## 47            pedestrian_crossing_human_control2         -9.401    0.000
## 48                             light_conditions4          1.182    3.260
## 49                             light_conditions5          1.713    5.548
## 50                             light_conditions6         -0.097    0.907
## 51                             light_conditions7          1.112    3.041
## 52                      road_surface_conditions2         -0.156    0.855
## 53                      road_surface_conditions3        -24.393    0.000
## 54                      road_surface_conditions4         -0.868    0.420
## 55                      road_surface_conditions5          1.711    5.533
## 56 did_police_officer_attend_scene_of_collision1          2.784   16.180
##    Std_Err_Fatal P_value_Fatal Estimate_Serious OR_Serious Std_Err_Serious
## 1          0.006         0.000           -1.624      0.197           0.016
## 2          0.005         0.955           -0.003      0.997           0.001
## 3          0.016         0.000           -0.418      0.658           0.041
## 4          0.080         0.001            0.063      1.065           0.036
## 5          0.007         0.000            0.009      1.009           0.002
## 6          0.001         0.000           -0.352      0.703           0.085
## 7          0.000         0.000           -0.179      0.836           0.016
## 8          0.002         0.000            0.101      1.106           0.015
## 9          0.002         0.000            0.038      1.039           0.069
## 10         0.001         0.000           -0.348      0.706           0.018
## 11         0.002         0.000           -0.082      0.922           0.125
## 12         0.003         0.000           -0.221      0.802           0.081
## 13         0.000         0.000           -0.555      0.574           0.001
## 14         0.002         0.000           -0.248      0.780           0.070
## 15         0.000         0.000            0.024      1.024           0.003
## 16         0.042         0.000            0.055      1.057           0.017
## 17         0.000         0.380            0.000      1.000           0.000
## 18         0.000         0.000           -0.530      0.589           0.001
## 19         0.000         0.000           -0.244      0.784           0.004
## 20         0.005         0.000            0.167      1.182           0.059
## 21         0.000         0.000            0.691      1.995           0.002
## 22         0.001         0.000           -0.033      0.967           0.008
## 23         0.001         0.000           -0.484      0.616           0.001
## 24         0.003         0.000           -0.222      0.801           0.062
## 25         0.000         0.000           -0.715      0.489           0.000
## 26         0.000         0.000           -0.452      0.636           0.002
## 27         0.000         0.000          -24.024      0.000           0.000
## 28         0.006         0.000            0.857      2.357           0.079
## 29         0.006         0.000           -1.624      0.197           0.016
## 30         0.005         0.955           -0.003      0.997           0.001
## 31         0.016         0.000           -0.418      0.658           0.041
## 32         0.080         0.001            0.063      1.065           0.036
## 33         0.007         0.000            0.009      1.009           0.002
## 34         0.001         0.000           -0.352      0.703           0.085
## 35         0.000         0.000           -0.179      0.836           0.016
## 36         0.002         0.000            0.101      1.106           0.015
## 37         0.002         0.000            0.038      1.039           0.069
## 38         0.001         0.000           -0.348      0.706           0.018
## 39         0.002         0.000           -0.082      0.922           0.125
## 40         0.003         0.000           -0.221      0.802           0.081
## 41         0.000         0.000           -0.555      0.574           0.001
## 42         0.002         0.000           -0.248      0.780           0.070
## 43         0.000         0.000            0.024      1.024           0.003
## 44         0.042         0.000            0.055      1.057           0.017
## 45         0.000         0.380            0.000      1.000           0.000
## 46         0.000         0.000           -0.530      0.589           0.001
## 47         0.000         0.000           -0.244      0.784           0.004
## 48         0.005         0.000            0.167      1.182           0.059
## 49         0.000         0.000            0.691      1.995           0.002
## 50         0.001         0.000           -0.033      0.967           0.008
## 51         0.001         0.000           -0.484      0.616           0.001
## 52         0.003         0.000           -0.222      0.801           0.062
## 53         0.000         0.000           -0.715      0.489           0.000
## 54         0.000         0.000           -0.452      0.636           0.002
## 55         0.000         0.000          -24.024      0.000           0.000
## 56         0.006         0.000            0.857      2.357           0.079
##    P_value_Serious
## 1            0.000
## 2            0.034
## 3            0.000
## 4            0.076
## 5            0.000
## 6            0.000
## 7            0.000
## 8            0.000
## 9            0.583
## 10           0.000
## 11           0.513
## 12           0.006
## 13           0.000
## 14           0.000
## 15           0.000
## 16           0.001
## 17           0.011
## 18           0.000
## 19           0.000
## 20           0.005
## 21           0.000
## 22           0.000
## 23           0.000
## 24           0.000
## 25           0.000
## 26           0.000
## 27           0.000
## 28           0.000
## 29           0.000
## 30           0.034
## 31           0.000
## 32           0.076
## 33           0.000
## 34           0.000
## 35           0.000
## 36           0.000
## 37           0.583
## 38           0.000
## 39           0.513
## 40           0.006
## 41           0.000
## 42           0.000
## 43           0.000
## 44           0.001
## 45           0.011
## 46           0.000
## 47           0.000
## 48           0.005
## 49           0.000
## 50           0.000
## 51           0.000
## 52           0.000
## 53           0.000
## 54           0.000
## 55           0.000
## 56           0.000
view(Table4_2)

#💚9 elasticities 弹性are used to measure the impact of variables on outcome probabilities as interpreting coefficients in MNL is challenging

####🌰2 Modeling of Ordered Logit Regression:

####Ordered logit/probit model: multivariate; ordered

If the outcome variable is categorical, but ordinal in a standard order(ascending/descending), use an ordered logit / ordered probit model

The default logistic case is Proportional Odds logistic regression.
where y is Ordered Factor Response, x is continuous numeric/categorical factor

If we think that severity 1, 2,3 has no order, and pick 3:Slight a Baseline, we get 🌰1 above; Instead, if we think that response is Severity with 3 levels: 1,2,3 (from high to low) and in a natural (descending) order, hence we can use this model

#level = c(“1”, “2”, “3”))

#💚0 load
library(MASS)
library(stargazer)
library(erer)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
library(fpp3)

#💚1 Log-Odds Ratio of Ordered logit models   
str(data4)   #11 facotors, 1 ordered factor, 9 numeric
## 'data.frame':    9550 obs. of  21 variables:
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : Factor w/ 3 levels "3","1","2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ number_of_vehicles                          : int  1 2 2 2 2 1 2 1 2 2 ...
##  $ number_of_casualties                        : int  1 1 1 1 3 1 1 1 1 1 ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 2 2 2 ...
##  $ first_road_class                            : int  5 3 3 3 6 3 4 3 3 3 ...
##  $ first_road_number                           : int  0 437 3220 3 0 503 167 501 114 41 ...
##  $ road_type                                   : Factor w/ 5 levels "1","2","3","6",..: 2 1 4 4 1 3 2 2 4 4 ...
##  $ speed_limit                                 : int  20 30 30 20 20 30 30 20 30 20 ...
##  $ junction_detail                             : Factor w/ 8 levels "3","1","2","5",..: 8 2 7 5 2 5 1 5 8 1 ...
##  $ junction_control                            : Factor w/ 4 levels "4","1","2","3": 1 1 1 3 1 3 1 3 1 1 ...
##  $ second_road_class                           : int  5 6 6 3 6 3 6 3 6 6 ...
##  $ second_road_number                          : int  0 0 0 3202 0 105 0 501 0 0 ...
##  $ pedestrian_crossing_human_control           : Factor w/ 3 levels "0","1","2": 3 1 1 1 1 1 1 1 1 1 ...
##  $ pedestrian_crossing_physical_facilities     : Factor w/ 6 levels "0","1","4","5",..: 4 1 1 1 1 4 1 3 1 1 ...
##  $ light_conditions                            : Factor w/ 5 levels "1","4","5","6",..: 2 2 2 2 2 2 4 2 2 1 ...
##  $ weather_conditions                          : Factor w/ 8 levels "1","2","3","4",..: 8 1 1 1 2 2 1 8 1 1 ...
##  $ road_surface_conditions                     : Factor w/ 5 levels "1","2","3","4",..: 2 1 1 2 2 2 1 2 1 1 ...
##  $ special_conditions_at_site                  : Factor w/ 8 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ carriageway_hazards                         : Factor w/ 6 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ did_police_officer_attend_scene_of_collision: Factor w/ 2 levels "2","1": 2 2 2 2 2 2 2 2 2 2 ...
is.factor(data4$legacy_collision_severity)
## [1] TRUE
unique(data4$legacy_collision_severity)   #3,1,2
## [1] 3 2 1
## Levels: 3 1 2
#💛1_1. Run a Ordered logit full model       💜7
#21 predictors

library(MASS)
data4$legacy_collision_severity <- ordered(data4$legacy_collision_severity, level = c("1", "2", "3"))
unique(data4$legacy_collision_severity)
## [1] 3 2 1
## Levels: 1 < 2 < 3
full_test2 <- polr(legacy_collision_severity ~ ., data = data4, Hess = TRUE)  
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
summary(full_test2) 
## Call:
## polr(formula = legacy_collision_severity ~ ., data = data4, Hess = TRUE)
## 
## Coefficients:
##                                                    Value Std. Error    t value
## police_force                                   3.231e-03  1.374e-03  2.352e+00
## number_of_vehicles                             4.265e-01  4.155e-02  1.026e+01
## number_of_casualties                          -8.423e-02  3.422e-02 -2.461e+00
## day_of_week                                   -1.037e-02  1.223e-02 -8.480e-01
## first_road_class                               4.844e-03  1.934e-02  2.505e-01
## first_road_number                             -2.126e-05  2.073e-05 -1.026e+00
## road_type2                                     2.486e-01  5.642e-02  4.406e+00
## road_type3                                     5.334e-02  8.558e-02  6.233e-01
## road_type6                                    -2.105e-02  6.547e-02 -3.216e-01
## road_type7                                    -1.120e-01  2.937e-02 -3.813e+00
## speed_limit                                   -1.028e-02  2.209e-03 -4.652e+00
## junction_detail1                               3.643e-01  8.595e-02  4.239e+00
## junction_detail2                               1.713e-01  3.047e-02  5.620e+00
## junction_detail5                              -9.276e-02  2.405e-02 -3.857e+00
## junction_detail6                              -4.699e-02  6.814e-02 -6.896e-01
## junction_detail7                               2.827e-01  1.770e-02  1.597e+01
## junction_detail8                               9.585e-02  1.215e-01  7.886e-01
## junction_detail9                               1.726e-01  7.906e-02  2.183e+00
## junction_control1                              6.181e-01  3.352e-03  1.844e+02
## junction_control2                              2.911e-01  7.855e-02  3.706e+00
## junction_control3                              5.519e-02  5.146e-03  1.073e+01
## second_road_class                             -6.095e-02  2.317e-02 -2.630e+00
## second_road_number                            -4.870e-05  2.875e-05 -1.694e+00
## pedestrian_crossing_human_control1             5.624e-01  2.322e-03  2.422e+02
## pedestrian_crossing_human_control2             2.864e-01  1.209e-02  2.369e+01
## pedestrian_crossing_physical_facilities1       2.318e-01  1.085e-01  2.136e+00
## pedestrian_crossing_physical_facilities4      -4.873e-02  8.582e-02 -5.678e-01
## pedestrian_crossing_physical_facilities5      -7.346e-02  8.316e-02 -8.833e-01
## pedestrian_crossing_physical_facilities7      -1.573e-03  1.449e-03 -1.086e+00
## pedestrian_crossing_physical_facilities8      -1.405e-01  8.586e-02 -1.637e+00
## light_conditions4                             -2.301e-01  5.796e-02 -3.970e+00
## light_conditions5                             -7.831e-01  1.628e-03 -4.810e+02
## light_conditions6                              5.327e-02  1.442e-02  3.693e+00
## light_conditions7                              3.422e-01  1.814e-03  1.886e+02
## weather_conditions2                            9.196e-02  9.978e-02  9.216e-01
## weather_conditions3                           -6.675e-02  3.220e-03 -2.073e+01
## weather_conditions4                           -1.123e-01  4.874e-03 -2.305e+01
## weather_conditions5                           -1.247e-01  1.024e-02 -1.217e+01
## weather_conditions6                            2.305e-01  4.508e-04  5.112e+02
## weather_conditions7                            2.807e-01  1.535e-03  1.829e+02
## weather_conditions8                            2.404e-03  2.449e-02  9.815e-02
## road_surface_conditions2                       1.861e-01  7.124e-02  2.612e+00
## road_surface_conditions3                       8.091e-01  2.860e-04  2.829e+03
## road_surface_conditions4                       4.565e-01  2.168e-03  2.105e+02
## road_surface_conditions5                       1.219e-01  3.203e-04  3.805e+02
## special_conditions_at_site1                    1.149e+00  3.199e-04  3.592e+03
## special_conditions_at_site2                   -8.861e-01  2.477e-04 -3.577e+03
## special_conditions_at_site3                   -1.811e-01  9.392e-04 -1.928e+02
## special_conditions_at_site4                   -1.144e-02  2.242e-03 -5.104e+00
## special_conditions_at_site5                    5.278e-01  6.564e-04  8.041e+02
## special_conditions_at_site6                    1.071e+00  2.453e-04  4.367e+03
## special_conditions_at_site7                   -1.133e+00  9.170e-04 -1.236e+03
## carriageway_hazards1                          -3.497e-01  7.490e-04 -4.668e+02
## carriageway_hazards2                          -2.249e-02  2.628e-03 -8.559e+00
## carriageway_hazards3                          -6.124e-01  6.456e-04 -9.485e+02
## carriageway_hazards6                           2.409e-01  1.086e-03  2.219e+02
## carriageway_hazards7                          -4.971e-01  6.343e-04 -7.837e+02
## did_police_officer_attend_scene_of_collision1 -9.058e-01  8.026e-02 -1.129e+01
## 
## Intercepts:
##     Value      Std. Error t value   
## 1|2    -5.2394     0.0152  -344.6144
## 2|3    -1.7801     0.0882   -20.1784
## 
## Residual Deviance: 11213.90 
## AIC: 11333.90
summary(full_test2)$coef
##                                                       Value   Std. Error
## police_force                                   3.230595e-03 1.373585e-03
## number_of_vehicles                             4.265101e-01 4.155237e-02
## number_of_casualties                          -8.422624e-02 3.421859e-02
## day_of_week                                   -1.037475e-02 1.223468e-02
## first_road_class                               4.844015e-03 1.933777e-02
## first_road_number                             -2.125853e-05 2.072712e-05
## road_type2                                     2.485913e-01 5.641744e-02
## road_type3                                     5.334475e-02 8.557896e-02
## road_type6                                    -2.105413e-02 6.546775e-02
## road_type7                                    -1.119921e-01 2.936768e-02
## speed_limit                                   -1.027694e-02 2.208917e-03
## junction_detail1                               3.643206e-01 8.594962e-02
## junction_detail2                               1.712716e-01 3.047423e-02
## junction_detail5                              -9.276249e-02 2.405273e-02
## junction_detail6                              -4.698872e-02 6.814328e-02
## junction_detail7                               2.827486e-01 1.770464e-02
## junction_detail8                               9.584854e-02 1.215361e-01
## junction_detail9                               1.726160e-01 7.905967e-02
## junction_control1                              6.180706e-01 3.352450e-03
## junction_control2                              2.910535e-01 7.854581e-02
## junction_control3                              5.518884e-02 5.145758e-03
## second_road_class                             -6.095171e-02 2.317174e-02
## second_road_number                            -4.870301e-05 2.875283e-05
## pedestrian_crossing_human_control1             5.624002e-01 2.321910e-03
## pedestrian_crossing_human_control2             2.864052e-01 1.208853e-02
## pedestrian_crossing_physical_facilities1       2.317927e-01 1.085146e-01
## pedestrian_crossing_physical_facilities4      -4.873031e-02 8.582157e-02
## pedestrian_crossing_physical_facilities5      -7.346324e-02 8.316488e-02
## pedestrian_crossing_physical_facilities7      -1.572874e-03 1.448924e-03
## pedestrian_crossing_physical_facilities8      -1.405312e-01 8.585613e-02
## light_conditions4                             -2.300793e-01 5.795571e-02
## light_conditions5                             -7.831407e-01 1.628151e-03
## light_conditions6                              5.327328e-02 1.442372e-02
## light_conditions7                              3.421531e-01 1.813784e-03
## weather_conditions2                            9.196373e-02 9.978474e-02
## weather_conditions3                           -6.675492e-02 3.219935e-03
## weather_conditions4                           -1.123286e-01 4.873776e-03
## weather_conditions5                           -1.247158e-01 1.024380e-02
## weather_conditions6                            2.304587e-01 4.507887e-04
## weather_conditions7                            2.807177e-01 1.534522e-03
## weather_conditions8                            2.403537e-03 2.448874e-02
## road_surface_conditions2                       1.861046e-01 7.123883e-02
## road_surface_conditions3                       8.091304e-01 2.860129e-04
## road_surface_conditions4                       4.564709e-01 2.168251e-03
## road_surface_conditions5                       1.218938e-01 3.203473e-04
## special_conditions_at_site1                    1.149044e+00 3.198556e-04
## special_conditions_at_site2                   -8.860794e-01 2.477089e-04
## special_conditions_at_site3                   -1.810893e-01 9.392374e-04
## special_conditions_at_site4                   -1.144464e-02 2.242366e-03
## special_conditions_at_site5                    5.277993e-01 6.564248e-04
## special_conditions_at_site6                    1.071381e+00 2.453307e-04
## special_conditions_at_site7                   -1.133183e+00 9.169879e-04
## carriageway_hazards1                          -3.496611e-01 7.490099e-04
## carriageway_hazards2                          -2.249431e-02 2.628279e-03
## carriageway_hazards3                          -6.123622e-01 6.455854e-04
## carriageway_hazards6                           2.408518e-01 1.085590e-03
## carriageway_hazards7                          -4.971114e-01 6.342787e-04
## did_police_officer_attend_scene_of_collision1 -9.057968e-01 8.026315e-02
## 1|2                                           -5.239448e+00 1.520380e-02
## 2|3                                           -1.780145e+00 8.822015e-02
##                                                     t value
## police_force                                   2.351943e+00
## number_of_vehicles                             1.026440e+01
## number_of_casualties                          -2.461417e+00
## day_of_week                                   -8.479791e-01
## first_road_class                               2.504950e-01
## first_road_number                             -1.025638e+00
## road_type2                                     4.406285e+00
## road_type3                                     6.233395e-01
## road_type6                                    -3.215954e-01
## road_type7                                    -3.813445e+00
## speed_limit                                   -4.652481e+00
## junction_detail1                               4.238769e+00
## junction_detail2                               5.620210e+00
## junction_detail5                              -3.856630e+00
## junction_detail6                              -6.895577e-01
## junction_detail7                               1.597031e+01
## junction_detail8                               7.886426e-01
## junction_detail9                               2.183363e+00
## junction_control1                              1.843638e+02
## junction_control2                              3.705525e+00
## junction_control3                              1.072511e+01
## second_road_class                             -2.630433e+00
## second_road_number                            -1.693851e+00
## pedestrian_crossing_human_control1             2.422144e+02
## pedestrian_crossing_human_control2             2.369232e+01
## pedestrian_crossing_physical_facilities1       2.136051e+00
## pedestrian_crossing_physical_facilities4      -5.678097e-01
## pedestrian_crossing_physical_facilities5      -8.833445e-01
## pedestrian_crossing_physical_facilities7      -1.085546e+00
## pedestrian_crossing_physical_facilities8      -1.636822e+00
## light_conditions4                             -3.969916e+00
## light_conditions5                             -4.810000e+02
## light_conditions6                              3.693449e+00
## light_conditions7                              1.886405e+02
## weather_conditions2                            9.216212e-01
## weather_conditions3                           -2.073176e+01
## weather_conditions4                           -2.304756e+01
## weather_conditions5                           -1.217476e+01
## weather_conditions6                            5.112343e+02
## weather_conditions7                            1.829350e+02
## weather_conditions8                            9.814868e-02
## road_surface_conditions2                       2.612404e+00
## road_surface_conditions3                       2.829000e+03
## road_surface_conditions4                       2.105250e+02
## road_surface_conditions5                       3.805050e+02
## special_conditions_at_site1                    3.592385e+03
## special_conditions_at_site2                   -3.577099e+03
## special_conditions_at_site3                   -1.928046e+02
## special_conditions_at_site4                   -5.103824e+00
## special_conditions_at_site5                    8.040515e+02
## special_conditions_at_site6                    4.367089e+03
## special_conditions_at_site7                   -1.235767e+03
## carriageway_hazards1                          -4.668310e+02
## carriageway_hazards2                          -8.558573e+00
## carriageway_hazards3                          -9.485379e+02
## carriageway_hazards6                           2.218626e+02
## carriageway_hazards7                          -7.837429e+02
## did_police_officer_attend_scene_of_collision1 -1.128534e+01
## 1|2                                           -3.446144e+02
## 2|3                                           -2.017844e+01
coef(full_test2)   # the values of Log odds ratio (or: estimates)
##                                  police_force 
##                                  3.230595e-03 
##                            number_of_vehicles 
##                                  4.265101e-01 
##                          number_of_casualties 
##                                 -8.422624e-02 
##                                   day_of_week 
##                                 -1.037475e-02 
##                              first_road_class 
##                                  4.844015e-03 
##                             first_road_number 
##                                 -2.125853e-05 
##                                    road_type2 
##                                  2.485913e-01 
##                                    road_type3 
##                                  5.334475e-02 
##                                    road_type6 
##                                 -2.105413e-02 
##                                    road_type7 
##                                 -1.119921e-01 
##                                   speed_limit 
##                                 -1.027694e-02 
##                              junction_detail1 
##                                  3.643206e-01 
##                              junction_detail2 
##                                  1.712716e-01 
##                              junction_detail5 
##                                 -9.276249e-02 
##                              junction_detail6 
##                                 -4.698872e-02 
##                              junction_detail7 
##                                  2.827486e-01 
##                              junction_detail8 
##                                  9.584854e-02 
##                              junction_detail9 
##                                  1.726160e-01 
##                             junction_control1 
##                                  6.180706e-01 
##                             junction_control2 
##                                  2.910535e-01 
##                             junction_control3 
##                                  5.518884e-02 
##                             second_road_class 
##                                 -6.095171e-02 
##                            second_road_number 
##                                 -4.870301e-05 
##            pedestrian_crossing_human_control1 
##                                  5.624002e-01 
##            pedestrian_crossing_human_control2 
##                                  2.864052e-01 
##      pedestrian_crossing_physical_facilities1 
##                                  2.317927e-01 
##      pedestrian_crossing_physical_facilities4 
##                                 -4.873031e-02 
##      pedestrian_crossing_physical_facilities5 
##                                 -7.346324e-02 
##      pedestrian_crossing_physical_facilities7 
##                                 -1.572874e-03 
##      pedestrian_crossing_physical_facilities8 
##                                 -1.405312e-01 
##                             light_conditions4 
##                                 -2.300793e-01 
##                             light_conditions5 
##                                 -7.831407e-01 
##                             light_conditions6 
##                                  5.327328e-02 
##                             light_conditions7 
##                                  3.421531e-01 
##                           weather_conditions2 
##                                  9.196373e-02 
##                           weather_conditions3 
##                                 -6.675492e-02 
##                           weather_conditions4 
##                                 -1.123286e-01 
##                           weather_conditions5 
##                                 -1.247158e-01 
##                           weather_conditions6 
##                                  2.304587e-01 
##                           weather_conditions7 
##                                  2.807177e-01 
##                           weather_conditions8 
##                                  2.403537e-03 
##                      road_surface_conditions2 
##                                  1.861046e-01 
##                      road_surface_conditions3 
##                                  8.091304e-01 
##                      road_surface_conditions4 
##                                  4.564709e-01 
##                      road_surface_conditions5 
##                                  1.218938e-01 
##                   special_conditions_at_site1 
##                                  1.149044e+00 
##                   special_conditions_at_site2 
##                                 -8.860794e-01 
##                   special_conditions_at_site3 
##                                 -1.810893e-01 
##                   special_conditions_at_site4 
##                                 -1.144464e-02 
##                   special_conditions_at_site5 
##                                  5.277993e-01 
##                   special_conditions_at_site6 
##                                  1.071381e+00 
##                   special_conditions_at_site7 
##                                 -1.133183e+00 
##                          carriageway_hazards1 
##                                 -3.496611e-01 
##                          carriageway_hazards2 
##                                 -2.249431e-02 
##                          carriageway_hazards3 
##                                 -6.123622e-01 
##                          carriageway_hazards6 
##                                  2.408518e-01 
##                          carriageway_hazards7 
##                                 -4.971114e-01 
## did_police_officer_attend_scene_of_collision1 
##                                 -9.057968e-01
vcov(full_test2) 
##                                                police_force number_of_vehicles
## police_force                                   1.886737e-06       1.555969e-06
## number_of_vehicles                             1.555969e-06       1.726599e-03
## number_of_casualties                          -8.103884e-07      -2.893199e-04
## day_of_week                                    2.667126e-07      -2.457802e-05
## first_road_class                              -2.684467e-06      -3.319803e-05
## first_road_number                             -2.062321e-09      -3.593408e-08
## road_type2                                     1.081965e-06       1.483395e-04
## road_type3                                     7.691370e-06      -1.772907e-04
## road_type6                                    -3.209095e-06      -1.464191e-04
## road_type7                                     1.799298e-07       9.346579e-05
## speed_limit                                   -1.038335e-06      -1.394010e-05
## junction_detail1                              -8.476320e-06      -2.152733e-04
## junction_detail2                               1.875343e-07       9.850898e-05
## junction_detail5                               8.826999e-07       7.756960e-05
## junction_detail6                               3.262339e-06      -1.067627e-04
## junction_detail7                               4.035131e-07       1.022438e-05
## junction_detail8                               1.324548e-06      -9.704399e-05
## junction_detail9                               9.326970e-06       4.710631e-05
## junction_control1                              3.355075e-08      -3.154932e-06
## junction_control2                              4.953724e-06      -6.837069e-05
## junction_control3                             -4.518904e-08       8.534071e-06
## second_road_class                             -8.859821e-07      -1.708132e-04
## second_road_number                             5.292789e-11      -1.344528e-07
## pedestrian_crossing_human_control1             2.395724e-07      -2.591938e-06
## pedestrian_crossing_human_control2             8.186182e-07       1.765982e-06
## pedestrian_crossing_physical_facilities1       1.100931e-05       6.608274e-05
## pedestrian_crossing_physical_facilities4       1.211945e-06      -2.052710e-05
## pedestrian_crossing_physical_facilities5      -2.309675e-07       1.905057e-05
## pedestrian_crossing_physical_facilities7       1.000949e-08      -4.085538e-06
## pedestrian_crossing_physical_facilities8      -3.989746e-06      -1.577418e-04
## light_conditions4                              3.338447e-06      -8.852067e-06
## light_conditions5                              3.440040e-08       4.332744e-06
## light_conditions6                             -2.864342e-07      -1.186900e-05
## light_conditions7                             -8.826791e-08      -7.252018e-06
## weather_conditions2                            3.654867e-06      -1.452480e-05
## weather_conditions3                           -2.425865e-07       3.653098e-07
## weather_conditions4                           -3.126842e-07      -4.935825e-06
## weather_conditions5                           -3.791987e-07       4.400429e-06
## weather_conditions6                           -1.376562e-08      -4.006140e-07
## weather_conditions7                           -9.645402e-08      -7.587749e-07
## weather_conditions8                           -8.777134e-07      -2.819668e-06
## road_surface_conditions2                      -3.255989e-06       8.583735e-05
## road_surface_conditions3                      -2.590015e-08      -1.659052e-07
## road_surface_conditions4                       8.206903e-08      -4.241581e-06
## road_surface_conditions5                       2.099580e-08      -1.447830e-06
## special_conditions_at_site1                    3.429748e-08      -2.080034e-06
## special_conditions_at_site2                    1.645315e-08      -7.282838e-07
## special_conditions_at_site3                   -1.002923e-08      -1.090523e-06
## special_conditions_at_site4                    4.301413e-08      -9.880938e-06
## special_conditions_at_site5                    1.995857e-08      -4.196987e-06
## special_conditions_at_site6                   -1.722562e-08      -1.174517e-06
## special_conditions_at_site7                    7.641651e-08      -2.729197e-06
## carriageway_hazards1                           1.977874e-08       1.581826e-06
## carriageway_hazards2                          -8.041210e-09      -1.129240e-05
## carriageway_hazards3                           3.576785e-09       3.410978e-06
## carriageway_hazards6                           7.868256e-08      -5.501600e-06
## carriageway_hazards7                          -1.530965e-08      -6.501792e-06
## did_police_officer_attend_scene_of_collision1  2.986699e-06      -3.853562e-04
## 1|2                                           -6.164406e-07       4.235817e-05
## 2|3                                           -3.224082e-06       4.968151e-04
##                                               number_of_casualties
## police_force                                         -8.103884e-07
## number_of_vehicles                                   -2.893199e-04
## number_of_casualties                                  1.170912e-03
## day_of_week                                          -6.997333e-06
## first_road_class                                     -2.255606e-05
## first_road_number                                    -1.981089e-08
## road_type2                                            6.155803e-06
## road_type3                                           -6.127292e-05
## road_type6                                           -3.159066e-05
## road_type7                                            8.904981e-06
## speed_limit                                          -1.208706e-05
## junction_detail1                                      7.515443e-05
## junction_detail2                                     -5.156174e-06
## junction_detail5                                     -6.775242e-06
## junction_detail6                                     -9.832077e-05
## junction_detail7                                     -6.661817e-06
## junction_detail8                                      4.610802e-05
## junction_detail9                                     -5.633512e-06
## junction_control1                                     1.138980e-06
## junction_control2                                    -3.962748e-05
## junction_control3                                    -2.859499e-06
## second_road_class                                    -2.155419e-05
## second_road_number                                   -1.865061e-08
## pedestrian_crossing_human_control1                    1.940823e-06
## pedestrian_crossing_human_control2                   -1.593325e-06
## pedestrian_crossing_physical_facilities1              4.535281e-05
## pedestrian_crossing_physical_facilities4             -2.500148e-05
## pedestrian_crossing_physical_facilities5             -1.204955e-05
## pedestrian_crossing_physical_facilities7             -7.687258e-07
## pedestrian_crossing_physical_facilities8             -3.081081e-05
## light_conditions4                                    -6.112524e-05
## light_conditions5                                    -2.706390e-07
## light_conditions6                                     1.471186e-05
## light_conditions7                                     1.121667e-06
## weather_conditions2                                  -5.397066e-05
## weather_conditions3                                   3.855454e-06
## weather_conditions4                                  -7.831525e-08
## weather_conditions5                                   6.013573e-06
## weather_conditions6                                   7.046943e-07
## weather_conditions7                                   1.267847e-06
## weather_conditions8                                   1.161873e-05
## road_surface_conditions2                              1.662691e-05
## road_surface_conditions3                              1.431581e-06
## road_surface_conditions4                             -4.221556e-07
## road_surface_conditions5                              6.636802e-07
## special_conditions_at_site1                          -2.226568e-07
## special_conditions_at_site2                           9.310267e-07
## special_conditions_at_site3                           8.168708e-07
## special_conditions_at_site4                          -3.161915e-06
## special_conditions_at_site5                          -1.479899e-07
## special_conditions_at_site6                           4.003749e-07
## special_conditions_at_site7                           1.901628e-06
## carriageway_hazards1                                  6.952161e-07
## carriageway_hazards2                                  3.031399e-06
## carriageway_hazards3                                 -1.442696e-06
## carriageway_hazards6                                  1.342230e-06
## carriageway_hazards7                                  7.477654e-08
## did_police_officer_attend_scene_of_collision1        -1.954746e-04
## 1|2                                                   2.820080e-05
## 2|3                                                   8.598727e-05
##                                                 day_of_week first_road_class
## police_force                                   2.667126e-07    -2.684467e-06
## number_of_vehicles                            -2.457802e-05    -3.319803e-05
## number_of_casualties                          -6.997333e-06    -2.255606e-05
## day_of_week                                    1.496873e-04    -2.111203e-05
## first_road_class                              -2.111203e-05     3.739494e-04
## first_road_number                             -1.067973e-08     1.425629e-07
## road_type2                                     7.292089e-06     7.219380e-05
## road_type3                                    -6.499988e-06     7.691084e-05
## road_type6                                    -6.217268e-06    -2.021178e-04
## road_type7                                     5.120048e-06     3.244318e-05
## speed_limit                                   -1.802601e-06     2.893351e-06
## junction_detail1                              -5.490022e-05    -9.020762e-05
## junction_detail2                               1.002714e-05     2.449119e-05
## junction_detail5                               1.012138e-05     3.344044e-05
## junction_detail6                              -2.389056e-06    -8.072953e-05
## junction_detail7                              -2.045013e-06     1.402604e-05
## junction_detail8                              -7.274604e-06     1.122556e-04
## junction_detail9                              -1.196743e-05    -3.290767e-05
## junction_control1                             -5.333783e-07    -7.280937e-07
## junction_control2                             -3.150967e-05     8.300519e-05
## junction_control3                              8.974881e-07    -4.963417e-06
## second_road_class                             -3.566963e-05    -1.934877e-04
## second_road_number                            -1.909807e-08    -1.190741e-07
## pedestrian_crossing_human_control1            -6.607910e-07     1.173898e-07
## pedestrian_crossing_human_control2            -6.122904e-06     7.872740e-06
## pedestrian_crossing_physical_facilities1      -1.987012e-05    -4.928994e-05
## pedestrian_crossing_physical_facilities4      -2.333226e-05     9.533088e-05
## pedestrian_crossing_physical_facilities5      -2.738445e-05     4.768079e-05
## pedestrian_crossing_physical_facilities7      -7.040723e-07    -1.224189e-06
## pedestrian_crossing_physical_facilities8       1.592437e-05    -5.750225e-05
## light_conditions4                             -2.245483e-05    -1.541136e-05
## light_conditions5                             -2.184557e-07     4.428563e-07
## light_conditions6                              4.968723e-06     1.175066e-05
## light_conditions7                              8.899349e-08    -1.407821e-06
## weather_conditions2                            5.018876e-07     4.660674e-06
## weather_conditions3                            2.209587e-07     6.595495e-07
## weather_conditions4                           -2.140482e-07    -9.474610e-07
## weather_conditions5                           -2.569880e-07    -1.212825e-06
## weather_conditions6                            9.753035e-08     3.265477e-07
## weather_conditions7                            1.109791e-07     2.906533e-07
## weather_conditions8                           -2.550384e-06    -9.427671e-06
## road_surface_conditions2                      -4.427960e-06    -2.179501e-05
## road_surface_conditions3                       1.416382e-07     1.532015e-07
## road_surface_conditions4                      -3.980076e-07     1.797907e-06
## road_surface_conditions5                       2.240180e-08     6.666690e-08
## special_conditions_at_site1                   -2.102270e-07    -1.559875e-07
## special_conditions_at_site2                   -1.604014e-08     3.936902e-07
## special_conditions_at_site3                    1.922694e-07    -1.091389e-06
## special_conditions_at_site4                   -7.285520e-07    -3.144606e-07
## special_conditions_at_site5                    1.118298e-09    -2.582703e-07
## special_conditions_at_site6                   -6.102359e-08    -1.326278e-07
## special_conditions_at_site7                   -1.132727e-08     4.688727e-07
## carriageway_hazards1                          -3.634777e-07    -1.690171e-06
## carriageway_hazards2                          -5.736399e-07     8.173365e-07
## carriageway_hazards3                           1.013550e-07     9.070694e-08
## carriageway_hazards6                          -5.193584e-07    -1.315215e-06
## carriageway_hazards7                          -9.721569e-08     4.179124e-08
## did_police_officer_attend_scene_of_collision1 -7.186979e-05    -7.504961e-05
## 1|2                                            2.300141e-05     2.395279e-05
## 2|3                                            1.142515e-04     2.608138e-04
##                                               first_road_number    road_type2
## police_force                                      -2.062321e-09  1.081965e-06
## number_of_vehicles                                -3.593408e-08  1.483395e-04
## number_of_casualties                              -1.981089e-08  6.155803e-06
## day_of_week                                       -1.067973e-08  7.292089e-06
## first_road_class                                   1.425629e-07  7.219380e-05
## first_road_number                                  4.296134e-10  4.718107e-08
## road_type2                                         4.718107e-08  3.182928e-03
## road_type3                                         1.157112e-08 -3.875923e-03
## road_type6                                        -7.877999e-08 -2.916630e-03
## road_type7                                         2.238895e-08  1.615698e-03
## speed_limit                                        1.209054e-09  1.594316e-05
## junction_detail1                                  -1.147916e-07 -1.967862e-03
## junction_detail2                                   1.963607e-08  1.282337e-03
## junction_detail5                                   3.019394e-08  9.298085e-04
## junction_detail6                                  -1.370500e-08  1.196955e-04
## junction_detail7                                  -3.567350e-09 -1.928606e-04
## junction_detail8                                   3.636449e-08  6.370044e-04
## junction_detail9                                  -1.567563e-08  2.260588e-04
## junction_control1                                  2.294013e-09 -2.334400e-05
## junction_control2                                 -9.582243e-08  5.220049e-04
## junction_control3                                  4.225361e-09  1.007770e-05
## second_road_class                                 -1.249362e-07  1.919732e-04
## second_road_number                                -1.305317e-10  6.268159e-08
## pedestrian_crossing_human_control1                -1.843998e-09 -1.394039e-05
## pedestrian_crossing_human_control2                -5.767009e-09  9.705035e-05
## pedestrian_crossing_physical_facilities1          -8.640246e-08 -1.134795e-04
## pedestrian_crossing_physical_facilities4          -2.642959e-08  2.481052e-04
## pedestrian_crossing_physical_facilities5           1.268558e-08  9.646316e-05
## pedestrian_crossing_physical_facilities7          -1.684605e-09 -4.414609e-05
## pedestrian_crossing_physical_facilities8          -1.391147e-08 -3.727068e-04
## light_conditions4                                 -1.575577e-08  9.051436e-05
## light_conditions5                                 -8.042325e-10 -1.001280e-05
## light_conditions6                                  1.895849e-08  3.922986e-04
## light_conditions7                                 -1.022405e-09 -7.534560e-05
## weather_conditions2                               -4.294791e-08  8.516988e-05
## weather_conditions3                                8.241682e-10 -1.618062e-05
## weather_conditions4                                2.254528e-09  1.043209e-05
## weather_conditions5                                1.917917e-09 -2.664647e-05
## weather_conditions6                                3.724708e-10  1.377727e-07
## weather_conditions7                                9.760717e-10 -5.124489e-06
## weather_conditions8                                6.618772e-09 -1.263417e-04
## road_surface_conditions2                          -1.321295e-08 -1.009045e-05
## road_surface_conditions3                           4.968273e-11 -3.339204e-06
## road_surface_conditions4                           1.011285e-09  1.838743e-05
## road_surface_conditions5                           4.754474e-11  4.664398e-06
## special_conditions_at_site1                       -1.704632e-10 -1.467458e-06
## special_conditions_at_site2                        1.711933e-10 -5.327296e-06
## special_conditions_at_site3                        4.355219e-10  1.225612e-05
## special_conditions_at_site4                       -8.731031e-10  2.255809e-05
## special_conditions_at_site5                        1.618820e-11 -1.656590e-06
## special_conditions_at_site6                       -2.520327e-10  3.895022e-07
## special_conditions_at_site7                       -4.959390e-11 -9.665485e-06
## carriageway_hazards1                              -1.183625e-09 -1.440483e-06
## carriageway_hazards2                               2.177423e-09 -2.055365e-06
## carriageway_hazards3                               5.226263e-10  2.551955e-05
## carriageway_hazards6                              -8.415179e-10 -2.291645e-05
## carriageway_hazards7                               1.779472e-10  9.244321e-06
## did_police_officer_attend_scene_of_collision1      1.866811e-08  4.340672e-04
## 1|2                                                2.937416e-08  4.410000e-04
## 2|3                                               -1.454376e-08  1.112211e-04
##                                                  road_type3    road_type6
## police_force                                   7.691370e-06 -3.209095e-06
## number_of_vehicles                            -1.772907e-04 -1.464191e-04
## number_of_casualties                          -6.127292e-05 -3.159066e-05
## day_of_week                                   -6.499989e-06 -6.217268e-06
## first_road_class                               7.691084e-05 -2.021178e-04
## first_road_number                              1.157112e-08 -7.877999e-08
## road_type2                                    -3.875923e-03 -2.916630e-03
## road_type3                                     7.323758e-03  2.428464e-03
## road_type6                                     2.428464e-03  4.286026e-03
## road_type7                                    -2.028487e-03 -1.484417e-03
## speed_limit                                   -2.872288e-05 -3.824177e-06
## junction_detail1                               3.507988e-05  1.064516e-03
## junction_detail2                              -1.520750e-03 -1.168265e-03
## junction_detail5                              -7.770318e-04 -8.862583e-04
## junction_detail6                              -2.403994e-04 -2.889961e-04
## junction_detail7                               3.769658e-04  2.445431e-04
## junction_detail8                               1.357750e-04 -3.257996e-04
## junction_detail9                              -2.499946e-04 -1.084868e-04
## junction_control1                              5.807042e-05  5.754346e-06
## junction_control2                             -9.493209e-04 -1.037216e-04
## junction_control3                              1.824122e-08 -2.573908e-05
## second_road_class                             -2.731018e-04 -3.923356e-04
## second_road_number                            -1.444126e-08 -9.247464e-08
## pedestrian_crossing_human_control1             3.032577e-05  2.129922e-05
## pedestrian_crossing_human_control2            -1.225074e-04 -5.640583e-05
## pedestrian_crossing_physical_facilities1       4.098452e-04  4.517594e-04
## pedestrian_crossing_physical_facilities4      -2.290365e-04 -7.306496e-05
## pedestrian_crossing_physical_facilities5      -4.168168e-04 -5.683936e-05
## pedestrian_crossing_physical_facilities7       4.551011e-05  2.865684e-05
## pedestrian_crossing_physical_facilities8       8.976454e-05  2.208877e-04
## light_conditions4                             -1.458473e-04  6.630137e-05
## light_conditions5                              2.034515e-05  4.643546e-06
## light_conditions6                             -3.233771e-04 -3.149924e-04
## light_conditions7                              8.364626e-05  5.541140e-05
## weather_conditions2                           -1.769635e-04  7.507361e-05
## weather_conditions3                            1.715041e-05  3.340711e-06
## weather_conditions4                           -1.855376e-05 -2.305474e-05
## weather_conditions5                            5.133310e-05  2.207632e-05
## weather_conditions6                            5.405714e-06 -6.628924e-07
## weather_conditions7                            1.142506e-05  1.666455e-06
## weather_conditions8                            1.738559e-04  5.829870e-05
## road_surface_conditions2                      -3.416976e-06 -8.118537e-05
## road_surface_conditions3                       2.379961e-06 -1.221009e-06
## road_surface_conditions4                      -1.000452e-05 -5.182040e-06
## road_surface_conditions5                      -6.668051e-06 -2.860908e-06
## special_conditions_at_site1                    1.755030e-06  2.071559e-06
## special_conditions_at_site2                    1.198631e-05  1.904700e-06
## special_conditions_at_site3                   -1.790975e-05 -1.276609e-05
## special_conditions_at_site4                   -3.401684e-05 -2.295655e-05
## special_conditions_at_site5                    7.875097e-06  4.819074e-06
## special_conditions_at_site6                   -7.051805e-06 -2.188543e-06
## special_conditions_at_site7                    2.155168e-05  1.171749e-05
## carriageway_hazards1                          -9.263255e-06  3.502052e-06
## carriageway_hazards2                           2.528652e-05  8.101784e-06
## carriageway_hazards3                          -3.043037e-05 -1.851094e-05
## carriageway_hazards6                           2.780769e-05  2.645597e-05
## carriageway_hazards7                          -1.775486e-05 -7.649359e-06
## did_police_officer_attend_scene_of_collision1 -3.227329e-05 -4.131410e-05
## 1|2                                           -4.000678e-04 -4.294955e-04
## 2|3                                           -1.329248e-04 -1.344349e-04
##                                                  road_type7   speed_limit
## police_force                                   1.799298e-07 -1.038335e-06
## number_of_vehicles                             9.346579e-05 -1.394010e-05
## number_of_casualties                           8.904981e-06 -1.208706e-05
## day_of_week                                    5.120048e-06 -1.802601e-06
## first_road_class                               3.244318e-05  2.893351e-06
## first_road_number                              2.238895e-08  1.209054e-09
## road_type2                                     1.615698e-03  1.594316e-05
## road_type3                                    -2.028487e-03 -2.872288e-05
## road_type6                                    -1.484417e-03 -3.824177e-06
## road_type7                                     8.624608e-04  8.957988e-06
## speed_limit                                    8.957988e-06  4.879313e-06
## junction_detail1                              -1.051373e-03 -2.430043e-05
## junction_detail2                               7.576655e-04  9.250482e-06
## junction_detail5                               5.520503e-04  6.794957e-06
## junction_detail6                              -6.230842e-05 -2.981435e-06
## junction_detail7                              -1.514697e-05  1.256240e-06
## junction_detail8                              -3.774955e-04 -9.728445e-06
## junction_detail9                              -7.318926e-05  3.910602e-07
## junction_control1                             -1.036824e-05 -4.494749e-07
## junction_control2                              2.807232e-04  1.101766e-05
## junction_control3                              8.116157e-06 -3.096979e-07
## second_road_class                              1.086145e-04 -5.511312e-06
## second_road_number                             3.061298e-08 -7.871999e-09
## pedestrian_crossing_human_control1            -3.205710e-06  1.045784e-07
## pedestrian_crossing_human_control2             6.859331e-05  1.371494e-06
## pedestrian_crossing_physical_facilities1       4.147893e-05  7.168176e-06
## pedestrian_crossing_physical_facilities4       1.583457e-04  9.726765e-06
## pedestrian_crossing_physical_facilities5       6.482772e-05  3.269362e-06
## pedestrian_crossing_physical_facilities7      -2.458880e-05 -5.102692e-07
## pedestrian_crossing_physical_facilities8      -9.139674e-05 -7.136594e-06
## light_conditions4                              4.418842e-05  1.368351e-05
## light_conditions5                             -7.782024e-06 -4.055649e-07
## light_conditions6                              2.070094e-04  1.014246e-06
## light_conditions7                             -3.620399e-05 -3.752515e-07
## weather_conditions2                           -9.207657e-05  9.917999e-06
## weather_conditions3                           -5.615003e-06 -4.071687e-07
## weather_conditions4                            7.106744e-06 -1.005429e-06
## weather_conditions5                           -6.231402e-06 -1.296655e-06
## weather_conditions6                           -6.022120e-07 -6.406259e-08
## weather_conditions7                           -7.037370e-08 -2.322525e-07
## weather_conditions8                           -2.729344e-05 -4.076081e-06
## road_surface_conditions2                       6.240510e-05 -9.911844e-06
## road_surface_conditions3                      -1.766357e-06 -1.169816e-08
## road_surface_conditions4                       1.406212e-05  4.513662e-07
## road_surface_conditions5                       2.054913e-06  7.977031e-08
## special_conditions_at_site1                   -5.796795e-07 -4.048213e-08
## special_conditions_at_site2                   -3.086737e-06 -5.818062e-08
## special_conditions_at_site3                    8.038609e-06 -1.069904e-09
## special_conditions_at_site4                    5.534031e-06 -2.728809e-07
## special_conditions_at_site5                   -3.596505e-06 -9.932059e-08
## special_conditions_at_site6                    5.517725e-07 -1.598983e-08
## special_conditions_at_site7                   -6.765466e-06 -4.496477e-08
## carriageway_hazards1                           1.059248e-06 -1.769049e-08
## carriageway_hazards2                          -1.041317e-05 -3.461342e-07
## carriageway_hazards3                           1.333963e-05  1.046289e-07
## carriageway_hazards6                          -9.262549e-06 -1.029233e-07
## carriageway_hazards7                           1.687483e-06  2.683215e-09
## did_police_officer_attend_scene_of_collision1  1.572097e-04 -3.438190e-05
## 1|2                                            2.155708e-04  7.297049e-06
## 2|3                                            4.568178e-05  3.659183e-05
##                                               junction_detail1 junction_detail2
## police_force                                     -8.476320e-06     1.875343e-07
## number_of_vehicles                               -2.152733e-04     9.850898e-05
## number_of_casualties                              7.515443e-05    -5.156174e-06
## day_of_week                                      -5.490022e-05     1.002714e-05
## first_road_class                                 -9.020762e-05     2.449119e-05
## first_road_number                                -1.147916e-07     1.963607e-08
## road_type2                                       -1.967862e-03     1.282337e-03
## road_type3                                        3.507988e-05    -1.520750e-03
## road_type6                                        1.064516e-03    -1.168265e-03
## road_type7                                       -1.051373e-03     7.576655e-04
## speed_limit                                      -2.430043e-05     9.250482e-06
## junction_detail1                                  7.387337e-03    -1.410104e-03
## junction_detail2                                 -1.410104e-03     9.286788e-04
## junction_detail5                                 -1.531735e-03     6.650294e-04
## junction_detail6                                  6.593481e-04    -3.655734e-04
## junction_detail7                                 -4.718569e-04     1.834102e-04
## junction_detail8                                  3.459282e-04    -1.589247e-03
## junction_detail9                                  5.916906e-04    -5.138245e-04
## junction_control1                                 2.446775e-06    -2.375696e-05
## junction_control2                                -1.928299e-04     5.353975e-04
## junction_control3                                -2.481114e-05    -1.082205e-05
## second_road_class                                 1.769926e-04     9.008522e-05
## second_road_number                               -1.572121e-07     2.208561e-08
## pedestrian_crossing_human_control1               -6.542835e-06    -7.465869e-07
## pedestrian_crossing_human_control2                2.315588e-05    -3.286340e-06
## pedestrian_crossing_physical_facilities1          3.358498e-05     1.623626e-04
## pedestrian_crossing_physical_facilities4          4.586071e-05    -1.387852e-04
## pedestrian_crossing_physical_facilities5          5.979178e-04    -3.956059e-04
## pedestrian_crossing_physical_facilities7          7.671492e-05    -2.324834e-05
## pedestrian_crossing_physical_facilities8         -2.001378e-04     7.033420e-04
## light_conditions4                                -2.652497e-04     5.393385e-05
## light_conditions5                                 2.228328e-05    -1.668300e-05
## light_conditions6                                -5.984611e-04     1.135859e-04
## light_conditions7                                 7.791597e-05    -3.291390e-05
## weather_conditions2                              -1.300379e-04     3.872605e-04
## weather_conditions3                               2.560367e-05    -2.208118e-05
## weather_conditions4                               2.984246e-05    -2.093221e-05
## weather_conditions5                               8.663384e-06    -6.457565e-05
## weather_conditions6                              -5.926857e-06    -4.006732e-06
## weather_conditions7                              -6.972257e-06    -5.042608e-06
## weather_conditions8                               1.408798e-04    -1.526582e-04
## road_surface_conditions2                          8.694944e-05    -1.839566e-04
## road_surface_conditions3                          8.629213e-06    -9.721015e-07
## road_surface_conditions4                         -4.536957e-05     1.292346e-05
## road_surface_conditions5                         -3.613650e-06     2.552354e-06
## special_conditions_at_site1                       1.822389e-06    -3.309941e-07
## special_conditions_at_site2                       2.013612e-07    -3.862069e-06
## special_conditions_at_site3                      -3.274834e-06     4.111542e-06
## special_conditions_at_site4                       2.810909e-05    -9.496505e-07
## special_conditions_at_site5                      -4.557773e-06    -5.316897e-06
## special_conditions_at_site6                       1.378797e-05     1.095367e-06
## special_conditions_at_site7                       5.619767e-07    -1.175150e-05
## carriageway_hazards1                              1.739649e-05     1.587058e-06
## carriageway_hazards2                              1.161674e-06    -4.251629e-05
## carriageway_hazards3                             -3.062830e-05     1.438224e-05
## carriageway_hazards6                              1.327795e-05    -6.370226e-06
## carriageway_hazards7                              1.461400e-05    -4.963960e-06
## did_police_officer_attend_scene_of_collision1    -2.724846e-04     1.260651e-04
## 1|2                                              -7.397416e-04     1.777469e-04
## 2|3                                               1.693721e-04     1.487892e-05
##                                               junction_detail5 junction_detail6
## police_force                                      8.826999e-07     3.262339e-06
## number_of_vehicles                                7.756960e-05    -1.067627e-04
## number_of_casualties                             -6.775242e-06    -9.832077e-05
## day_of_week                                       1.012138e-05    -2.389056e-06
## first_road_class                                  3.344044e-05    -8.072953e-05
## first_road_number                                 3.019394e-08    -1.370500e-08
## road_type2                                        9.298085e-04     1.196955e-04
## road_type3                                       -7.770318e-04    -2.403994e-04
## road_type6                                       -8.862583e-04    -2.889961e-04
## road_type7                                        5.520503e-04    -6.230842e-05
## speed_limit                                       6.794957e-06    -2.981435e-06
## junction_detail1                                 -1.531735e-03     6.593481e-04
## junction_detail2                                  6.650294e-04    -3.655734e-04
## junction_detail5                                  5.785340e-04    -3.447797e-04
## junction_detail6                                 -3.447797e-04     4.643506e-03
## junction_detail7                                  1.839135e-04    -7.416881e-04
## junction_detail8                                 -1.194193e-03     4.214845e-04
## junction_detail9                                 -4.927937e-04     8.608847e-04
## junction_control1                                 6.540642e-06     2.416972e-05
## junction_control2                                -4.223387e-05    -1.218146e-03
## junction_control3                                 2.021489e-05     1.266791e-04
## second_road_class                                 3.730539e-05     3.861182e-05
## second_road_number                                3.973306e-08    -3.058136e-08
## pedestrian_crossing_human_control1                9.497720e-07    -2.644613e-05
## pedestrian_crossing_human_control2                4.033146e-05    -4.302420e-05
## pedestrian_crossing_physical_facilities1          1.323253e-05    -2.175293e-04
## pedestrian_crossing_physical_facilities4          6.274623e-05    -5.308074e-05
## pedestrian_crossing_physical_facilities5          1.061452e-04    -5.180848e-04
## pedestrian_crossing_physical_facilities7         -2.580589e-05     1.241786e-05
## pedestrian_crossing_physical_facilities8          6.332121e-05    -3.668934e-04
## light_conditions4                                 9.688379e-05     8.980499e-05
## light_conditions5                                -1.229060e-05     1.351357e-05
## light_conditions6                                 1.525544e-04    -3.345232e-05
## light_conditions7                                -2.226997e-05     6.414744e-06
## weather_conditions2                               7.967548e-05    -2.718325e-05
## weather_conditions3                              -1.108683e-05    -1.323382e-05
## weather_conditions4                              -1.072355e-05     2.210899e-05
## weather_conditions5                              -2.473661e-05    -1.432281e-05
## weather_conditions6                              -1.267222e-06     8.100694e-07
## weather_conditions7                               8.752305e-07    -2.673950e-06
## weather_conditions8                              -4.211623e-05     5.899949e-05
## road_surface_conditions2                         -4.906893e-05    -4.030411e-05
## road_surface_conditions3                         -1.950752e-06    -2.237338e-06
## road_surface_conditions4                          1.702209e-05    -5.251206e-05
## road_surface_conditions5                          1.692704e-06     1.774863e-06
## special_conditions_at_site1                      -8.719756e-07     5.613576e-06
## special_conditions_at_site2                      -1.278427e-06     3.462760e-06
## special_conditions_at_site3                       5.137442e-06     3.621537e-05
## special_conditions_at_site4                      -1.407178e-05     3.820879e-05
## special_conditions_at_site5                      -5.684792e-06     4.525824e-06
## special_conditions_at_site6                      -1.224550e-06     3.076304e-07
## special_conditions_at_site7                      -7.533178e-06     7.823929e-07
## carriageway_hazards1                             -1.763124e-06     1.102020e-05
## carriageway_hazards2                             -1.528362e-05     3.234813e-05
## carriageway_hazards3                              1.104152e-05    -8.587571e-06
## carriageway_hazards6                             -2.280675e-06    -1.506878e-05
## carriageway_hazards7                             -5.264590e-06     9.427612e-06
## did_police_officer_attend_scene_of_collision1     1.712476e-04     7.354760e-05
## 1|2                                               1.758574e-04     1.326485e-04
## 2|3                                              -2.617590e-05    -6.464154e-06
##                                               junction_detail7 junction_detail8
## police_force                                      4.035131e-07     1.324548e-06
## number_of_vehicles                                1.022438e-05    -9.704399e-05
## number_of_casualties                             -6.661817e-06     4.610802e-05
## day_of_week                                      -2.045013e-06    -7.274604e-06
## first_road_class                                  1.402604e-05     1.122556e-04
## first_road_number                                -3.567350e-09     3.636449e-08
## road_type2                                       -1.928606e-04     6.370044e-04
## road_type3                                        3.769658e-04     1.357750e-04
## road_type6                                        2.445431e-04    -3.257996e-04
## road_type7                                       -1.514697e-05    -3.774955e-04
## speed_limit                                       1.256240e-06    -9.728445e-06
## junction_detail1                                 -4.718569e-04     3.459282e-04
## junction_detail2                                  1.834102e-04    -1.589247e-03
## junction_detail5                                  1.839135e-04    -1.194193e-03
## junction_detail6                                 -7.416881e-04     4.214845e-04
## junction_detail7                                  3.134542e-04    -1.210293e-03
## junction_detail8                                 -1.210293e-03     1.477102e-02
## junction_detail9                                 -6.368152e-04     6.326749e-04
## junction_control1                                 2.809984e-06    -9.344635e-05
## junction_control2                                 3.282205e-04     1.233873e-03
## junction_control3                                -1.702607e-05    -2.218093e-04
## second_road_class                                -3.334143e-05    -1.426791e-04
## second_road_number                               -1.530615e-08     7.152835e-08
## pedestrian_crossing_human_control1                1.803164e-05    -4.009148e-05
## pedestrian_crossing_human_control2                5.530483e-05    -3.483925e-04
## pedestrian_crossing_physical_facilities1          5.000222e-04    -4.803027e-04
## pedestrian_crossing_physical_facilities4          1.058069e-04    -7.873165e-04
## pedestrian_crossing_physical_facilities5          1.805313e-04    -1.231473e-03
## pedestrian_crossing_physical_facilities7         -6.171080e-06     3.835682e-05
## pedestrian_crossing_physical_facilities8          7.694212e-05    -1.693201e-03
## light_conditions4                                -6.622260e-05     2.397676e-04
## light_conditions5                                -4.222162e-06     4.474216e-05
## light_conditions6                                 5.583595e-07     2.056936e-04
## light_conditions7                                 4.422005e-06    -7.209957e-05
## weather_conditions2                              -3.009953e-05     3.702778e-05
## weather_conditions3                              -2.049653e-06     3.782734e-05
## weather_conditions4                              -1.501084e-05     4.704677e-05
## weather_conditions5                              -1.587484e-06     1.339403e-04
## weather_conditions6                              -1.361026e-06     2.524745e-05
## weather_conditions7                               2.257983e-06    -1.042625e-05
## weather_conditions8                               9.740937e-06    -2.696521e-04
## road_surface_conditions2                          1.629483e-05    -4.414214e-05
## road_surface_conditions3                         -1.190370e-06     3.384767e-06
## road_surface_conditions4                          1.738546e-05    -1.847907e-05
## road_surface_conditions5                         -5.652281e-07    -5.438994e-06
## special_conditions_at_site1                       1.655807e-07    -6.358358e-06
## special_conditions_at_site2                      -5.326332e-09     2.306863e-06
## special_conditions_at_site3                      -2.377651e-06    -3.444092e-05
## special_conditions_at_site4                      -1.846806e-05     1.272811e-04
## special_conditions_at_site5                      -4.749104e-06     5.710636e-05
## special_conditions_at_site6                      -4.607644e-07    -9.674383e-06
## special_conditions_at_site7                      -1.157540e-06     4.481174e-05
## carriageway_hazards1                              1.166037e-06    -2.094380e-05
## carriageway_hazards2                             -1.872825e-05     1.652200e-04
## carriageway_hazards3                              1.023769e-06    -5.974176e-06
## carriageway_hazards6                              9.873871e-06    -4.960623e-05
## carriageway_hazards7                             -8.392756e-06     4.488358e-05
## did_police_officer_attend_scene_of_collision1     6.467093e-05     3.256850e-04
## 1|2                                              -7.379851e-05     2.858743e-04
## 2|3                                               2.655956e-05     4.996023e-05
##                                               junction_detail9
## police_force                                      9.326970e-06
## number_of_vehicles                                4.710631e-05
## number_of_casualties                             -5.633512e-06
## day_of_week                                      -1.196743e-05
## first_road_class                                 -3.290767e-05
## first_road_number                                -1.567563e-08
## road_type2                                        2.260588e-04
## road_type3                                       -2.499946e-04
## road_type6                                       -1.084868e-04
## road_type7                                       -7.318926e-05
## speed_limit                                       3.910602e-07
## junction_detail1                                  5.916906e-04
## junction_detail2                                 -5.138245e-04
## junction_detail5                                 -4.927937e-04
## junction_detail6                                  8.608847e-04
## junction_detail7                                 -6.368152e-04
## junction_detail8                                  6.326749e-04
## junction_detail9                                  6.250431e-03
## junction_control1                                -4.366449e-06
## junction_control2                                -5.412868e-05
## junction_control3                                 7.733924e-05
## second_road_class                                -9.554641e-05
## second_road_number                               -1.037174e-07
## pedestrian_crossing_human_control1                6.576820e-08
## pedestrian_crossing_human_control2                7.805708e-05
## pedestrian_crossing_physical_facilities1         -7.543038e-05
## pedestrian_crossing_physical_facilities4         -1.513339e-04
## pedestrian_crossing_physical_facilities5          5.144921e-05
## pedestrian_crossing_physical_facilities7          2.290549e-05
## pedestrian_crossing_physical_facilities8         -1.834510e-04
## light_conditions4                                 2.140368e-05
## light_conditions5                                 2.537683e-05
## light_conditions6                                -7.457889e-05
## light_conditions7                                 7.509601e-06
## weather_conditions2                               1.838473e-04
## weather_conditions3                              -1.368988e-05
## weather_conditions4                               2.789658e-05
## weather_conditions5                              -8.416677e-06
## weather_conditions6                              -3.607001e-06
## weather_conditions7                              -1.471846e-05
## weather_conditions8                               8.242865e-05
## road_surface_conditions2                         -1.011395e-04
## road_surface_conditions3                          4.846497e-07
## road_surface_conditions4                         -4.329883e-05
## road_surface_conditions5                          7.622799e-06
## special_conditions_at_site1                       7.829839e-06
## special_conditions_at_site2                       1.884580e-07
## special_conditions_at_site3                      -5.016003e-06
## special_conditions_at_site4                       2.960289e-05
## special_conditions_at_site5                       8.796193e-06
## special_conditions_at_site6                       3.476219e-06
## special_conditions_at_site7                       1.798408e-05
## carriageway_hazards1                             -2.405485e-06
## carriageway_hazards2                              1.818098e-05
## carriageway_hazards3                             -1.693944e-06
## carriageway_hazards6                              3.843292e-06
## carriageway_hazards7                              2.263260e-05
## did_police_officer_attend_scene_of_collision1    -1.935263e-04
## 1|2                                              -3.206487e-05
## 2|3                                               1.049512e-04
##                                               junction_control1
## police_force                                       3.355075e-08
## number_of_vehicles                                -3.154932e-06
## number_of_casualties                               1.138980e-06
## day_of_week                                       -5.333783e-07
## first_road_class                                  -7.280936e-07
## first_road_number                                  2.294013e-09
## road_type2                                        -2.334400e-05
## road_type3                                         5.807042e-05
## road_type6                                         5.754346e-06
## road_type7                                        -1.036824e-05
## speed_limit                                       -4.494749e-07
## junction_detail1                                   2.446776e-06
## junction_detail2                                  -2.375696e-05
## junction_detail5                                   6.540642e-06
## junction_detail6                                   2.416972e-05
## junction_detail7                                   2.809984e-06
## junction_detail8                                  -9.344635e-05
## junction_detail9                                  -4.366449e-06
## junction_control1                                  1.123892e-05
## junction_control2                                 -2.220423e-04
## junction_control3                                  1.484511e-05
## second_road_class                                 -4.866020e-06
## second_road_number                                 6.710704e-09
## pedestrian_crossing_human_control1                 4.202505e-08
## pedestrian_crossing_human_control2                 2.121557e-05
## pedestrian_crossing_physical_facilities1          -3.884074e-05
## pedestrian_crossing_physical_facilities4           8.705454e-05
## pedestrian_crossing_physical_facilities5           1.924183e-04
## pedestrian_crossing_physical_facilities7          -2.443937e-06
## pedestrian_crossing_physical_facilities8          -2.034267e-04
## light_conditions4                                  1.229727e-05
## light_conditions5                                 -1.035433e-07
## light_conditions6                                  5.091528e-06
## light_conditions7                                  2.576231e-06
## weather_conditions2                               -1.109812e-05
## weather_conditions3                               -7.330432e-07
## weather_conditions4                               -1.021416e-06
## weather_conditions5                               -8.340227e-07
## weather_conditions6                               -2.912897e-08
## weather_conditions7                                2.977259e-07
## weather_conditions8                                1.410061e-05
## road_surface_conditions2                          -2.089439e-05
## road_surface_conditions3                          -3.798377e-07
## road_surface_conditions4                           1.345123e-06
## road_surface_conditions5                           2.058944e-07
## special_conditions_at_site1                       -2.573672e-07
## special_conditions_at_site2                        5.319799e-07
## special_conditions_at_site3                        1.214545e-06
## special_conditions_at_site4                       -5.468399e-06
## special_conditions_at_site5                       -1.351378e-06
## special_conditions_at_site6                       -2.807191e-07
## special_conditions_at_site7                       -2.338561e-07
## carriageway_hazards1                              -7.019083e-07
## carriageway_hazards2                               5.611615e-06
## carriageway_hazards3                              -2.751106e-07
## carriageway_hazards6                               1.481517e-06
## carriageway_hazards7                              -1.863378e-07
## did_police_officer_attend_scene_of_collision1      5.610785e-05
## 1|2                                               -1.637443e-06
## 2|3                                               -5.056436e-06
##                                               junction_control2
## police_force                                       4.953724e-06
## number_of_vehicles                                -6.837069e-05
## number_of_casualties                              -3.962748e-05
## day_of_week                                       -3.150967e-05
## first_road_class                                   8.300519e-05
## first_road_number                                 -9.582243e-08
## road_type2                                         5.220049e-04
## road_type3                                        -9.493209e-04
## road_type6                                        -1.037216e-04
## road_type7                                         2.807232e-04
## speed_limit                                        1.101766e-05
## junction_detail1                                  -1.928299e-04
## junction_detail2                                   5.353975e-04
## junction_detail5                                  -4.223387e-05
## junction_detail6                                  -1.218146e-03
## junction_detail7                                   3.282205e-04
## junction_detail8                                   1.233873e-03
## junction_detail9                                  -5.412868e-05
## junction_control1                                 -2.220423e-04
## junction_control2                                  6.169445e-03
## junction_control3                                 -3.459578e-04
## second_road_class                                  6.149467e-05
## second_road_number                                -2.663309e-07
## pedestrian_crossing_human_control1                 3.745325e-05
## pedestrian_crossing_human_control2                -1.516668e-04
## pedestrian_crossing_physical_facilities1           1.593208e-03
## pedestrian_crossing_physical_facilities4          -4.626917e-04
## pedestrian_crossing_physical_facilities5          -2.715628e-03
## pedestrian_crossing_physical_facilities7           4.527045e-05
## pedestrian_crossing_physical_facilities8           3.376411e-03
## light_conditions4                                 -3.335997e-04
## light_conditions5                                  3.227937e-06
## light_conditions6                                 -9.184295e-05
## light_conditions7                                 -5.433020e-05
## weather_conditions2                               -2.082748e-04
## weather_conditions3                                1.503495e-05
## weather_conditions4                                9.924740e-06
## weather_conditions5                                3.517761e-05
## weather_conditions6                               -5.630630e-07
## weather_conditions7                               -5.571605e-06
## weather_conditions8                               -2.273801e-04
## road_surface_conditions2                           2.197832e-04
## road_surface_conditions3                           3.556385e-06
## road_surface_conditions4                           4.741007e-06
## road_surface_conditions5                          -4.095462e-06
## special_conditions_at_site1                        9.429157e-06
## special_conditions_at_site2                       -8.906644e-06
## special_conditions_at_site3                       -3.162289e-05
## special_conditions_at_site4                        1.027285e-04
## special_conditions_at_site5                        2.194411e-05
## special_conditions_at_site6                        4.922483e-06
## special_conditions_at_site7                        7.225453e-06
## carriageway_hazards1                               1.637207e-05
## carriageway_hazards2                              -1.180279e-04
## carriageway_hazards3                               5.252020e-06
## carriageway_hazards6                              -1.361346e-05
## carriageway_hazards7                              -6.835701e-07
## did_police_officer_attend_scene_of_collision1     -7.027094e-04
## 1|2                                               -2.452352e-04
## 2|3                                                5.307537e-04
##                                               junction_control3
## police_force                                      -4.518904e-08
## number_of_vehicles                                 8.534071e-06
## number_of_casualties                              -2.859499e-06
## day_of_week                                        8.974881e-07
## first_road_class                                  -4.963417e-06
## first_road_number                                  4.225361e-09
## road_type2                                         1.007770e-05
## road_type3                                         1.824074e-08
## road_type6                                        -2.573908e-05
## road_type7                                         8.116157e-06
## speed_limit                                       -3.096979e-07
## junction_detail1                                  -2.481114e-05
## junction_detail2                                  -1.082205e-05
## junction_detail5                                   2.021489e-05
## junction_detail6                                   1.266791e-04
## junction_detail7                                  -1.702607e-05
## junction_detail8                                  -2.218093e-04
## junction_detail9                                   7.733925e-05
## junction_control1                                  1.484511e-05
## junction_control2                                 -3.459578e-04
## junction_control3                                  2.647883e-05
## second_road_class                                 -8.922666e-07
## second_road_number                                 9.963103e-09
## pedestrian_crossing_human_control1                -3.213865e-06
## pedestrian_crossing_human_control2                 1.954622e-05
## pedestrian_crossing_physical_facilities1          -1.817226e-04
## pedestrian_crossing_physical_facilities4           7.701193e-05
## pedestrian_crossing_physical_facilities5           2.558335e-04
## pedestrian_crossing_physical_facilities7          -3.946308e-06
## pedestrian_crossing_physical_facilities8          -2.036175e-04
## light_conditions4                                  1.400378e-06
## light_conditions5                                 -3.307189e-07
## light_conditions6                                  1.138881e-05
## light_conditions7                                  3.211958e-06
## weather_conditions2                               -9.634146e-07
## weather_conditions3                               -9.931204e-07
## weather_conditions4                                7.947519e-07
## weather_conditions5                               -2.866939e-06
## weather_conditions6                               -1.903256e-07
## weather_conditions7                                5.083275e-07
## weather_conditions8                                2.036165e-05
## road_surface_conditions2                          -7.407196e-06
## road_surface_conditions3                          -4.459637e-07
## road_surface_conditions4                          -1.515992e-06
## road_surface_conditions5                           5.125526e-07
## special_conditions_at_site1                       -2.449237e-07
## special_conditions_at_site2                        6.595688e-07
## special_conditions_at_site3                        2.407771e-06
## special_conditions_at_site4                       -6.940690e-06
## special_conditions_at_site5                       -1.990027e-06
## special_conditions_at_site6                       -2.568171e-07
## special_conditions_at_site7                       -1.256396e-06
## carriageway_hazards1                              -1.211496e-06
## carriageway_hazards2                               6.626702e-06
## carriageway_hazards3                               2.419794e-07
## carriageway_hazards6                               7.089931e-07
## carriageway_hazards7                               2.175256e-07
## did_police_officer_attend_scene_of_collision1      4.381482e-05
## 1|2                                                1.772568e-05
## 2|3                                               -1.593870e-05
##                                               second_road_class
## police_force                                      -8.859821e-07
## number_of_vehicles                                -1.708132e-04
## number_of_casualties                              -2.155419e-05
## day_of_week                                       -3.566963e-05
## first_road_class                                  -1.934877e-04
## first_road_number                                 -1.249362e-07
## road_type2                                         1.919732e-04
## road_type3                                        -2.731018e-04
## road_type6                                        -3.923356e-04
## road_type7                                         1.086145e-04
## speed_limit                                       -5.511312e-06
## junction_detail1                                   1.769926e-04
## junction_detail2                                   9.008522e-05
## junction_detail5                                   3.730539e-05
## junction_detail6                                   3.861182e-05
## junction_detail7                                  -3.334143e-05
## junction_detail8                                  -1.426791e-04
## junction_detail9                                  -9.554641e-05
## junction_control1                                 -4.866020e-06
## junction_control2                                  6.149467e-05
## junction_control3                                 -8.922666e-07
## second_road_class                                  5.369294e-04
## second_road_number                                 2.878171e-07
## pedestrian_crossing_human_control1                -4.230335e-06
## pedestrian_crossing_human_control2                -8.888119e-06
## pedestrian_crossing_physical_facilities1          -1.355548e-04
## pedestrian_crossing_physical_facilities4          -7.713600e-05
## pedestrian_crossing_physical_facilities5           4.639397e-05
## pedestrian_crossing_physical_facilities7          -7.485765e-07
## pedestrian_crossing_physical_facilities8           8.585618e-05
## light_conditions4                                 -7.300303e-05
## light_conditions5                                 -1.350814e-06
## light_conditions6                                  5.528062e-06
## light_conditions7                                  1.214792e-06
## weather_conditions2                               -3.736692e-05
## weather_conditions3                                4.313042e-06
## weather_conditions4                                1.768710e-06
## weather_conditions5                               -1.759960e-06
## weather_conditions6                               -3.269920e-07
## weather_conditions7                               -5.857977e-07
## weather_conditions8                               -2.766982e-06
## road_surface_conditions2                           1.550949e-05
## road_surface_conditions3                           1.454370e-06
## road_surface_conditions4                          -2.303456e-06
## road_surface_conditions5                           7.151434e-08
## special_conditions_at_site1                       -7.039635e-07
## special_conditions_at_site2                       -2.420964e-07
## special_conditions_at_site3                        1.187851e-06
## special_conditions_at_site4                        6.014593e-07
## special_conditions_at_site5                       -1.354101e-06
## special_conditions_at_site6                        9.306651e-07
## special_conditions_at_site7                       -2.272080e-06
## carriageway_hazards1                               4.437174e-07
## carriageway_hazards2                              -6.686805e-06
## carriageway_hazards3                              -5.754750e-08
## carriageway_hazards6                              -3.342501e-06
## carriageway_hazards7                               1.084561e-06
## did_police_officer_attend_scene_of_collision1     -4.538232e-04
## 1|2                                                5.977153e-05
## 2|3                                                5.994620e-04
##                                               second_road_number
## police_force                                        5.292789e-11
## number_of_vehicles                                 -1.344528e-07
## number_of_casualties                               -1.865061e-08
## day_of_week                                        -1.909807e-08
## first_road_class                                   -1.190741e-07
## first_road_number                                  -1.305317e-10
## road_type2                                          6.268159e-08
## road_type3                                         -1.444126e-08
## road_type6                                         -9.247464e-08
## road_type7                                          3.061298e-08
## speed_limit                                        -7.871999e-09
## junction_detail1                                   -1.572121e-07
## junction_detail2                                    2.208561e-08
## junction_detail5                                    3.973306e-08
## junction_detail6                                   -3.058136e-08
## junction_detail7                                   -1.530615e-08
## junction_detail8                                    7.152835e-08
## junction_detail9                                   -1.037174e-07
## junction_control1                                   6.710705e-09
## junction_control2                                  -2.663309e-07
## junction_control3                                   9.963103e-09
## second_road_class                                   2.878171e-07
## second_road_number                                  8.267255e-10
## pedestrian_crossing_human_control1                 -1.476259e-09
## pedestrian_crossing_human_control2                 -4.060253e-09
## pedestrian_crossing_physical_facilities1           -4.728962e-08
## pedestrian_crossing_physical_facilities4           -2.276316e-08
## pedestrian_crossing_physical_facilities5            2.972981e-08
## pedestrian_crossing_physical_facilities7           -3.937938e-09
## pedestrian_crossing_physical_facilities8           -1.293845e-07
## light_conditions4                                  -4.070604e-08
## light_conditions5                                  -1.137410e-09
## light_conditions6                                   2.697183e-08
## light_conditions7                                   9.991399e-10
## weather_conditions2                                -3.356918e-08
## weather_conditions3                                 9.865819e-10
## weather_conditions4                                -1.208937e-09
## weather_conditions5                                 7.268857e-10
## weather_conditions6                                 4.770229e-10
## weather_conditions7                                 2.413786e-10
## weather_conditions8                                 3.295760e-09
## road_surface_conditions2                           -3.783028e-08
## road_surface_conditions3                            3.375062e-10
## road_surface_conditions4                            2.687627e-09
## road_surface_conditions5                            3.544074e-11
## special_conditions_at_site1                        -1.175081e-09
## special_conditions_at_site2                         1.534083e-10
## special_conditions_at_site3                         1.287873e-09
## special_conditions_at_site4                        -4.671520e-09
## special_conditions_at_site5                        -2.992739e-10
## special_conditions_at_site6                        -4.718425e-10
## special_conditions_at_site7                         4.428527e-11
## carriageway_hazards1                               -1.218699e-09
## carriageway_hazards2                                4.358387e-09
## carriageway_hazards3                               -6.921288e-11
## carriageway_hazards6                               -7.027293e-10
## carriageway_hazards7                                7.047332e-11
## did_police_officer_attend_scene_of_collision1      -1.480564e-07
## 1|2                                                 5.732749e-08
## 2|3                                                 2.868652e-07
##                                               pedestrian_crossing_human_control1
## police_force                                                        2.395724e-07
## number_of_vehicles                                                 -2.591938e-06
## number_of_casualties                                                1.940823e-06
## day_of_week                                                        -6.607910e-07
## first_road_class                                                    1.173898e-07
## first_road_number                                                  -1.843998e-09
## road_type2                                                         -1.394039e-05
## road_type3                                                          3.032577e-05
## road_type6                                                          2.129922e-05
## road_type7                                                         -3.205710e-06
## speed_limit                                                         1.045784e-07
## junction_detail1                                                   -6.542835e-06
## junction_detail2                                                   -7.465869e-07
## junction_detail5                                                    9.497719e-07
## junction_detail6                                                   -2.644613e-05
## junction_detail7                                                    1.803164e-05
## junction_detail8                                                   -4.009148e-05
## junction_detail9                                                    6.576843e-08
## junction_control1                                                   4.202505e-08
## junction_control2                                                   3.745325e-05
## junction_control3                                                  -3.213865e-06
## second_road_class                                                  -4.230335e-06
## second_road_number                                                 -1.476259e-09
## pedestrian_crossing_human_control1                                  5.391267e-06
## pedestrian_crossing_human_control2                                  1.771069e-05
## pedestrian_crossing_physical_facilities1                            2.315998e-04
## pedestrian_crossing_physical_facilities4                            3.114937e-05
## pedestrian_crossing_physical_facilities5                           -1.909016e-05
## pedestrian_crossing_physical_facilities7                            2.892801e-07
## pedestrian_crossing_physical_facilities8                           -8.441379e-05
## light_conditions4                                                  -1.831411e-05
## light_conditions5                                                   1.516527e-06
## light_conditions6                                                   2.270252e-06
## light_conditions7                                                   9.403857e-07
## weather_conditions2                                                -3.613171e-05
## weather_conditions3                                                 1.799963e-07
## weather_conditions4                                                -1.435644e-06
## weather_conditions5                                                 5.188391e-06
## weather_conditions6                                                 4.868144e-08
## weather_conditions7                                                 2.440994e-07
## weather_conditions8                                                 1.076350e-05
## road_surface_conditions2                                            2.408211e-05
## road_surface_conditions3                                           -2.842363e-07
## road_surface_conditions4                                            3.065137e-06
## road_surface_conditions5                                           -1.763322e-07
## special_conditions_at_site1                                         1.052893e-07
## special_conditions_at_site2                                        -2.527438e-08
## special_conditions_at_site3                                         5.705832e-07
## special_conditions_at_site4                                        -9.959504e-07
## special_conditions_at_site5                                        -1.700828e-07
## special_conditions_at_site6                                         1.132731e-08
## special_conditions_at_site7                                         1.541308e-06
## carriageway_hazards1                                                1.090760e-06
## carriageway_hazards2                                               -7.138995e-07
## carriageway_hazards3                                               -6.669961e-07
## carriageway_hazards6                                                1.940882e-06
## carriageway_hazards7                                               -8.424209e-07
## did_police_officer_attend_scene_of_collision1                      -5.526165e-06
## 1|2                                                                -1.417520e-05
## 2|3                                                                -2.795677e-07
##                                               pedestrian_crossing_human_control2
## police_force                                                        8.186182e-07
## number_of_vehicles                                                  1.765982e-06
## number_of_casualties                                               -1.593325e-06
## day_of_week                                                        -6.122904e-06
## first_road_class                                                    7.872740e-06
## first_road_number                                                  -5.767009e-09
## road_type2                                                          9.705035e-05
## road_type3                                                         -1.225074e-04
## road_type6                                                         -5.640583e-05
## road_type7                                                          6.859331e-05
## speed_limit                                                         1.371494e-06
## junction_detail1                                                    2.315588e-05
## junction_detail2                                                   -3.286340e-06
## junction_detail5                                                    4.033146e-05
## junction_detail6                                                   -4.302420e-05
## junction_detail7                                                    5.530483e-05
## junction_detail8                                                   -3.483925e-04
## junction_detail9                                                    7.805708e-05
## junction_control1                                                   2.121557e-05
## junction_control2                                                  -1.516668e-04
## junction_control3                                                   1.954622e-05
## second_road_class                                                  -8.888119e-06
## second_road_number                                                 -4.060253e-09
## pedestrian_crossing_human_control1                                  1.771069e-05
## pedestrian_crossing_human_control2                                  1.461325e-04
## pedestrian_crossing_physical_facilities1                            5.364639e-04
## pedestrian_crossing_physical_facilities4                            6.635721e-04
## pedestrian_crossing_physical_facilities5                            4.221363e-04
## pedestrian_crossing_physical_facilities7                           -6.469576e-06
## pedestrian_crossing_physical_facilities8                           -7.924309e-04
## light_conditions4                                                  -6.206959e-05
## light_conditions5                                                   6.782579e-06
## light_conditions6                                                   4.837291e-05
## light_conditions7                                                   5.694500e-06
## weather_conditions2                                                -2.548522e-04
## weather_conditions3                                                 3.787984e-06
## weather_conditions4                                                 1.006096e-06
## weather_conditions5                                                 2.931905e-05
## weather_conditions6                                                 3.117539e-07
## weather_conditions7                                                 3.028495e-06
## weather_conditions8                                                 9.300558e-05
## road_surface_conditions2                                            1.612014e-04
## road_surface_conditions3                                           -2.213269e-06
## road_surface_conditions4                                            1.268434e-05
## road_surface_conditions5                                           -2.368425e-07
## special_conditions_at_site1                                        -3.152995e-07
## special_conditions_at_site2                                         5.060348e-07
## special_conditions_at_site3                                         4.437342e-06
## special_conditions_at_site4                                        -1.278019e-05
## special_conditions_at_site5                                        -4.185750e-06
## special_conditions_at_site6                                        -2.635243e-07
## special_conditions_at_site7                                         3.638359e-06
## carriageway_hazards1                                                2.284101e-06
## carriageway_hazards2                                                1.046928e-05
## carriageway_hazards3                                               -2.126509e-06
## carriageway_hazards6                                                7.474515e-06
## carriageway_hazards7                                               -2.400604e-06
## did_police_officer_attend_scene_of_collision1                       1.724801e-05
## 1|2                                                                -4.249021e-05
## 2|3                                                                 3.742400e-05
##                                               pedestrian_crossing_physical_facilities1
## police_force                                                              1.100931e-05
## number_of_vehicles                                                        6.608274e-05
## number_of_casualties                                                      4.535281e-05
## day_of_week                                                              -1.987012e-05
## first_road_class                                                         -4.928994e-05
## first_road_number                                                        -8.640246e-08
## road_type2                                                               -1.134795e-04
## road_type3                                                                4.098452e-04
## road_type6                                                                4.517594e-04
## road_type7                                                                4.147893e-05
## speed_limit                                                               7.168176e-06
## junction_detail1                                                          3.358498e-05
## junction_detail2                                                          1.623626e-04
## junction_detail5                                                          1.323253e-05
## junction_detail6                                                         -2.175293e-04
## junction_detail7                                                          5.000222e-04
## junction_detail8                                                         -4.803027e-04
## junction_detail9                                                         -7.543038e-05
## junction_control1                                                        -3.884074e-05
## junction_control2                                                         1.593208e-03
## junction_control3                                                        -1.817226e-04
## second_road_class                                                        -1.355548e-04
## second_road_number                                                       -4.728962e-08
## pedestrian_crossing_human_control1                                        2.315998e-04
## pedestrian_crossing_human_control2                                        5.364639e-04
## pedestrian_crossing_physical_facilities1                                  1.177541e-02
## pedestrian_crossing_physical_facilities4                                 -9.229430e-04
## pedestrian_crossing_physical_facilities5                                 -1.667646e-03
## pedestrian_crossing_physical_facilities7                                  2.215668e-05
## pedestrian_crossing_physical_facilities8                                 -3.335096e-03
## light_conditions4                                                        -1.224142e-04
## light_conditions5                                                         5.151092e-05
## light_conditions6                                                        -1.129632e-04
## light_conditions7                                                         1.705932e-05
## weather_conditions2                                                       2.799663e-05
## weather_conditions3                                                      -5.127263e-05
## weather_conditions4                                                      -1.457986e-04
## weather_conditions5                                                       5.331443e-05
## weather_conditions6                                                      -3.499556e-06
## weather_conditions7                                                      -2.080921e-05
## weather_conditions8                                                      -2.887044e-06
## road_surface_conditions2                                                 -1.952313e-05
## road_surface_conditions3                                                 -9.460345e-06
## road_surface_conditions4                                                  1.284562e-04
## road_surface_conditions5                                                 -3.165802e-06
## special_conditions_at_site1                                               5.431175e-06
## special_conditions_at_site2                                              -3.202997e-06
## special_conditions_at_site3                                               2.977817e-05
## special_conditions_at_site4                                              -1.858321e-05
## special_conditions_at_site5                                              -1.768836e-06
## special_conditions_at_site6                                               3.005658e-06
## special_conditions_at_site7                                               6.974366e-05
## carriageway_hazards1                                                      5.625131e-05
## carriageway_hazards2                                                     -5.694752e-05
## carriageway_hazards3                                                     -2.499424e-05
## carriageway_hazards6                                                      8.083507e-05
## carriageway_hazards7                                                     -3.093454e-05
## did_police_officer_attend_scene_of_collision1                            -3.737895e-04
## 1|2                                                                      -5.228420e-04
## 2|3                                                                      -3.822358e-05
##                                               pedestrian_crossing_physical_facilities4
## police_force                                                              1.211945e-06
## number_of_vehicles                                                       -2.052710e-05
## number_of_casualties                                                     -2.500148e-05
## day_of_week                                                              -2.333226e-05
## first_road_class                                                          9.533088e-05
## first_road_number                                                        -2.642959e-08
## road_type2                                                                2.481052e-04
## road_type3                                                               -2.290365e-04
## road_type6                                                               -7.306496e-05
## road_type7                                                                1.583457e-04
## speed_limit                                                               9.726765e-06
## junction_detail1                                                          4.586071e-05
## junction_detail2                                                         -1.387852e-04
## junction_detail5                                                          6.274623e-05
## junction_detail6                                                         -5.308074e-05
## junction_detail7                                                          1.058069e-04
## junction_detail8                                                         -7.873165e-04
## junction_detail9                                                         -1.513339e-04
## junction_control1                                                         8.705454e-05
## junction_control2                                                        -4.626917e-04
## junction_control3                                                         7.701193e-05
## second_road_class                                                        -7.713600e-05
## second_road_number                                                       -2.276316e-08
## pedestrian_crossing_human_control1                                        3.114937e-05
## pedestrian_crossing_human_control2                                        6.635721e-04
## pedestrian_crossing_physical_facilities1                                 -9.229430e-04
## pedestrian_crossing_physical_facilities4                                  7.365342e-03
## pedestrian_crossing_physical_facilities5                                  4.157933e-05
## pedestrian_crossing_physical_facilities7                                 -3.292976e-05
## pedestrian_crossing_physical_facilities8                                 -2.804694e-03
## light_conditions4                                                        -1.657606e-04
## light_conditions5                                                         2.275665e-05
## light_conditions6                                                         6.900834e-05
## light_conditions7                                                         1.465033e-05
## weather_conditions2                                                       3.387410e-05
## weather_conditions3                                                      -1.133246e-05
## weather_conditions4                                                      -2.371079e-05
## weather_conditions5                                                      -3.627364e-06
## weather_conditions6                                                      -1.850814e-06
## weather_conditions7                                                       4.757167e-07
## weather_conditions8                                                       3.976824e-05
## road_surface_conditions2                                                 -3.826238e-06
## road_surface_conditions3                                                 -8.131918e-06
## road_surface_conditions4                                                  1.971019e-05
## road_surface_conditions5                                                 -1.313509e-06
## special_conditions_at_site1                                              -1.180059e-05
## special_conditions_at_site2                                              -1.854990e-06
## special_conditions_at_site3                                              -4.040440e-06
## special_conditions_at_site4                                              -3.624528e-05
## special_conditions_at_site5                                              -1.509150e-05
## special_conditions_at_site6                                              -2.075439e-06
## special_conditions_at_site7                                              -7.498738e-06
## carriageway_hazards1                                                     -7.214091e-06
## carriageway_hazards2                                                      5.490107e-05
## carriageway_hazards3                                                     -1.500156e-05
## carriageway_hazards6                                                     -3.044927e-06
## carriageway_hazards7                                                     -1.167285e-05
## did_police_officer_attend_scene_of_collision1                            -1.771239e-04
## 1|2                                                                      -1.483107e-04
## 2|3                                                                       1.778656e-04
##                                               pedestrian_crossing_physical_facilities5
## police_force                                                             -2.309675e-07
## number_of_vehicles                                                        1.905057e-05
## number_of_casualties                                                     -1.204955e-05
## day_of_week                                                              -2.738445e-05
## first_road_class                                                          4.768079e-05
## first_road_number                                                         1.268558e-08
## road_type2                                                                9.646316e-05
## road_type3                                                               -4.168168e-04
## road_type6                                                               -5.683936e-05
## road_type7                                                                6.482772e-05
## speed_limit                                                               3.269362e-06
## junction_detail1                                                          5.979178e-04
## junction_detail2                                                         -3.956059e-04
## junction_detail5                                                          1.061452e-04
## junction_detail6                                                         -5.180848e-04
## junction_detail7                                                          1.805313e-04
## junction_detail8                                                         -1.231473e-03
## junction_detail9                                                          5.144921e-05
## junction_control1                                                         1.924183e-04
## junction_control2                                                        -2.715628e-03
## junction_control3                                                         2.558335e-04
## second_road_class                                                         4.639397e-05
## second_road_number                                                        2.972981e-08
## pedestrian_crossing_human_control1                                       -1.909016e-05
## pedestrian_crossing_human_control2                                        4.221363e-04
## pedestrian_crossing_physical_facilities1                                 -1.667646e-03
## pedestrian_crossing_physical_facilities4                                  4.157933e-05
## pedestrian_crossing_physical_facilities5                                  6.916396e-03
## pedestrian_crossing_physical_facilities7                                 -6.090116e-05
## pedestrian_crossing_physical_facilities8                                 -4.330399e-03
## light_conditions4                                                        -1.398282e-04
## light_conditions5                                                         3.831468e-07
## light_conditions6                                                         1.178602e-04
## light_conditions7                                                         4.942927e-05
## weather_conditions2                                                       2.511130e-04
## weather_conditions3                                                       3.575062e-07
## weather_conditions4                                                      -2.745816e-05
## weather_conditions5                                                      -2.660607e-05
## weather_conditions6                                                      -1.067526e-06
## weather_conditions7                                                      -1.097740e-06
## weather_conditions8                                                       1.888672e-04
## road_surface_conditions2                                                 -1.289023e-04
## road_surface_conditions3                                                 -7.429853e-06
## road_surface_conditions4                                                  9.486572e-06
## road_surface_conditions5                                                  8.258771e-06
## special_conditions_at_site1                                              -1.698729e-06
## special_conditions_at_site2                                               1.388724e-05
## special_conditions_at_site3                                               1.088155e-05
## special_conditions_at_site4                                              -1.243884e-04
## special_conditions_at_site5                                              -3.309806e-05
## special_conditions_at_site6                                              -3.991947e-06
## special_conditions_at_site7                                              -8.338341e-06
## carriageway_hazards1                                                     -2.276037e-05
## carriageway_hazards2                                                      1.074067e-04
## carriageway_hazards3                                                      7.495099e-06
## carriageway_hazards6                                                      2.907911e-05
## carriageway_hazards7                                                      9.970576e-06
## did_police_officer_attend_scene_of_collision1                            -9.001660e-05
## 1|2                                                                       5.062914e-05
## 2|3                                                                       2.423078e-04
##                                               pedestrian_crossing_physical_facilities7
## police_force                                                              1.000949e-08
## number_of_vehicles                                                       -4.085538e-06
## number_of_casualties                                                     -7.687258e-07
## day_of_week                                                              -7.040723e-07
## first_road_class                                                         -1.224189e-06
## first_road_number                                                        -1.684605e-09
## road_type2                                                               -4.414609e-05
## road_type3                                                                4.551011e-05
## road_type6                                                                2.865684e-05
## road_type7                                                               -2.458880e-05
## speed_limit                                                              -5.102692e-07
## junction_detail1                                                          7.671492e-05
## junction_detail2                                                         -2.324834e-05
## junction_detail5                                                         -2.580589e-05
## junction_detail6                                                          1.241786e-05
## junction_detail7                                                         -6.171080e-06
## junction_detail8                                                          3.835682e-05
## junction_detail9                                                          2.290549e-05
## junction_control1                                                        -2.443937e-06
## junction_control2                                                         4.527045e-05
## junction_control3                                                        -3.946308e-06
## second_road_class                                                        -7.485765e-07
## second_road_number                                                       -3.937938e-09
## pedestrian_crossing_human_control1                                        2.892801e-07
## pedestrian_crossing_human_control2                                       -6.469576e-06
## pedestrian_crossing_physical_facilities1                                  2.215668e-05
## pedestrian_crossing_physical_facilities4                                 -3.292976e-05
## pedestrian_crossing_physical_facilities5                                 -6.090116e-05
## pedestrian_crossing_physical_facilities7                                  2.099379e-06
## pedestrian_crossing_physical_facilities8                                  5.699683e-05
## light_conditions4                                                        -1.252301e-06
## light_conditions5                                                         4.002507e-07
## light_conditions6                                                        -7.687013e-06
## light_conditions7                                                         5.793275e-07
## weather_conditions2                                                      -2.908202e-05
## weather_conditions3                                                       1.154416e-06
## weather_conditions4                                                       1.833297e-06
## weather_conditions5                                                       3.141770e-06
## weather_conditions6                                                       7.955478e-08
## weather_conditions7                                                       2.759278e-07
## weather_conditions8                                                       5.684301e-06
## road_surface_conditions2                                                  1.216139e-05
## road_surface_conditions3                                                  1.986913e-07
## road_surface_conditions4                                                 -6.352496e-07
## road_surface_conditions5                                                 -1.980105e-07
## special_conditions_at_site1                                               2.112267e-07
## special_conditions_at_site2                                              -5.279531e-08
## special_conditions_at_site3                                              -2.746061e-07
## special_conditions_at_site4                                               2.065626e-06
## special_conditions_at_site5                                               5.298364e-07
## special_conditions_at_site6                                               1.438162e-07
## special_conditions_at_site7                                               3.966352e-07
## carriageway_hazards1                                                      4.600679e-07
## carriageway_hazards2                                                     -9.439215e-07
## carriageway_hazards3                                                     -5.167397e-07
## carriageway_hazards6                                                      2.733962e-08
## carriageway_hazards7                                                      1.296189e-07
## did_police_officer_attend_scene_of_collision1                             3.151922e-06
## 1|2                                                                      -1.217584e-05
## 2|3                                                                       1.980894e-06
##                                               pedestrian_crossing_physical_facilities8
## police_force                                                             -3.989746e-06
## number_of_vehicles                                                       -1.577418e-04
## number_of_casualties                                                     -3.081081e-05
## day_of_week                                                               1.592437e-05
## first_road_class                                                         -5.750225e-05
## first_road_number                                                        -1.391147e-08
## road_type2                                                               -3.727068e-04
## road_type3                                                                8.976454e-05
## road_type6                                                                2.208877e-04
## road_type7                                                               -9.139674e-05
## speed_limit                                                              -7.136594e-06
## junction_detail1                                                         -2.001378e-04
## junction_detail2                                                          7.033420e-04
## junction_detail5                                                          6.332121e-05
## junction_detail6                                                         -3.668934e-04
## junction_detail7                                                          7.694212e-05
## junction_detail8                                                         -1.693201e-03
## junction_detail9                                                         -1.834510e-04
## junction_control1                                                        -2.034267e-04
## junction_control2                                                         3.376411e-03
## junction_control3                                                        -2.036175e-04
## second_road_class                                                         8.585618e-05
## second_road_number                                                       -1.293845e-07
## pedestrian_crossing_human_control1                                       -8.441379e-05
## pedestrian_crossing_human_control2                                       -7.924309e-04
## pedestrian_crossing_physical_facilities1                                 -3.335096e-03
## pedestrian_crossing_physical_facilities4                                 -2.804694e-03
## pedestrian_crossing_physical_facilities5                                 -4.330399e-03
## pedestrian_crossing_physical_facilities7                                  5.699683e-05
## pedestrian_crossing_physical_facilities8                                  7.371276e-03
## light_conditions4                                                         1.221564e-05
## light_conditions5                                                        -4.450484e-05
## light_conditions6                                                        -2.067783e-04
## light_conditions7                                                        -4.513611e-05
## weather_conditions2                                                      -6.096083e-05
## weather_conditions3                                                       1.822313e-05
## weather_conditions4                                                       8.094481e-05
## weather_conditions5                                                      -4.832577e-05
## weather_conditions6                                                      -4.333533e-06
## weather_conditions7                                                       7.551618e-06
## weather_conditions8                                                      -2.054850e-04
## road_surface_conditions2                                                  3.278982e-05
## road_surface_conditions3                                                  1.310592e-05
## road_surface_conditions4                                                 -6.904045e-05
## road_surface_conditions5                                                 -3.294181e-06
## special_conditions_at_site1                                               9.506442e-06
## special_conditions_at_site2                                              -1.033060e-05
## special_conditions_at_site3                                              -2.760509e-05
## special_conditions_at_site4                                               1.143290e-04
## special_conditions_at_site5                                               2.417476e-05
## special_conditions_at_site6                                               6.865329e-06
## special_conditions_at_site7                                              -3.265842e-05
## carriageway_hazards1                                                      1.862047e-06
## carriageway_hazards2                                                     -1.510750e-04
## carriageway_hazards3                                                      1.588106e-05
## carriageway_hazards6                                                     -4.397980e-05
## carriageway_hazards7                                                      2.834526e-06
## did_police_officer_attend_scene_of_collision1                             4.669494e-04
## 1|2                                                                      -2.004433e-05
## 2|3                                                                       1.480809e-05
##                                               light_conditions4
## police_force                                       3.338447e-06
## number_of_vehicles                                -8.852067e-06
## number_of_casualties                              -6.112524e-05
## day_of_week                                       -2.245483e-05
## first_road_class                                  -1.541136e-05
## first_road_number                                 -1.575576e-08
## road_type2                                         9.051436e-05
## road_type3                                        -1.458473e-04
## road_type6                                         6.630137e-05
## road_type7                                         4.418842e-05
## speed_limit                                        1.368351e-05
## junction_detail1                                  -2.652497e-04
## junction_detail2                                   5.393385e-05
## junction_detail5                                   9.688379e-05
## junction_detail6                                   8.980499e-05
## junction_detail7                                  -6.622260e-05
## junction_detail8                                   2.397676e-04
## junction_detail9                                   2.140368e-05
## junction_control1                                  1.229727e-05
## junction_control2                                 -3.335997e-04
## junction_control3                                  1.400378e-06
## second_road_class                                 -7.300303e-05
## second_road_number                                -4.070604e-08
## pedestrian_crossing_human_control1                -1.831411e-05
## pedestrian_crossing_human_control2                -6.206959e-05
## pedestrian_crossing_physical_facilities1          -1.224142e-04
## pedestrian_crossing_physical_facilities4          -1.657606e-04
## pedestrian_crossing_physical_facilities5          -1.398282e-04
## pedestrian_crossing_physical_facilities7          -1.252301e-06
## pedestrian_crossing_physical_facilities8           1.221564e-05
## light_conditions4                                  3.358865e-03
## light_conditions5                                 -5.748685e-05
## light_conditions6                                 -1.132953e-04
## light_conditions7                                 -3.660373e-05
## weather_conditions2                               -7.672835e-05
## weather_conditions3                               -1.040670e-05
## weather_conditions4                               -1.831053e-05
## weather_conditions5                               -3.051822e-05
## weather_conditions6                               -2.069363e-06
## weather_conditions7                               -4.839760e-06
## weather_conditions8                               -5.559567e-05
## road_surface_conditions2                          -6.380663e-04
## road_surface_conditions3                           2.552370e-06
## road_surface_conditions4                           3.895286e-05
## road_surface_conditions5                           2.123963e-06
## special_conditions_at_site1                        2.831204e-06
## special_conditions_at_site2                       -2.322340e-06
## special_conditions_at_site3                       -1.490569e-06
## special_conditions_at_site4                        1.007614e-05
## special_conditions_at_site5                       -1.088635e-06
## special_conditions_at_site6                       -2.971014e-06
## special_conditions_at_site7                       -8.957476e-06
## carriageway_hazards1                               7.658515e-06
## carriageway_hazards2                               1.260440e-05
## carriageway_hazards3                               3.283326e-06
## carriageway_hazards6                              -3.586787e-06
## carriageway_hazards7                               2.586929e-06
## did_police_officer_attend_scene_of_collision1     -2.801903e-04
## 1|2                                                3.685951e-05
## 2|3                                                2.239431e-04
##                                               light_conditions5
## police_force                                       3.440040e-08
## number_of_vehicles                                 4.332744e-06
## number_of_casualties                              -2.706390e-07
## day_of_week                                       -2.184557e-07
## first_road_class                                   4.428563e-07
## first_road_number                                 -8.042325e-10
## road_type2                                        -1.001280e-05
## road_type3                                         2.034515e-05
## road_type6                                         4.643546e-06
## road_type7                                        -7.782024e-06
## speed_limit                                       -4.055649e-07
## junction_detail1                                   2.228328e-05
## junction_detail2                                  -1.668300e-05
## junction_detail5                                  -1.229060e-05
## junction_detail6                                   1.351357e-05
## junction_detail7                                  -4.222162e-06
## junction_detail8                                   4.474216e-05
## junction_detail9                                   2.537683e-05
## junction_control1                                 -1.035433e-07
## junction_control2                                  3.227937e-06
## junction_control3                                 -3.307189e-07
## second_road_class                                 -1.350814e-06
## second_road_number                                -1.137410e-09
## pedestrian_crossing_human_control1                 1.516527e-06
## pedestrian_crossing_human_control2                 6.782579e-06
## pedestrian_crossing_physical_facilities1           5.151092e-05
## pedestrian_crossing_physical_facilities4           2.275665e-05
## pedestrian_crossing_physical_facilities5           3.831468e-07
## pedestrian_crossing_physical_facilities7           4.002507e-07
## pedestrian_crossing_physical_facilities8          -4.450484e-05
## light_conditions4                                 -5.748685e-05
## light_conditions5                                  2.650877e-06
## light_conditions6                                  5.318193e-06
## light_conditions7                                  1.245675e-06
## weather_conditions2                               -4.900760e-06
## weather_conditions3                                1.338566e-06
## weather_conditions4                                1.481689e-06
## weather_conditions5                                5.782393e-06
## weather_conditions6                                2.609089e-07
## weather_conditions7                                5.283739e-07
## weather_conditions8                                1.003347e-05
## road_surface_conditions2                           7.057843e-05
## road_surface_conditions3                          -2.108440e-07
## road_surface_conditions4                          -1.003536e-06
## road_surface_conditions5                          -1.542939e-07
## special_conditions_at_site1                       -3.830156e-08
## special_conditions_at_site2                        7.354770e-08
## special_conditions_at_site3                        2.245362e-07
## special_conditions_at_site4                       -1.344393e-08
## special_conditions_at_site5                        1.886375e-07
## special_conditions_at_site6                        4.476581e-08
## special_conditions_at_site7                        9.487826e-07
## carriageway_hazards1                               1.362732e-07
## carriageway_hazards2                               1.067562e-06
## carriageway_hazards3                              -4.009784e-07
## carriageway_hazards6                               3.392399e-07
## carriageway_hazards7                               6.957222e-09
## did_police_officer_attend_scene_of_collision1     -1.556824e-06
## 1|2                                               -3.720682e-06
## 2|3                                                3.348277e-06
##                                               light_conditions6
## police_force                                      -2.864342e-07
## number_of_vehicles                                -1.186900e-05
## number_of_casualties                               1.471186e-05
## day_of_week                                        4.968723e-06
## first_road_class                                   1.175066e-05
## first_road_number                                  1.895849e-08
## road_type2                                         3.922986e-04
## road_type3                                        -3.233771e-04
## road_type6                                        -3.149924e-04
## road_type7                                         2.070094e-04
## speed_limit                                        1.014246e-06
## junction_detail1                                  -5.984611e-04
## junction_detail2                                   1.135859e-04
## junction_detail5                                   1.525544e-04
## junction_detail6                                  -3.345232e-05
## junction_detail7                                   5.583593e-07
## junction_detail8                                   2.056936e-04
## junction_detail9                                  -7.457889e-05
## junction_control1                                  5.091528e-06
## junction_control2                                 -9.184295e-05
## junction_control3                                  1.138881e-05
## second_road_class                                  5.528062e-06
## second_road_number                                 2.697183e-08
## pedestrian_crossing_human_control1                 2.270252e-06
## pedestrian_crossing_human_control2                 4.837291e-05
## pedestrian_crossing_physical_facilities1          -1.129632e-04
## pedestrian_crossing_physical_facilities4           6.900834e-05
## pedestrian_crossing_physical_facilities5           1.178602e-04
## pedestrian_crossing_physical_facilities7          -7.687013e-06
## pedestrian_crossing_physical_facilities8          -2.067783e-04
## light_conditions4                                 -1.132953e-04
## light_conditions5                                  5.318193e-06
## light_conditions6                                  2.080437e-04
## light_conditions7                                 -7.937847e-06
## weather_conditions2                               -9.898416e-04
## weather_conditions3                                3.194100e-05
## weather_conditions4                                5.036231e-05
## weather_conditions5                                1.113001e-04
## weather_conditions6                                5.083679e-06
## weather_conditions7                                1.695745e-05
## weather_conditions8                                2.504545e-04
## road_surface_conditions2                           6.540474e-04
## road_surface_conditions3                          -1.515880e-06
## road_surface_conditions4                           1.066214e-05
## road_surface_conditions5                          -2.289515e-06
## special_conditions_at_site1                        5.564587e-07
## special_conditions_at_site2                        3.937000e-08
## special_conditions_at_site3                        6.667136e-06
## special_conditions_at_site4                        1.657860e-06
## special_conditions_at_site5                        1.166415e-06
## special_conditions_at_site6                       -1.733748e-06
## special_conditions_at_site7                        3.375830e-06
## carriageway_hazards1                               6.456368e-07
## carriageway_hazards2                               1.549914e-05
## carriageway_hazards3                               2.646468e-06
## carriageway_hazards6                              -1.955632e-06
## carriageway_hazards7                              -2.297145e-08
## did_police_officer_attend_scene_of_collision1      1.339064e-04
## 1|2                                                9.487252e-05
## 2|3                                               -2.644072e-05
##                                               light_conditions7
## police_force                                      -8.826791e-08
## number_of_vehicles                                -7.252018e-06
## number_of_casualties                               1.121667e-06
## day_of_week                                        8.899349e-08
## first_road_class                                  -1.407821e-06
## first_road_number                                 -1.022405e-09
## road_type2                                        -7.534560e-05
## road_type3                                         8.364626e-05
## road_type6                                         5.541140e-05
## road_type7                                        -3.620399e-05
## speed_limit                                       -3.752515e-07
## junction_detail1                                   7.791597e-05
## junction_detail2                                  -3.291390e-05
## junction_detail5                                  -2.226997e-05
## junction_detail6                                   6.414744e-06
## junction_detail7                                   4.422005e-06
## junction_detail8                                  -7.209957e-05
## junction_detail9                                   7.509601e-06
## junction_control1                                  2.576231e-06
## junction_control2                                 -5.433020e-05
## junction_control3                                  3.211958e-06
## second_road_class                                  1.214792e-06
## second_road_number                                 9.991399e-10
## pedestrian_crossing_human_control1                 9.403857e-07
## pedestrian_crossing_human_control2                 5.694500e-06
## pedestrian_crossing_physical_facilities1           1.705932e-05
## pedestrian_crossing_physical_facilities4           1.465033e-05
## pedestrian_crossing_physical_facilities5           4.942927e-05
## pedestrian_crossing_physical_facilities7           5.793275e-07
## pedestrian_crossing_physical_facilities8          -4.513611e-05
## light_conditions4                                 -3.660373e-05
## light_conditions5                                  1.245675e-06
## light_conditions6                                 -7.937847e-06
## light_conditions7                                  3.289814e-06
## weather_conditions2                                1.263621e-06
## weather_conditions3                                6.600947e-07
## weather_conditions4                               -3.536532e-07
## weather_conditions5                                1.490322e-06
## weather_conditions6                               -5.065320e-08
## weather_conditions7                                2.362800e-07
## weather_conditions8                                8.637214e-06
## road_surface_conditions2                           2.317358e-05
## road_surface_conditions3                          -5.733803e-09
## road_surface_conditions4                          -8.580281e-07
## road_surface_conditions5                          -7.253679e-08
## special_conditions_at_site1                       -6.414990e-08
## special_conditions_at_site2                        2.369461e-07
## special_conditions_at_site3                        1.901538e-07
## special_conditions_at_site4                       -2.158201e-06
## special_conditions_at_site5                       -4.742019e-07
## special_conditions_at_site6                        8.485019e-08
## special_conditions_at_site7                        3.634039e-07
## carriageway_hazards1                               2.932262e-08
## carriageway_hazards2                               5.468780e-07
## carriageway_hazards3                              -8.209314e-07
## carriageway_hazards6                               1.007700e-06
## carriageway_hazards7                              -3.009194e-07
## did_police_officer_attend_scene_of_collision1     -3.607977e-05
## 1|2                                               -9.566984e-06
## 2|3                                               -1.045864e-05
##                                               weather_conditions2
## police_force                                         3.654867e-06
## number_of_vehicles                                  -1.452480e-05
## number_of_casualties                                -5.397066e-05
## day_of_week                                          5.018876e-07
## first_road_class                                     4.660674e-06
## first_road_number                                   -4.294791e-08
## road_type2                                           8.516988e-05
## road_type3                                          -1.769635e-04
## road_type6                                           7.507361e-05
## road_type7                                          -9.207657e-05
## speed_limit                                          9.917999e-06
## junction_detail1                                    -1.300379e-04
## junction_detail2                                     3.872605e-04
## junction_detail5                                     7.967548e-05
## junction_detail6                                    -2.718325e-05
## junction_detail7                                    -3.009953e-05
## junction_detail8                                     3.702778e-05
## junction_detail9                                     1.838473e-04
## junction_control1                                   -1.109812e-05
## junction_control2                                   -2.082748e-04
## junction_control3                                   -9.634146e-07
## second_road_class                                   -3.736692e-05
## second_road_number                                  -3.356918e-08
## pedestrian_crossing_human_control1                  -3.613171e-05
## pedestrian_crossing_human_control2                  -2.548522e-04
## pedestrian_crossing_physical_facilities1             2.799663e-05
## pedestrian_crossing_physical_facilities4             3.387410e-05
## pedestrian_crossing_physical_facilities5             2.511130e-04
## pedestrian_crossing_physical_facilities7            -2.908202e-05
## pedestrian_crossing_physical_facilities8            -6.096083e-05
## light_conditions4                                   -7.672835e-05
## light_conditions5                                   -4.900760e-06
## light_conditions6                                   -9.898416e-04
## light_conditions7                                    1.263621e-06
## weather_conditions2                                  9.956994e-03
## weather_conditions3                                 -2.875611e-04
## weather_conditions4                                 -4.298901e-04
## weather_conditions5                                 -9.293558e-04
## weather_conditions6                                 -3.461867e-05
## weather_conditions7                                 -1.395043e-04
## weather_conditions8                                 -2.285005e-03
## road_surface_conditions2                            -3.788401e-03
## road_surface_conditions3                            -1.765865e-06
## road_surface_conditions4                            -1.022506e-04
## road_surface_conditions5                             2.567727e-05
## special_conditions_at_site1                         -1.337328e-05
## special_conditions_at_site2                         -6.194163e-07
## special_conditions_at_site3                         -4.440892e-05
## special_conditions_at_site4                         -4.562835e-05
## special_conditions_at_site5                         -9.136809e-06
## special_conditions_at_site6                          7.466654e-06
## special_conditions_at_site7                         -2.724817e-05
## carriageway_hazards1                                -3.095940e-05
## carriageway_hazards2                                -6.527877e-05
## carriageway_hazards3                                 1.335981e-05
## carriageway_hazards6                                -7.047761e-06
## carriageway_hazards7                                 7.736443e-06
## did_police_officer_attend_scene_of_collision1       -6.081096e-05
## 1|2                                                 -9.965870e-06
## 2|3                                                  6.233126e-05
##                                               weather_conditions3
## police_force                                        -2.425865e-07
## number_of_vehicles                                   3.653098e-07
## number_of_casualties                                 3.855454e-06
## day_of_week                                          2.209587e-07
## first_road_class                                     6.595495e-07
## first_road_number                                    8.241682e-10
## road_type2                                          -1.618062e-05
## road_type3                                           1.715041e-05
## road_type6                                           3.340711e-06
## road_type7                                          -5.615003e-06
## speed_limit                                         -4.071687e-07
## junction_detail1                                     2.560367e-05
## junction_detail2                                    -2.208118e-05
## junction_detail5                                    -1.108683e-05
## junction_detail6                                    -1.323382e-05
## junction_detail7                                    -2.049653e-06
## junction_detail8                                     3.782734e-05
## junction_detail9                                    -1.368988e-05
## junction_control1                                   -7.330432e-07
## junction_control2                                    1.503495e-05
## junction_control3                                   -9.931204e-07
## second_road_class                                    4.313042e-06
## second_road_number                                   9.865819e-10
## pedestrian_crossing_human_control1                   1.799963e-07
## pedestrian_crossing_human_control2                   3.787984e-06
## pedestrian_crossing_physical_facilities1            -5.127263e-05
## pedestrian_crossing_physical_facilities4            -1.133246e-05
## pedestrian_crossing_physical_facilities5             3.575062e-07
## pedestrian_crossing_physical_facilities7             1.154416e-06
## pedestrian_crossing_physical_facilities8             1.822313e-05
## light_conditions4                                   -1.040670e-05
## light_conditions5                                    1.338566e-06
## light_conditions6                                    3.194100e-05
## light_conditions7                                    6.600947e-07
## weather_conditions2                                 -2.875611e-04
## weather_conditions3                                  1.036798e-05
## weather_conditions4                                  1.462113e-05
## weather_conditions5                                  3.182749e-05
## weather_conditions6                                  1.255961e-06
## weather_conditions7                                  4.719949e-06
## weather_conditions8                                  7.312818e-05
## road_surface_conditions2                             1.806898e-04
## road_surface_conditions3                             7.752189e-08
## road_surface_conditions4                             1.331767e-06
## road_surface_conditions5                            -8.833579e-07
## special_conditions_at_site1                          3.037889e-07
## special_conditions_at_site2                          4.441020e-08
## special_conditions_at_site3                          9.822268e-07
## special_conditions_at_site4                          1.466269e-06
## special_conditions_at_site5                          4.295544e-07
## special_conditions_at_site6                         -1.871495e-07
## special_conditions_at_site7                          9.188682e-07
## carriageway_hazards1                                 6.793092e-07
## carriageway_hazards2                                 2.400189e-06
## carriageway_hazards3                                -4.594512e-07
## carriageway_hazards6                                -2.817544e-07
## carriageway_hazards7                                -3.106315e-08
## did_police_officer_attend_scene_of_collision1       -3.423998e-05
## 1|2                                                  4.207342e-06
## 2|3                                                 -7.381700e-07
##                                               weather_conditions4
## police_force                                        -3.126842e-07
## number_of_vehicles                                  -4.935825e-06
## number_of_casualties                                -7.831525e-08
## day_of_week                                         -2.140482e-07
## first_road_class                                    -9.474610e-07
## first_road_number                                    2.254528e-09
## road_type2                                           1.043209e-05
## road_type3                                          -1.855376e-05
## road_type6                                          -2.305474e-05
## road_type7                                           7.106744e-06
## speed_limit                                         -1.005429e-06
## junction_detail1                                     2.984246e-05
## junction_detail2                                    -2.093221e-05
## junction_detail5                                    -1.072355e-05
## junction_detail6                                     2.210899e-05
## junction_detail7                                    -1.501084e-05
## junction_detail8                                     4.704677e-05
## junction_detail9                                     2.789658e-05
## junction_control1                                   -1.021416e-06
## junction_control2                                    9.924740e-06
## junction_control3                                    7.947519e-07
## second_road_class                                    1.768710e-06
## second_road_number                                  -1.208937e-09
## pedestrian_crossing_human_control1                  -1.435644e-06
## pedestrian_crossing_human_control2                   1.006096e-06
## pedestrian_crossing_physical_facilities1            -1.457986e-04
## pedestrian_crossing_physical_facilities4            -2.371079e-05
## pedestrian_crossing_physical_facilities5            -2.745816e-05
## pedestrian_crossing_physical_facilities7             1.833297e-06
## pedestrian_crossing_physical_facilities8             8.094481e-05
## light_conditions4                                   -1.831053e-05
## light_conditions5                                    1.481689e-06
## light_conditions6                                    5.036231e-05
## light_conditions7                                   -3.536532e-07
## weather_conditions2                                 -4.298901e-04
## weather_conditions3                                  1.462113e-05
## weather_conditions4                                  2.375369e-05
## weather_conditions5                                  4.532362e-05
## weather_conditions6                                  1.772252e-06
## weather_conditions7                                  6.992980e-06
## weather_conditions8                                  1.081287e-04
## road_surface_conditions2                             2.530600e-04
## road_surface_conditions3                             5.724807e-08
## road_surface_conditions4                             9.712095e-07
## road_surface_conditions5                            -1.189473e-06
## special_conditions_at_site1                          6.645169e-07
## special_conditions_at_site2                         -3.765561e-08
## special_conditions_at_site3                          1.707721e-06
## special_conditions_at_site4                          4.030549e-06
## special_conditions_at_site5                          9.456835e-07
## special_conditions_at_site6                         -2.021108e-07
## special_conditions_at_site7                          7.623679e-07
## carriageway_hazards1                                 8.689760e-07
## carriageway_hazards2                                 3.695436e-06
## carriageway_hazards3                                -1.573282e-07
## carriageway_hazards6                                -9.733995e-07
## carriageway_hazards7                                 4.575100e-07
## did_police_officer_attend_scene_of_collision1        5.281111e-05
## 1|2                                                  3.321433e-06
## 2|3                                                  3.025955e-06
##                                               weather_conditions5
## police_force                                        -3.791987e-07
## number_of_vehicles                                   4.400429e-06
## number_of_casualties                                 6.013573e-06
## day_of_week                                         -2.569880e-07
## first_road_class                                    -1.212825e-06
## first_road_number                                    1.917917e-09
## road_type2                                          -2.664647e-05
## road_type3                                           5.133310e-05
## road_type6                                           2.207632e-05
## road_type7                                          -6.231402e-06
## speed_limit                                         -1.296655e-06
## junction_detail1                                     8.663384e-06
## junction_detail2                                    -6.457565e-05
## junction_detail5                                    -2.473661e-05
## junction_detail6                                    -1.432281e-05
## junction_detail7                                    -1.587484e-06
## junction_detail8                                     1.339403e-04
## junction_detail9                                    -8.416676e-06
## junction_control1                                   -8.340227e-07
## junction_control2                                    3.517761e-05
## junction_control3                                   -2.866939e-06
## second_road_class                                   -1.759960e-06
## second_road_number                                   7.268857e-10
## pedestrian_crossing_human_control1                   5.188391e-06
## pedestrian_crossing_human_control2                   2.931905e-05
## pedestrian_crossing_physical_facilities1             5.331443e-05
## pedestrian_crossing_physical_facilities4            -3.627364e-06
## pedestrian_crossing_physical_facilities5            -2.660607e-05
## pedestrian_crossing_physical_facilities7             3.141770e-06
## pedestrian_crossing_physical_facilities8            -4.832577e-05
## light_conditions4                                   -3.051822e-05
## light_conditions5                                    5.782393e-06
## light_conditions6                                    1.113001e-04
## light_conditions7                                    1.490322e-06
## weather_conditions2                                 -9.293558e-04
## weather_conditions3                                  3.182749e-05
## weather_conditions4                                  4.532362e-05
## weather_conditions5                                  1.049355e-04
## weather_conditions6                                  4.105809e-06
## weather_conditions7                                  1.507066e-05
## weather_conditions8                                  2.402818e-04
## road_surface_conditions2                             5.949054e-04
## road_surface_conditions3                            -3.227517e-07
## road_surface_conditions4                             7.027803e-06
## road_surface_conditions5                            -2.828913e-06
## special_conditions_at_site1                          1.139927e-06
## special_conditions_at_site2                          9.323406e-08
## special_conditions_at_site3                          4.200971e-06
## special_conditions_at_site4                          4.401197e-06
## special_conditions_at_site5                          1.528958e-06
## special_conditions_at_site6                         -7.389519e-07
## special_conditions_at_site7                          4.461962e-06
## carriageway_hazards1                                 3.078199e-06
## carriageway_hazards2                                 8.963786e-06
## carriageway_hazards3                                -1.628566e-06
## carriageway_hazards6                                 7.515132e-07
## carriageway_hazards7                                -5.616576e-07
## did_police_officer_attend_scene_of_collision1       -2.461830e-05
## 1|2                                                  3.370038e-06
## 2|3                                                 -2.201691e-06
##                                               weather_conditions6
## police_force                                        -1.376562e-08
## number_of_vehicles                                  -4.006140e-07
## number_of_casualties                                 7.046943e-07
## day_of_week                                          9.753035e-08
## first_road_class                                     3.265477e-07
## first_road_number                                    3.724708e-10
## road_type2                                           1.377727e-07
## road_type3                                           5.405714e-06
## road_type6                                          -6.628924e-07
## road_type7                                          -6.022120e-07
## speed_limit                                         -6.406259e-08
## junction_detail1                                    -5.926857e-06
## junction_detail2                                    -4.006732e-06
## junction_detail5                                    -1.267222e-06
## junction_detail6                                     8.100694e-07
## junction_detail7                                    -1.361026e-06
## junction_detail8                                     2.524745e-05
## junction_detail9                                    -3.607001e-06
## junction_control1                                   -2.912897e-08
## junction_control2                                   -5.630630e-07
## junction_control3                                   -1.903256e-07
## second_road_class                                   -3.269920e-07
## second_road_number                                   4.770229e-10
## pedestrian_crossing_human_control1                   4.868144e-08
## pedestrian_crossing_human_control2                   3.117539e-07
## pedestrian_crossing_physical_facilities1            -3.499556e-06
## pedestrian_crossing_physical_facilities4            -1.850814e-06
## pedestrian_crossing_physical_facilities5            -1.067526e-06
## pedestrian_crossing_physical_facilities7             7.955478e-08
## pedestrian_crossing_physical_facilities8            -4.333533e-06
## light_conditions4                                   -2.069363e-06
## light_conditions5                                    2.609089e-07
## light_conditions6                                    5.083679e-06
## light_conditions7                                   -5.065320e-08
## weather_conditions2                                 -3.461867e-05
## weather_conditions3                                  1.255961e-06
## weather_conditions4                                  1.772252e-06
## weather_conditions5                                  4.105809e-06
## weather_conditions6                                  2.032105e-07
## weather_conditions7                                  5.796949e-07
## weather_conditions8                                  8.628488e-06
## road_surface_conditions2                             2.239402e-05
## road_surface_conditions3                            -1.190289e-08
## road_surface_conditions4                             2.141222e-07
## road_surface_conditions5                            -1.133779e-07
## special_conditions_at_site1                          2.314144e-08
## special_conditions_at_site2                          2.137110e-08
## special_conditions_at_site3                          1.241316e-07
## special_conditions_at_site4                          2.518712e-07
## special_conditions_at_site5                          1.318466e-07
## special_conditions_at_site6                         -6.014939e-08
## special_conditions_at_site7                          2.055856e-07
## carriageway_hazards1                                 3.656773e-08
## carriageway_hazards2                                 6.445255e-07
## carriageway_hazards3                                -4.781555e-08
## carriageway_hazards6                                -7.307642e-08
## carriageway_hazards7                                 2.610770e-08
## did_police_officer_attend_scene_of_collision1       -2.102814e-07
## 1|2                                                  1.550810e-06
## 2|3                                                 -9.324359e-07
##                                               weather_conditions7
## police_force                                        -9.645402e-08
## number_of_vehicles                                  -7.587749e-07
## number_of_casualties                                 1.267847e-06
## day_of_week                                          1.109791e-07
## first_road_class                                     2.906533e-07
## first_road_number                                    9.760717e-10
## road_type2                                          -5.124489e-06
## road_type3                                           1.142506e-05
## road_type6                                           1.666455e-06
## road_type7                                          -7.037370e-08
## speed_limit                                         -2.322525e-07
## junction_detail1                                    -6.972257e-06
## junction_detail2                                    -5.042608e-06
## junction_detail5                                     8.752305e-07
## junction_detail6                                    -2.673950e-06
## junction_detail7                                     2.257983e-06
## junction_detail8                                    -1.042625e-05
## junction_detail9                                    -1.471846e-05
## junction_control1                                    2.977259e-07
## junction_control2                                   -5.571605e-06
## junction_control3                                    5.083275e-07
## second_road_class                                   -5.857977e-07
## second_road_number                                   2.413786e-10
## pedestrian_crossing_human_control1                   2.440994e-07
## pedestrian_crossing_human_control2                   3.028495e-06
## pedestrian_crossing_physical_facilities1            -2.080921e-05
## pedestrian_crossing_physical_facilities4             4.757168e-07
## pedestrian_crossing_physical_facilities5            -1.097740e-06
## pedestrian_crossing_physical_facilities7             2.759278e-07
## pedestrian_crossing_physical_facilities8             7.551618e-06
## light_conditions4                                   -4.839760e-06
## light_conditions5                                    5.283739e-07
## light_conditions6                                    1.695745e-05
## light_conditions7                                    2.362800e-07
## weather_conditions2                                 -1.395043e-04
## weather_conditions3                                  4.719949e-06
## weather_conditions4                                  6.992980e-06
## weather_conditions5                                  1.507066e-05
## weather_conditions6                                  5.796949e-07
## weather_conditions7                                  2.354756e-06
## weather_conditions8                                  3.609971e-05
## road_surface_conditions2                             8.609633e-05
## road_surface_conditions3                            -3.660934e-08
## road_surface_conditions4                             8.967569e-07
## road_surface_conditions5                            -4.134316e-07
## special_conditions_at_site1                          1.637444e-07
## special_conditions_at_site2                          2.249692e-08
## special_conditions_at_site3                          6.592255e-07
## special_conditions_at_site4                          4.285599e-07
## special_conditions_at_site5                          1.288446e-07
## special_conditions_at_site6                         -1.175894e-07
## special_conditions_at_site7                          3.578301e-07
## carriageway_hazards1                                 3.446050e-07
## carriageway_hazards2                                 1.149961e-06
## carriageway_hazards3                                -1.399122e-07
## carriageway_hazards6                                 1.206708e-08
## carriageway_hazards7                                -1.484087e-07
## did_police_officer_attend_scene_of_collision1        5.900113e-06
## 1|2                                                  1.295850e-06
## 2|3                                                 -1.264115e-06
##                                               weather_conditions8
## police_force                                        -8.777134e-07
## number_of_vehicles                                  -2.819668e-06
## number_of_casualties                                 1.161873e-05
## day_of_week                                         -2.550384e-06
## first_road_class                                    -9.427671e-06
## first_road_number                                    6.618772e-09
## road_type2                                          -1.263417e-04
## road_type3                                           1.738559e-04
## road_type6                                           5.829870e-05
## road_type7                                          -2.729344e-05
## speed_limit                                         -4.076081e-06
## junction_detail1                                     1.408798e-04
## junction_detail2                                    -1.526582e-04
## junction_detail5                                    -4.211623e-05
## junction_detail6                                     5.899949e-05
## junction_detail7                                     9.740937e-06
## junction_detail8                                    -2.696521e-04
## junction_detail9                                     8.242865e-05
## junction_control1                                    1.410061e-05
## junction_control2                                   -2.273801e-04
## junction_control3                                    2.036165e-05
## second_road_class                                   -2.766982e-06
## second_road_number                                   3.295759e-09
## pedestrian_crossing_human_control1                   1.076350e-05
## pedestrian_crossing_human_control2                   9.300558e-05
## pedestrian_crossing_physical_facilities1            -2.887044e-06
## pedestrian_crossing_physical_facilities4             3.976824e-05
## pedestrian_crossing_physical_facilities5             1.888672e-04
## pedestrian_crossing_physical_facilities7             5.684301e-06
## pedestrian_crossing_physical_facilities8            -2.054850e-04
## light_conditions4                                   -5.559567e-05
## light_conditions5                                    1.003347e-05
## light_conditions6                                    2.504545e-04
## light_conditions7                                    8.637214e-06
## weather_conditions2                                 -2.285005e-03
## weather_conditions3                                  7.312818e-05
## weather_conditions4                                  1.081287e-04
## weather_conditions5                                  2.402818e-04
## weather_conditions6                                  8.628488e-06
## weather_conditions7                                  3.609971e-05
## weather_conditions8                                  5.996983e-04
## road_surface_conditions2                             1.290181e-03
## road_surface_conditions3                            -8.330143e-07
## road_surface_conditions4                             1.768453e-05
## road_surface_conditions5                            -6.150166e-06
## special_conditions_at_site1                          3.147315e-06
## special_conditions_at_site2                          8.019356e-07
## special_conditions_at_site3                          1.265527e-05
## special_conditions_at_site4                          3.151493e-06
## special_conditions_at_site5                          5.896008e-07
## special_conditions_at_site6                         -1.511212e-06
## special_conditions_at_site7                          8.113927e-06
## carriageway_hazards1                                 7.264815e-06
## carriageway_hazards2                                 2.204472e-05
## carriageway_hazards3                                -4.062837e-06
## carriageway_hazards6                                 4.681417e-06
## carriageway_hazards7                                -1.945698e-06
## did_police_officer_attend_scene_of_collision1        6.716495e-05
## 1|2                                                 -1.565405e-05
## 2|3                                                 -1.081486e-05
##                                               road_surface_conditions2
## police_force                                             -3.255989e-06
## number_of_vehicles                                        8.583735e-05
## number_of_casualties                                      1.662691e-05
## day_of_week                                              -4.427960e-06
## first_road_class                                         -2.179501e-05
## first_road_number                                        -1.321295e-08
## road_type2                                               -1.009045e-05
## road_type3                                               -3.416976e-06
## road_type6                                               -8.118537e-05
## road_type7                                                6.240510e-05
## speed_limit                                              -9.911844e-06
## junction_detail1                                          8.694944e-05
## junction_detail2                                         -1.839566e-04
## junction_detail5                                         -4.906893e-05
## junction_detail6                                         -4.030411e-05
## junction_detail7                                          1.629483e-05
## junction_detail8                                         -4.414214e-05
## junction_detail9                                         -1.011395e-04
## junction_control1                                        -2.089439e-05
## junction_control2                                         2.197832e-04
## junction_control3                                        -7.407196e-06
## second_road_class                                         1.550949e-05
## second_road_number                                       -3.783028e-08
## pedestrian_crossing_human_control1                        2.408211e-05
## pedestrian_crossing_human_control2                        1.612014e-04
## pedestrian_crossing_physical_facilities1                 -1.952313e-05
## pedestrian_crossing_physical_facilities4                 -3.826238e-06
## pedestrian_crossing_physical_facilities5                 -1.289023e-04
## pedestrian_crossing_physical_facilities7                  1.216139e-05
## pedestrian_crossing_physical_facilities8                  3.278982e-05
## light_conditions4                                        -6.380663e-04
## light_conditions5                                         7.057843e-05
## light_conditions6                                         6.540474e-04
## light_conditions7                                         2.317358e-05
## weather_conditions2                                      -3.788401e-03
## weather_conditions3                                       1.806898e-04
## weather_conditions4                                       2.530600e-04
## weather_conditions5                                       5.949054e-04
## weather_conditions6                                       2.239402e-05
## weather_conditions7                                       8.609633e-05
## weather_conditions8                                       1.290181e-03
## road_surface_conditions2                                  5.074971e-03
## road_surface_conditions3                                 -5.964442e-06
## road_surface_conditions4                                 -1.008782e-05
## road_surface_conditions5                                 -1.514809e-05
## special_conditions_at_site1                               4.597119e-06
## special_conditions_at_site2                              -5.196685e-07
## special_conditions_at_site3                               2.325380e-05
## special_conditions_at_site4                               1.619856e-05
## special_conditions_at_site5                               6.476042e-06
## special_conditions_at_site6                              -9.121875e-07
## special_conditions_at_site7                               2.450857e-05
## carriageway_hazards1                                      1.556911e-05
## carriageway_hazards2                                      3.888519e-05
## carriageway_hazards3                                     -5.466587e-06
## carriageway_hazards6                                      1.440517e-07
## carriageway_hazards7                                     -2.937426e-06
## did_police_officer_attend_scene_of_collision1            -2.310414e-04
## 1|2                                                       5.221363e-05
## 2|3                                                       6.540907e-05
##                                               road_surface_conditions3
## police_force                                             -2.590015e-08
## number_of_vehicles                                       -1.659052e-07
## number_of_casualties                                      1.431581e-06
## day_of_week                                               1.416382e-07
## first_road_class                                          1.532015e-07
## first_road_number                                         4.968273e-11
## road_type2                                               -3.339204e-06
## road_type3                                                2.379961e-06
## road_type6                                               -1.221009e-06
## road_type7                                               -1.766357e-06
## speed_limit                                              -1.169816e-08
## junction_detail1                                          8.629213e-06
## junction_detail2                                         -9.721015e-07
## junction_detail5                                         -1.950752e-06
## junction_detail6                                         -2.237338e-06
## junction_detail7                                         -1.190370e-06
## junction_detail8                                          3.384767e-06
## junction_detail9                                          4.846497e-07
## junction_control1                                        -3.798377e-07
## junction_control2                                         3.556385e-06
## junction_control3                                        -4.459637e-07
## second_road_class                                         1.454370e-06
## second_road_number                                        3.375062e-10
## pedestrian_crossing_human_control1                       -2.842363e-07
## pedestrian_crossing_human_control2                       -2.213269e-06
## pedestrian_crossing_physical_facilities1                 -9.460345e-06
## pedestrian_crossing_physical_facilities4                 -8.131918e-06
## pedestrian_crossing_physical_facilities5                 -7.429853e-06
## pedestrian_crossing_physical_facilities7                  1.986913e-07
## pedestrian_crossing_physical_facilities8                  1.310592e-05
## light_conditions4                                         2.552370e-06
## light_conditions5                                        -2.108440e-07
## light_conditions6                                        -1.515880e-06
## light_conditions7                                        -5.733803e-09
## weather_conditions2                                      -1.765865e-06
## weather_conditions3                                       7.752189e-08
## weather_conditions4                                       5.724807e-08
## weather_conditions5                                      -3.227517e-07
## weather_conditions6                                      -1.190289e-08
## weather_conditions7                                      -3.660934e-08
## weather_conditions8                                      -8.330143e-07
## road_surface_conditions2                                 -5.964442e-06
## road_surface_conditions3                                  8.180335e-08
## road_surface_conditions4                                 -1.112490e-07
## road_surface_conditions5                                 -7.860928e-09
## special_conditions_at_site1                              -4.687420e-09
## special_conditions_at_site2                              -1.113438e-08
## special_conditions_at_site3                              -9.788754e-08
## special_conditions_at_site4                               2.016286e-07
## special_conditions_at_site5                               3.526269e-08
## special_conditions_at_site6                               1.896664e-08
## special_conditions_at_site7                              -7.348473e-08
## carriageway_hazards1                                     -1.318028e-08
## carriageway_hazards2                                     -2.708613e-07
## carriageway_hazards3                                     -2.540435e-08
## carriageway_hazards6                                     -1.312958e-07
## carriageway_hazards7                                      3.123178e-08
## did_police_officer_attend_scene_of_collision1            -9.985607e-06
## 1|2                                                       6.835259e-07
## 2|3                                                      -1.168433e-06
##                                               road_surface_conditions4
## police_force                                              8.206903e-08
## number_of_vehicles                                       -4.241581e-06
## number_of_casualties                                     -4.221556e-07
## day_of_week                                              -3.980076e-07
## first_road_class                                          1.797907e-06
## first_road_number                                         1.011285e-09
## road_type2                                                1.838743e-05
## road_type3                                               -1.000452e-05
## road_type6                                               -5.182040e-06
## road_type7                                                1.406212e-05
## speed_limit                                               4.513662e-07
## junction_detail1                                         -4.536957e-05
## junction_detail2                                          1.292346e-05
## junction_detail5                                          1.702209e-05
## junction_detail6                                         -5.251206e-05
## junction_detail7                                          1.738546e-05
## junction_detail8                                         -1.847907e-05
## junction_detail9                                         -4.329883e-05
## junction_control1                                         1.345123e-06
## junction_control2                                         4.741007e-06
## junction_control3                                        -1.515992e-06
## second_road_class                                        -2.303456e-06
## second_road_number                                        2.687627e-09
## pedestrian_crossing_human_control1                        3.065137e-06
## pedestrian_crossing_human_control2                        1.268434e-05
## pedestrian_crossing_physical_facilities1                  1.284562e-04
## pedestrian_crossing_physical_facilities4                  1.971019e-05
## pedestrian_crossing_physical_facilities5                  9.486572e-06
## pedestrian_crossing_physical_facilities7                 -6.352496e-07
## pedestrian_crossing_physical_facilities8                 -6.904045e-05
## light_conditions4                                         3.895286e-05
## light_conditions5                                        -1.003536e-06
## light_conditions6                                         1.066214e-05
## light_conditions7                                        -8.580281e-07
## weather_conditions2                                      -1.022506e-04
## weather_conditions3                                       1.331767e-06
## weather_conditions4                                       9.712095e-07
## weather_conditions5                                       7.027803e-06
## weather_conditions6                                       2.141222e-07
## weather_conditions7                                       8.967569e-07
## weather_conditions8                                       1.768453e-05
## road_surface_conditions2                                 -1.008782e-05
## road_surface_conditions3                                 -1.112490e-07
## road_surface_conditions4                                  4.701311e-06
## road_surface_conditions5                                 -2.027528e-07
## special_conditions_at_site1                               7.137005e-08
## special_conditions_at_site2                              -5.189291e-08
## special_conditions_at_site3                               5.762669e-07
## special_conditions_at_site4                              -8.963272e-07
## special_conditions_at_site5                              -2.397491e-07
## special_conditions_at_site6                              -1.943415e-07
## special_conditions_at_site7                               6.554070e-07
## carriageway_hazards1                                      7.030552e-07
## carriageway_hazards2                                      5.161128e-07
## carriageway_hazards3                                     -1.034028e-07
## carriageway_hazards6                                      1.186293e-06
## carriageway_hazards7                                     -6.161019e-07
## did_police_officer_attend_scene_of_collision1             1.242466e-05
## 1|2                                                      -3.644309e-06
## 2|3                                                      -9.350655e-07
##                                               road_surface_conditions5
## police_force                                              2.099580e-08
## number_of_vehicles                                       -1.447830e-06
## number_of_casualties                                      6.636802e-07
## day_of_week                                               2.240180e-08
## first_road_class                                          6.666690e-08
## first_road_number                                         4.754474e-11
## road_type2                                                4.664398e-06
## road_type3                                               -6.668051e-06
## road_type6                                               -2.860908e-06
## road_type7                                                2.054913e-06
## speed_limit                                               7.977031e-08
## junction_detail1                                         -3.613650e-06
## junction_detail2                                          2.552354e-06
## junction_detail5                                          1.692704e-06
## junction_detail6                                          1.774863e-06
## junction_detail7                                         -5.652281e-07
## junction_detail8                                         -5.438994e-06
## junction_detail9                                          7.622799e-06
## junction_control1                                         2.058944e-07
## junction_control2                                        -4.095462e-06
## junction_control3                                         5.125526e-07
## second_road_class                                         7.151434e-08
## second_road_number                                        3.544074e-11
## pedestrian_crossing_human_control1                       -1.763322e-07
## pedestrian_crossing_human_control2                       -2.368425e-07
## pedestrian_crossing_physical_facilities1                 -3.165802e-06
## pedestrian_crossing_physical_facilities4                 -1.313509e-06
## pedestrian_crossing_physical_facilities5                  8.258771e-06
## pedestrian_crossing_physical_facilities7                 -1.980105e-07
## pedestrian_crossing_physical_facilities8                 -3.294181e-06
## light_conditions4                                         2.123963e-06
## light_conditions5                                        -1.542939e-07
## light_conditions6                                        -2.289515e-06
## light_conditions7                                        -7.253680e-08
## weather_conditions2                                       2.567727e-05
## weather_conditions3                                      -8.833579e-07
## weather_conditions4                                      -1.189473e-06
## weather_conditions5                                      -2.828913e-06
## weather_conditions6                                      -1.133779e-07
## weather_conditions7                                      -4.134316e-07
## weather_conditions8                                      -6.150166e-06
## road_surface_conditions2                                 -1.514809e-05
## road_surface_conditions3                                 -7.860928e-09
## road_surface_conditions4                                 -2.027528e-07
## road_surface_conditions5                                  1.026224e-07
## special_conditions_at_site1                              -1.865521e-08
## special_conditions_at_site2                               6.663866e-09
## special_conditions_at_site3                              -7.354968e-08
## special_conditions_at_site4                              -2.086081e-07
## special_conditions_at_site5                              -6.659770e-08
## special_conditions_at_site6                               1.661945e-08
## special_conditions_at_site7                              -1.159199e-07
## carriageway_hazards1                                     -1.059019e-07
## carriageway_hazards2                                     -1.018453e-07
## carriageway_hazards3                                      8.793915e-08
## carriageway_hazards6                                      2.067512e-10
## carriageway_hazards7                                      6.099879e-08
## did_police_officer_attend_scene_of_collision1             1.053380e-06
## 1|2                                                       6.780017e-07
## 2|3                                                       2.724365e-07
##                                               special_conditions_at_site1
## police_force                                                 3.429748e-08
## number_of_vehicles                                          -2.080034e-06
## number_of_casualties                                        -2.226568e-07
## day_of_week                                                 -2.102270e-07
## first_road_class                                            -1.559875e-07
## first_road_number                                           -1.704632e-10
## road_type2                                                  -1.467458e-06
## road_type3                                                   1.755030e-06
## road_type6                                                   2.071559e-06
## road_type7                                                  -5.796795e-07
## speed_limit                                                 -4.048213e-08
## junction_detail1                                             1.822389e-06
## junction_detail2                                            -3.309941e-07
## junction_detail5                                            -8.719756e-07
## junction_detail6                                             5.613576e-06
## junction_detail7                                             1.655807e-07
## junction_detail8                                            -6.358358e-06
## junction_detail9                                             7.829839e-06
## junction_control1                                           -2.573672e-07
## junction_control2                                            9.429157e-06
## junction_control3                                           -2.449238e-07
## second_road_class                                           -7.039635e-07
## second_road_number                                          -1.175081e-09
## pedestrian_crossing_human_control1                           1.052893e-07
## pedestrian_crossing_human_control2                          -3.152995e-07
## pedestrian_crossing_physical_facilities1                     5.431175e-06
## pedestrian_crossing_physical_facilities4                    -1.180059e-05
## pedestrian_crossing_physical_facilities5                    -1.698729e-06
## pedestrian_crossing_physical_facilities7                     2.112267e-07
## pedestrian_crossing_physical_facilities8                     9.506442e-06
## light_conditions4                                            2.831204e-06
## light_conditions5                                           -3.830156e-08
## light_conditions6                                            5.564586e-07
## light_conditions7                                           -6.414990e-08
## weather_conditions2                                         -1.337328e-05
## weather_conditions3                                          3.037889e-07
## weather_conditions4                                          6.645169e-07
## weather_conditions5                                          1.139927e-06
## weather_conditions6                                          2.314144e-08
## weather_conditions7                                          1.637444e-07
## weather_conditions8                                          3.147315e-06
## road_surface_conditions2                                     4.597119e-06
## road_surface_conditions3                                    -4.687420e-09
## road_surface_conditions4                                     7.137005e-08
## road_surface_conditions5                                    -1.865521e-08
## special_conditions_at_site1                                  1.023076e-07
## special_conditions_at_site2                                  1.650672e-09
## special_conditions_at_site3                                  7.993698e-08
## special_conditions_at_site4                                  3.187801e-07
## special_conditions_at_site5                                  5.756899e-08
## special_conditions_at_site6                                  8.367958e-09
## special_conditions_at_site7                                  5.387141e-08
## carriageway_hazards1                                         1.168368e-07
## carriageway_hazards2                                        -1.479543e-07
## carriageway_hazards3                                         9.329708e-09
## carriageway_hazards6                                         8.449724e-08
## carriageway_hazards7                                         2.624731e-08
## did_police_officer_attend_scene_of_collision1                8.297418e-06
## 1|2                                                         -1.833483e-06
## 2|3                                                          2.197358e-06
##                                               special_conditions_at_site2
## police_force                                                 1.645315e-08
## number_of_vehicles                                          -7.282838e-07
## number_of_casualties                                         9.310267e-07
## day_of_week                                                 -1.604014e-08
## first_road_class                                             3.936902e-07
## first_road_number                                            1.711933e-10
## road_type2                                                  -5.327296e-06
## road_type3                                                   1.198631e-05
## road_type6                                                   1.904700e-06
## road_type7                                                  -3.086737e-06
## speed_limit                                                 -5.818062e-08
## junction_detail1                                             2.013612e-07
## junction_detail2                                            -3.862069e-06
## junction_detail5                                            -1.278427e-06
## junction_detail6                                             3.462760e-06
## junction_detail7                                            -5.326335e-09
## junction_detail8                                             2.306863e-06
## junction_detail9                                             1.884580e-07
## junction_control1                                            5.319799e-07
## junction_control2                                           -8.906644e-06
## junction_control3                                            6.595688e-07
## second_road_class                                           -2.420964e-07
## second_road_number                                           1.534083e-10
## pedestrian_crossing_human_control1                          -2.527438e-08
## pedestrian_crossing_human_control2                           5.060348e-07
## pedestrian_crossing_physical_facilities1                    -3.202997e-06
## pedestrian_crossing_physical_facilities4                    -1.854990e-06
## pedestrian_crossing_physical_facilities5                     1.388724e-05
## pedestrian_crossing_physical_facilities7                    -5.279531e-08
## pedestrian_crossing_physical_facilities8                    -1.033060e-05
## light_conditions4                                           -2.322340e-06
## light_conditions5                                            7.354770e-08
## light_conditions6                                            3.937000e-08
## light_conditions7                                            2.369461e-07
## weather_conditions2                                         -6.194163e-07
## weather_conditions3                                          4.441020e-08
## weather_conditions4                                         -3.765561e-08
## weather_conditions5                                          9.323406e-08
## weather_conditions6                                          2.137110e-08
## weather_conditions7                                          2.249692e-08
## weather_conditions8                                          8.019356e-07
## road_surface_conditions2                                    -5.196685e-07
## road_surface_conditions3                                    -1.113438e-08
## road_surface_conditions4                                    -5.189291e-08
## road_surface_conditions5                                     6.663866e-09
## special_conditions_at_site1                                  1.650672e-09
## special_conditions_at_site2                                  6.135971e-08
## special_conditions_at_site3                                  3.313601e-08
## special_conditions_at_site4                                 -2.738470e-07
## special_conditions_at_site5                                 -3.825765e-08
## special_conditions_at_site6                                 -2.631539e-08
## special_conditions_at_site7                                  3.904082e-08
## carriageway_hazards1                                        -7.052475e-08
## carriageway_hazards2                                         3.591335e-07
## carriageway_hazards3                                        -4.137560e-08
## carriageway_hazards6                                         7.721645e-08
## carriageway_hazards7                                         9.328127e-09
## did_police_officer_attend_scene_of_collision1               -6.301170e-07
## 1|2                                                          6.790653e-08
## 2|3                                                          2.107637e-07
##                                               special_conditions_at_site3
## police_force                                                -1.002923e-08
## number_of_vehicles                                          -1.090523e-06
## number_of_casualties                                         8.168708e-07
## day_of_week                                                  1.922694e-07
## first_road_class                                            -1.091389e-06
## first_road_number                                            4.355219e-10
## road_type2                                                   1.225612e-05
## road_type3                                                  -1.790975e-05
## road_type6                                                  -1.276609e-05
## road_type7                                                   8.038609e-06
## speed_limit                                                 -1.069904e-09
## junction_detail1                                            -3.274834e-06
## junction_detail2                                             4.111542e-06
## junction_detail5                                             5.137442e-06
## junction_detail6                                             3.621537e-05
## junction_detail7                                            -2.377651e-06
## junction_detail8                                            -3.444092e-05
## junction_detail9                                            -5.016003e-06
## junction_control1                                            1.214545e-06
## junction_control2                                           -3.162289e-05
## junction_control3                                            2.407771e-06
## second_road_class                                            1.187851e-06
## second_road_number                                           1.287873e-09
## pedestrian_crossing_human_control1                           5.705832e-07
## pedestrian_crossing_human_control2                           4.437342e-06
## pedestrian_crossing_physical_facilities1                     2.977817e-05
## pedestrian_crossing_physical_facilities4                    -4.040440e-06
## pedestrian_crossing_physical_facilities5                     1.088155e-05
## pedestrian_crossing_physical_facilities7                    -2.746061e-07
## pedestrian_crossing_physical_facilities8                    -2.760509e-05
## light_conditions4                                           -1.490569e-06
## light_conditions5                                            2.245362e-07
## light_conditions6                                            6.667136e-06
## light_conditions7                                            1.901538e-07
## weather_conditions2                                         -4.440892e-05
## weather_conditions3                                          9.822268e-07
## weather_conditions4                                          1.707721e-06
## weather_conditions5                                          4.200971e-06
## weather_conditions6                                          1.241316e-07
## weather_conditions7                                          6.592255e-07
## weather_conditions8                                          1.265527e-05
## road_surface_conditions2                                     2.325380e-05
## road_surface_conditions3                                    -9.788754e-08
## road_surface_conditions4                                     5.762669e-07
## road_surface_conditions5                                    -7.354968e-08
## special_conditions_at_site1                                  7.993698e-08
## special_conditions_at_site2                                  3.313601e-08
## special_conditions_at_site3                                  8.821668e-07
## special_conditions_at_site4                                 -3.071518e-07
## special_conditions_at_site5                                 -1.794931e-07
## special_conditions_at_site6                                 -1.822794e-08
## special_conditions_at_site7                                  1.816137e-07
## carriageway_hazards1                                         3.704836e-07
## carriageway_hazards2                                         5.646051e-07
## carriageway_hazards3                                        -6.437543e-08
## carriageway_hazards6                                         2.717754e-07
## carriageway_hazards7                                        -1.209050e-07
## did_police_officer_attend_scene_of_collision1                6.439834e-06
## 1|2                                                          2.025078e-06
## 2|3                                                         -2.018041e-06
##                                               special_conditions_at_site4
## police_force                                                 4.301413e-08
## number_of_vehicles                                          -9.880938e-06
## number_of_casualties                                        -3.161915e-06
## day_of_week                                                 -7.285520e-07
## first_road_class                                            -3.144606e-07
## first_road_number                                           -8.731031e-10
## road_type2                                                   2.255809e-05
## road_type3                                                  -3.401684e-05
## road_type6                                                  -2.295655e-05
## road_type7                                                   5.534031e-06
## speed_limit                                                 -2.728809e-07
## junction_detail1                                             2.810909e-05
## junction_detail2                                            -9.496506e-07
## junction_detail5                                            -1.407178e-05
## junction_detail6                                             3.820879e-05
## junction_detail7                                            -1.846806e-05
## junction_detail8                                             1.272811e-04
## junction_detail9                                             2.960289e-05
## junction_control1                                           -5.468399e-06
## junction_control2                                            1.027285e-04
## junction_control3                                           -6.940690e-06
## second_road_class                                            6.014594e-07
## second_road_number                                          -4.671520e-09
## pedestrian_crossing_human_control1                          -9.959504e-07
## pedestrian_crossing_human_control2                          -1.278019e-05
## pedestrian_crossing_physical_facilities1                    -1.858321e-05
## pedestrian_crossing_physical_facilities4                    -3.624528e-05
## pedestrian_crossing_physical_facilities5                    -1.243884e-04
## pedestrian_crossing_physical_facilities7                     2.065626e-06
## pedestrian_crossing_physical_facilities8                     1.143290e-04
## light_conditions4                                            1.007614e-05
## light_conditions5                                           -1.344393e-08
## light_conditions6                                            1.657860e-06
## light_conditions7                                           -2.158201e-06
## weather_conditions2                                         -4.562835e-05
## weather_conditions3                                          1.466269e-06
## weather_conditions4                                          4.030549e-06
## weather_conditions5                                          4.401197e-06
## weather_conditions6                                          2.518712e-07
## weather_conditions7                                          4.285599e-07
## weather_conditions8                                          3.151493e-06
## road_surface_conditions2                                     1.619856e-05
## road_surface_conditions3                                     2.016286e-07
## road_surface_conditions4                                    -8.963272e-07
## road_surface_conditions5                                    -2.086081e-07
## special_conditions_at_site1                                  3.187801e-07
## special_conditions_at_site2                                 -2.738470e-07
## special_conditions_at_site3                                 -3.071518e-07
## special_conditions_at_site4                                  5.028206e-06
## special_conditions_at_site5                                  1.206669e-06
## special_conditions_at_site6                                  1.220619e-07
## special_conditions_at_site7                                  1.545845e-07
## carriageway_hazards1                                         4.546103e-07
## carriageway_hazards2                                        -1.108708e-06
## carriageway_hazards3                                         8.781129e-08
## carriageway_hazards6                                        -1.235376e-06
## carriageway_hazards7                                         6.282260e-07
## did_police_officer_attend_scene_of_collision1                4.046577e-05
## 1|2                                                         -3.715645e-06
## 2|3                                                          5.316805e-06
##                                               special_conditions_at_site5
## police_force                                                 1.995857e-08
## number_of_vehicles                                          -4.196987e-06
## number_of_casualties                                        -1.479899e-07
## day_of_week                                                  1.118297e-09
## first_road_class                                            -2.582703e-07
## first_road_number                                            1.618820e-11
## road_type2                                                  -1.656590e-06
## road_type3                                                   7.875097e-06
## road_type6                                                   4.819074e-06
## road_type7                                                  -3.596505e-06
## speed_limit                                                 -9.932059e-08
## junction_detail1                                            -4.557772e-06
## junction_detail2                                            -5.316897e-06
## junction_detail5                                            -5.684792e-06
## junction_detail6                                             4.525824e-06
## junction_detail7                                            -4.749104e-06
## junction_detail8                                             5.710636e-05
## junction_detail9                                             8.796194e-06
## junction_control1                                           -1.351378e-06
## junction_control2                                            2.194411e-05
## junction_control3                                           -1.990027e-06
## second_road_class                                           -1.354101e-06
## second_road_number                                          -2.992739e-10
## pedestrian_crossing_human_control1                          -1.700829e-07
## pedestrian_crossing_human_control2                          -4.185750e-06
## pedestrian_crossing_physical_facilities1                    -1.768836e-06
## pedestrian_crossing_physical_facilities4                    -1.509150e-05
## pedestrian_crossing_physical_facilities5                    -3.309806e-05
## pedestrian_crossing_physical_facilities7                     5.298364e-07
## pedestrian_crossing_physical_facilities8                     2.417476e-05
## light_conditions4                                           -1.088635e-06
## light_conditions5                                            1.886375e-07
## light_conditions6                                            1.166415e-06
## light_conditions7                                           -4.742019e-07
## weather_conditions2                                         -9.136809e-06
## weather_conditions3                                          4.295544e-07
## weather_conditions4                                          9.456835e-07
## weather_conditions5                                          1.528958e-06
## weather_conditions6                                          1.318466e-07
## weather_conditions7                                          1.288446e-07
## weather_conditions8                                          5.896008e-07
## road_surface_conditions2                                     6.476042e-06
## road_surface_conditions3                                     3.526270e-08
## road_surface_conditions4                                    -2.397491e-07
## road_surface_conditions5                                    -6.659770e-08
## special_conditions_at_site1                                  5.756899e-08
## special_conditions_at_site2                                 -3.825765e-08
## special_conditions_at_site3                                 -1.794931e-07
## special_conditions_at_site4                                  1.206669e-06
## special_conditions_at_site5                                  4.308935e-07
## special_conditions_at_site6                                 -2.334082e-08
## special_conditions_at_site7                                  2.210096e-07
## carriageway_hazards1                                         1.140043e-08
## carriageway_hazards2                                         1.270032e-07
## carriageway_hazards3                                        -1.132557e-08
## carriageway_hazards6                                        -2.775481e-07
## carriageway_hazards7                                         1.739129e-07
## did_police_officer_attend_scene_of_collision1                1.147691e-05
## 1|2                                                         -1.742560e-07
## 2|3                                                         -6.481691e-07
##                                               special_conditions_at_site6
## police_force                                                -1.722562e-08
## number_of_vehicles                                          -1.174517e-06
## number_of_casualties                                         4.003749e-07
## day_of_week                                                 -6.102359e-08
## first_road_class                                            -1.326278e-07
## first_road_number                                           -2.520327e-10
## road_type2                                                   3.895023e-07
## road_type3                                                  -7.051805e-06
## road_type6                                                  -2.188543e-06
## road_type7                                                   5.517725e-07
## speed_limit                                                 -1.598983e-08
## junction_detail1                                             1.378797e-05
## junction_detail2                                             1.095367e-06
## junction_detail5                                            -1.224550e-06
## junction_detail6                                             3.076304e-07
## junction_detail7                                            -4.607644e-07
## junction_detail8                                            -9.674383e-06
## junction_detail9                                             3.476219e-06
## junction_control1                                           -2.807191e-07
## junction_control2                                            4.922483e-06
## junction_control3                                           -2.568171e-07
## second_road_class                                            9.306651e-07
## second_road_number                                          -4.718425e-10
## pedestrian_crossing_human_control1                           1.132731e-08
## pedestrian_crossing_human_control2                          -2.635243e-07
## pedestrian_crossing_physical_facilities1                     3.005658e-06
## pedestrian_crossing_physical_facilities4                    -2.075439e-06
## pedestrian_crossing_physical_facilities5                    -3.991947e-06
## pedestrian_crossing_physical_facilities7                     1.438162e-07
## pedestrian_crossing_physical_facilities8                     6.865329e-06
## light_conditions4                                           -2.971014e-06
## light_conditions5                                            4.476581e-08
## light_conditions6                                           -1.733748e-06
## light_conditions7                                            8.485019e-08
## weather_conditions2                                          7.466654e-06
## weather_conditions3                                         -1.871495e-07
## weather_conditions4                                         -2.021108e-07
## weather_conditions5                                         -7.389519e-07
## weather_conditions6                                         -6.014939e-08
## weather_conditions7                                         -1.175894e-07
## weather_conditions8                                         -1.511212e-06
## road_surface_conditions2                                    -9.121875e-07
## road_surface_conditions3                                     1.896664e-08
## road_surface_conditions4                                    -1.943415e-07
## road_surface_conditions5                                     1.661945e-08
## special_conditions_at_site1                                  8.367958e-09
## special_conditions_at_site2                                 -2.631539e-08
## special_conditions_at_site3                                 -1.822794e-08
## special_conditions_at_site4                                  1.220619e-07
## special_conditions_at_site5                                 -2.334082e-08
## special_conditions_at_site6                                  6.018716e-08
## special_conditions_at_site7                                 -4.622164e-08
## carriageway_hazards1                                         5.674149e-08
## carriageway_hazards2                                        -3.701509e-07
## carriageway_hazards3                                        -1.259533e-08
## carriageway_hazards6                                         1.251998e-08
## carriageway_hazards7                                         2.127818e-08
## did_police_officer_attend_scene_of_collision1               -1.347724e-07
## 1|2                                                         -1.443598e-06
## 2|3                                                          2.793092e-07
##                                               special_conditions_at_site7
## police_force                                                 7.641651e-08
## number_of_vehicles                                          -2.729197e-06
## number_of_casualties                                         1.901628e-06
## day_of_week                                                 -1.132727e-08
## first_road_class                                             4.688727e-07
## first_road_number                                           -4.959390e-11
## road_type2                                                  -9.665485e-06
## road_type3                                                   2.155168e-05
## road_type6                                                   1.171749e-05
## road_type7                                                  -6.765466e-06
## speed_limit                                                 -4.496477e-08
## junction_detail1                                             5.619768e-07
## junction_detail2                                            -1.175150e-05
## junction_detail5                                            -7.533178e-06
## junction_detail6                                             7.823929e-07
## junction_detail7                                            -1.157540e-06
## junction_detail8                                             4.481174e-05
## junction_detail9                                             1.798408e-05
## junction_control1                                           -2.338561e-07
## junction_control2                                            7.225453e-06
## junction_control3                                           -1.256396e-06
## second_road_class                                           -2.272080e-06
## second_road_number                                           4.428527e-11
## pedestrian_crossing_human_control1                           1.541308e-06
## pedestrian_crossing_human_control2                           3.638359e-06
## pedestrian_crossing_physical_facilities1                     6.974366e-05
## pedestrian_crossing_physical_facilities4                    -7.498738e-06
## pedestrian_crossing_physical_facilities5                    -8.338341e-06
## pedestrian_crossing_physical_facilities7                     3.966352e-07
## pedestrian_crossing_physical_facilities8                    -3.265842e-05
## light_conditions4                                           -8.957476e-06
## light_conditions5                                            9.487826e-07
## light_conditions6                                            3.375830e-06
## light_conditions7                                            3.634039e-07
## weather_conditions2                                         -2.724817e-05
## weather_conditions3                                          9.188682e-07
## weather_conditions4                                          7.623679e-07
## weather_conditions5                                          4.461962e-06
## weather_conditions6                                          2.055856e-07
## weather_conditions7                                          3.578301e-07
## weather_conditions8                                          8.113927e-06
## road_surface_conditions2                                     2.450857e-05
## road_surface_conditions3                                    -7.348473e-08
## road_surface_conditions4                                     6.554070e-07
## road_surface_conditions5                                    -1.159199e-07
## special_conditions_at_site1                                  5.387141e-08
## special_conditions_at_site2                                  3.904082e-08
## special_conditions_at_site3                                  1.816137e-07
## special_conditions_at_site4                                  1.545845e-07
## special_conditions_at_site5                                  2.210096e-07
## special_conditions_at_site6                                 -4.622164e-08
## special_conditions_at_site7                                  8.408668e-07
## carriageway_hazards1                                         2.915940e-07
## carriageway_hazards2                                         6.967322e-07
## carriageway_hazards3                                        -3.084002e-07
## carriageway_hazards6                                         4.758395e-07
## carriageway_hazards7                                        -5.269364e-08
## did_police_officer_attend_scene_of_collision1               -7.221346e-06
## 1|2                                                         -2.230238e-06
## 2|3                                                         -1.675501e-06
##                                               carriageway_hazards1
## police_force                                          1.977874e-08
## number_of_vehicles                                    1.581826e-06
## number_of_casualties                                  6.952161e-07
## day_of_week                                          -3.634777e-07
## first_road_class                                     -1.690171e-06
## first_road_number                                    -1.183625e-09
## road_type2                                           -1.440483e-06
## road_type3                                           -9.263255e-06
## road_type6                                            3.502052e-06
## road_type7                                            1.059248e-06
## speed_limit                                          -1.769049e-08
## junction_detail1                                      1.739649e-05
## junction_detail2                                      1.587058e-06
## junction_detail5                                     -1.763124e-06
## junction_detail6                                      1.102020e-05
## junction_detail7                                      1.166037e-06
## junction_detail8                                     -2.094380e-05
## junction_detail9                                     -2.405484e-06
## junction_control1                                    -7.019083e-07
## junction_control2                                     1.637207e-05
## junction_control3                                    -1.211496e-06
## second_road_class                                     4.437175e-07
## second_road_number                                   -1.218699e-09
## pedestrian_crossing_human_control1                    1.090760e-06
## pedestrian_crossing_human_control2                    2.284101e-06
## pedestrian_crossing_physical_facilities1              5.625131e-05
## pedestrian_crossing_physical_facilities4             -7.214092e-06
## pedestrian_crossing_physical_facilities5             -2.276037e-05
## pedestrian_crossing_physical_facilities7              4.600679e-07
## pedestrian_crossing_physical_facilities8              1.862047e-06
## light_conditions4                                     7.658515e-06
## light_conditions5                                     1.362732e-07
## light_conditions6                                     6.456368e-07
## light_conditions7                                     2.932262e-08
## weather_conditions2                                  -3.095940e-05
## weather_conditions3                                   6.793092e-07
## weather_conditions4                                   8.689760e-07
## weather_conditions5                                   3.078199e-06
## weather_conditions6                                   3.656773e-08
## weather_conditions7                                   3.446050e-07
## weather_conditions8                                   7.264815e-06
## road_surface_conditions2                              1.556911e-05
## road_surface_conditions3                             -1.318028e-08
## road_surface_conditions4                              7.030552e-07
## road_surface_conditions5                             -1.059019e-07
## special_conditions_at_site1                           1.168368e-07
## special_conditions_at_site2                          -7.052475e-08
## special_conditions_at_site3                           3.704836e-07
## special_conditions_at_site4                           4.546103e-07
## special_conditions_at_site5                           1.140043e-08
## special_conditions_at_site6                           5.674149e-08
## special_conditions_at_site7                           2.915940e-07
## carriageway_hazards1                                  5.610158e-07
## carriageway_hazards2                                 -6.284278e-07
## carriageway_hazards3                                 -1.806736e-07
## carriageway_hazards6                                  3.319199e-07
## carriageway_hazards7                                 -1.774744e-07
## did_police_officer_attend_scene_of_collision1        -2.488067e-06
## 1|2                                                  -4.182360e-06
## 2|3                                                   2.633084e-06
##                                               carriageway_hazards2
## police_force                                         -8.041210e-09
## number_of_vehicles                                   -1.129240e-05
## number_of_casualties                                  3.031399e-06
## day_of_week                                          -5.736399e-07
## first_road_class                                      8.173365e-07
## first_road_number                                     2.177423e-09
## road_type2                                           -2.055365e-06
## road_type3                                            2.528652e-05
## road_type6                                            8.101784e-06
## road_type7                                           -1.041317e-05
## speed_limit                                          -3.461342e-07
## junction_detail1                                      1.161674e-06
## junction_detail2                                     -4.251629e-05
## junction_detail5                                     -1.528362e-05
## junction_detail6                                      3.234813e-05
## junction_detail7                                     -1.872825e-05
## junction_detail8                                      1.652200e-04
## junction_detail9                                      1.818098e-05
## junction_control1                                     5.611615e-06
## junction_control2                                    -1.180279e-04
## junction_control3                                     6.626702e-06
## second_road_class                                    -6.686805e-06
## second_road_number                                    4.358387e-09
## pedestrian_crossing_human_control1                   -7.138995e-07
## pedestrian_crossing_human_control2                    1.046928e-05
## pedestrian_crossing_physical_facilities1             -5.694752e-05
## pedestrian_crossing_physical_facilities4              5.490107e-05
## pedestrian_crossing_physical_facilities5              1.074067e-04
## pedestrian_crossing_physical_facilities7             -9.439215e-07
## pedestrian_crossing_physical_facilities8             -1.510750e-04
## light_conditions4                                     1.260440e-05
## light_conditions5                                     1.067562e-06
## light_conditions6                                     1.549914e-05
## light_conditions7                                     5.468780e-07
## weather_conditions2                                  -6.527877e-05
## weather_conditions3                                   2.400189e-06
## weather_conditions4                                   3.695436e-06
## weather_conditions5                                   8.963786e-06
## weather_conditions6                                   6.445255e-07
## weather_conditions7                                   1.149961e-06
## weather_conditions8                                   2.204472e-05
## road_surface_conditions2                              3.888519e-05
## road_surface_conditions3                             -2.708613e-07
## road_surface_conditions4                              5.161128e-07
## road_surface_conditions5                             -1.018453e-07
## special_conditions_at_site1                          -1.479543e-07
## special_conditions_at_site2                           3.591335e-07
## special_conditions_at_site3                           5.646051e-07
## special_conditions_at_site4                          -1.108708e-06
## special_conditions_at_site5                           1.270032e-07
## special_conditions_at_site6                          -3.701509e-07
## special_conditions_at_site7                           6.967322e-07
## carriageway_hazards1                                 -6.284278e-07
## carriageway_hazards2                                  6.907849e-06
## carriageway_hazards3                                 -2.697158e-07
## carriageway_hazards6                                  6.861970e-08
## carriageway_hazards7                                  6.639253e-07
## did_police_officer_attend_scene_of_collision1         4.226177e-05
## 1|2                                                   4.837639e-06
## 2|3                                                  -5.071663e-06
##                                               carriageway_hazards3
## police_force                                          3.576785e-09
## number_of_vehicles                                    3.410978e-06
## number_of_casualties                                 -1.442696e-06
## day_of_week                                           1.013550e-07
## first_road_class                                      9.070694e-08
## first_road_number                                     5.226263e-10
## road_type2                                            2.551955e-05
## road_type3                                           -3.043037e-05
## road_type6                                           -1.851094e-05
## road_type7                                            1.333963e-05
## speed_limit                                           1.046289e-07
## junction_detail1                                     -3.062830e-05
## junction_detail2                                      1.438224e-05
## junction_detail5                                      1.104152e-05
## junction_detail6                                     -8.587571e-06
## junction_detail7                                      1.023769e-06
## junction_detail8                                     -5.974176e-06
## junction_detail9                                     -1.693944e-06
## junction_control1                                    -2.751106e-07
## junction_control2                                     5.252020e-06
## junction_control3                                     2.419794e-07
## second_road_class                                    -5.754749e-08
## second_road_number                                   -6.921288e-11
## pedestrian_crossing_human_control1                   -6.669961e-07
## pedestrian_crossing_human_control2                   -2.126509e-06
## pedestrian_crossing_physical_facilities1             -2.499424e-05
## pedestrian_crossing_physical_facilities4             -1.500156e-05
## pedestrian_crossing_physical_facilities5              7.495099e-06
## pedestrian_crossing_physical_facilities7             -5.167397e-07
## pedestrian_crossing_physical_facilities8              1.588106e-05
## light_conditions4                                     3.283326e-06
## light_conditions5                                    -4.009784e-07
## light_conditions6                                     2.646468e-06
## light_conditions7                                    -8.209314e-07
## weather_conditions2                                   1.335981e-05
## weather_conditions3                                  -4.594512e-07
## weather_conditions4                                  -1.573282e-07
## weather_conditions5                                  -1.628566e-06
## weather_conditions6                                  -4.781555e-08
## weather_conditions7                                  -1.399122e-07
## weather_conditions8                                  -4.062837e-06
## road_surface_conditions2                             -5.466587e-06
## road_surface_conditions3                             -2.540435e-08
## road_surface_conditions4                             -1.034028e-07
## road_surface_conditions5                              8.793915e-08
## special_conditions_at_site1                           9.329709e-09
## special_conditions_at_site2                          -4.137560e-08
## special_conditions_at_site3                          -6.437543e-08
## special_conditions_at_site4                           8.781129e-08
## special_conditions_at_site5                          -1.132557e-08
## special_conditions_at_site6                          -1.259533e-08
## special_conditions_at_site7                          -3.084002e-07
## carriageway_hazards1                                 -1.806736e-07
## carriageway_hazards2                                 -2.697158e-07
## carriageway_hazards3                                  4.167806e-07
## carriageway_hazards6                                 -2.690564e-07
## carriageway_hazards7                                  1.069373e-07
## did_police_officer_attend_scene_of_collision1         1.545858e-05
## 1|2                                                   4.149717e-06
## 2|3                                                   2.212466e-06
##                                               carriageway_hazards6
## police_force                                          7.868256e-08
## number_of_vehicles                                   -5.501600e-06
## number_of_casualties                                  1.342230e-06
## day_of_week                                          -5.193584e-07
## first_road_class                                     -1.315215e-06
## first_road_number                                    -8.415179e-10
## road_type2                                           -2.291645e-05
## road_type3                                            2.780769e-05
## road_type6                                            2.645597e-05
## road_type7                                           -9.262549e-06
## speed_limit                                          -1.029233e-07
## junction_detail1                                      1.327795e-05
## junction_detail2                                     -6.370226e-06
## junction_detail5                                     -2.280675e-06
## junction_detail6                                     -1.506878e-05
## junction_detail7                                      9.873871e-06
## junction_detail8                                     -4.960623e-05
## junction_detail9                                      3.843292e-06
## junction_control1                                     1.481517e-06
## junction_control2                                    -1.361346e-05
## junction_control3                                     7.089931e-07
## second_road_class                                    -3.342500e-06
## second_road_number                                   -7.027293e-10
## pedestrian_crossing_human_control1                    1.940882e-06
## pedestrian_crossing_human_control2                    7.474515e-06
## pedestrian_crossing_physical_facilities1              8.083507e-05
## pedestrian_crossing_physical_facilities4             -3.044928e-06
## pedestrian_crossing_physical_facilities5              2.907911e-05
## pedestrian_crossing_physical_facilities7              2.733963e-08
## pedestrian_crossing_physical_facilities8             -4.397980e-05
## light_conditions4                                    -3.586787e-06
## light_conditions5                                     3.392399e-07
## light_conditions6                                    -1.955632e-06
## light_conditions7                                     1.007700e-06
## weather_conditions2                                  -7.047761e-06
## weather_conditions3                                  -2.817544e-07
## weather_conditions4                                  -9.733995e-07
## weather_conditions5                                   7.515132e-07
## weather_conditions6                                  -7.307642e-08
## weather_conditions7                                   1.206708e-08
## weather_conditions8                                   4.681417e-06
## road_surface_conditions2                              1.440517e-07
## road_surface_conditions3                             -1.312958e-07
## road_surface_conditions4                              1.186293e-06
## road_surface_conditions5                              2.067519e-10
## special_conditions_at_site1                           8.449724e-08
## special_conditions_at_site2                           7.721644e-08
## special_conditions_at_site3                           2.717754e-07
## special_conditions_at_site4                          -1.235376e-06
## special_conditions_at_site5                          -2.775481e-07
## special_conditions_at_site6                           1.251998e-08
## special_conditions_at_site7                           4.758395e-07
## carriageway_hazards1                                  3.319199e-07
## carriageway_hazards2                                  6.861970e-08
## carriageway_hazards3                                 -2.690564e-07
## carriageway_hazards6                                  1.178505e-06
## carriageway_hazards7                                 -3.105767e-07
## did_police_officer_attend_scene_of_collision1         1.526486e-05
## 1|2                                                  -9.614368e-06
## 2|3                                                  -1.208515e-06
##                                               carriageway_hazards7
## police_force                                         -1.530965e-08
## number_of_vehicles                                   -6.501792e-06
## number_of_casualties                                  7.477653e-08
## day_of_week                                          -9.721569e-08
## first_road_class                                      4.179124e-08
## first_road_number                                     1.779472e-10
## road_type2                                            9.244321e-06
## road_type3                                           -1.775486e-05
## road_type6                                           -7.649359e-06
## road_type7                                            1.687483e-06
## speed_limit                                           2.683215e-09
## junction_detail1                                      1.461400e-05
## junction_detail2                                     -4.963960e-06
## junction_detail5                                     -5.264590e-06
## junction_detail6                                      9.427612e-06
## junction_detail7                                     -8.392756e-06
## junction_detail8                                      4.488358e-05
## junction_detail9                                      2.263260e-05
## junction_control1                                    -1.863378e-07
## junction_control2                                    -6.835701e-07
## junction_control3                                     2.175256e-07
## second_road_class                                     1.084561e-06
## second_road_number                                    7.047333e-11
## pedestrian_crossing_human_control1                   -8.424209e-07
## pedestrian_crossing_human_control2                   -2.400604e-06
## pedestrian_crossing_physical_facilities1             -3.093454e-05
## pedestrian_crossing_physical_facilities4             -1.167285e-05
## pedestrian_crossing_physical_facilities5              9.970576e-06
## pedestrian_crossing_physical_facilities7              1.296189e-07
## pedestrian_crossing_physical_facilities8              2.834526e-06
## light_conditions4                                     2.586929e-06
## light_conditions5                                     6.957221e-09
## light_conditions6                                    -2.297146e-08
## light_conditions7                                    -3.009194e-07
## weather_conditions2                                   7.736443e-06
## weather_conditions3                                  -3.106315e-08
## weather_conditions4                                   4.575100e-07
## weather_conditions5                                  -5.616576e-07
## weather_conditions6                                   2.610770e-08
## weather_conditions7                                  -1.484087e-07
## weather_conditions8                                  -1.945698e-06
## road_surface_conditions2                             -2.937426e-06
## road_surface_conditions3                              3.123178e-08
## road_surface_conditions4                             -6.161019e-07
## road_surface_conditions5                              6.099879e-08
## special_conditions_at_site1                           2.624731e-08
## special_conditions_at_site2                           9.328127e-09
## special_conditions_at_site3                          -1.209050e-07
## special_conditions_at_site4                           6.282260e-07
## special_conditions_at_site5                           1.739129e-07
## special_conditions_at_site6                           2.127818e-08
## special_conditions_at_site7                          -5.269364e-08
## carriageway_hazards1                                 -1.774744e-07
## carriageway_hazards2                                  6.639253e-07
## carriageway_hazards3                                  1.069373e-07
## carriageway_hazards6                                 -3.105767e-07
## carriageway_hazards7                                  4.023095e-07
## did_police_officer_attend_scene_of_collision1         8.968779e-06
## 1|2                                                   1.305460e-06
## 2|3                                                   6.693966e-07
##                                               did_police_officer_attend_scene_of_collision1
## police_force                                                                   2.986699e-06
## number_of_vehicles                                                            -3.853562e-04
## number_of_casualties                                                          -1.954746e-04
## day_of_week                                                                   -7.186979e-05
## first_road_class                                                              -7.504961e-05
## first_road_number                                                              1.866811e-08
## road_type2                                                                     4.340672e-04
## road_type3                                                                    -3.227329e-05
## road_type6                                                                    -4.131410e-05
## road_type7                                                                     1.572097e-04
## speed_limit                                                                   -3.438190e-05
## junction_detail1                                                              -2.724846e-04
## junction_detail2                                                               1.260651e-04
## junction_detail5                                                               1.712476e-04
## junction_detail6                                                               7.354760e-05
## junction_detail7                                                               6.467093e-05
## junction_detail8                                                               3.256850e-04
## junction_detail9                                                              -1.935263e-04
## junction_control1                                                              5.610785e-05
## junction_control2                                                             -7.027094e-04
## junction_control3                                                              4.381482e-05
## second_road_class                                                             -4.538232e-04
## second_road_number                                                            -1.480564e-07
## pedestrian_crossing_human_control1                                            -5.526165e-06
## pedestrian_crossing_human_control2                                             1.724801e-05
## pedestrian_crossing_physical_facilities1                                      -3.737895e-04
## pedestrian_crossing_physical_facilities4                                      -1.771239e-04
## pedestrian_crossing_physical_facilities5                                      -9.001660e-05
## pedestrian_crossing_physical_facilities7                                       3.151922e-06
## pedestrian_crossing_physical_facilities8                                       4.669494e-04
## light_conditions4                                                             -2.801903e-04
## light_conditions5                                                             -1.556824e-06
## light_conditions6                                                              1.339064e-04
## light_conditions7                                                             -3.607977e-05
## weather_conditions2                                                           -6.081096e-05
## weather_conditions3                                                           -3.423998e-05
## weather_conditions4                                                            5.281111e-05
## weather_conditions5                                                           -2.461830e-05
## weather_conditions6                                                           -2.102814e-07
## weather_conditions7                                                            5.900113e-06
## weather_conditions8                                                            6.716495e-05
## road_surface_conditions2                                                      -2.310414e-04
## road_surface_conditions3                                                      -9.985607e-06
## road_surface_conditions4                                                       1.242466e-05
## road_surface_conditions5                                                       1.053380e-06
## special_conditions_at_site1                                                    8.297418e-06
## special_conditions_at_site2                                                   -6.301170e-07
## special_conditions_at_site3                                                    6.439834e-06
## special_conditions_at_site4                                                    4.046577e-05
## special_conditions_at_site5                                                    1.147691e-05
## special_conditions_at_site6                                                   -1.347724e-07
## special_conditions_at_site7                                                   -7.221346e-06
## carriageway_hazards1                                                          -2.488067e-06
## carriageway_hazards2                                                           4.226177e-05
## carriageway_hazards3                                                           1.545858e-05
## carriageway_hazards6                                                           1.526486e-05
## carriageway_hazards7                                                           8.968779e-06
## did_police_officer_attend_scene_of_collision1                                  6.442174e-03
## 1|2                                                                           -6.020997e-04
## 2|3                                                                            4.387679e-04
##                                                         1|2           2|3
## police_force                                  -6.164406e-07 -3.224082e-06
## number_of_vehicles                             4.235817e-05  4.968151e-04
## number_of_casualties                           2.820080e-05  8.598727e-05
## day_of_week                                    2.300141e-05  1.142515e-04
## first_road_class                               2.395279e-05  2.608138e-04
## first_road_number                              2.937416e-08 -1.454376e-08
## road_type2                                     4.410000e-04  1.112211e-04
## road_type3                                    -4.000678e-04 -1.329248e-04
## road_type6                                    -4.294955e-04 -1.344349e-04
## road_type7                                     2.155708e-04  4.568178e-05
## speed_limit                                    7.297049e-06  3.659183e-05
## junction_detail1                              -7.397416e-04  1.693721e-04
## junction_detail2                               1.777469e-04  1.487892e-05
## junction_detail5                               1.758574e-04 -2.617590e-05
## junction_detail6                               1.326485e-04 -6.464151e-06
## junction_detail7                              -7.379851e-05  2.655956e-05
## junction_detail8                               2.858743e-04  4.996023e-05
## junction_detail9                              -3.206487e-05  1.049512e-04
## junction_control1                             -1.637443e-06 -5.056435e-06
## junction_control2                             -2.452352e-04  5.307537e-04
## junction_control3                              1.772568e-05 -1.593870e-05
## second_road_class                              5.977153e-05  5.994621e-04
## second_road_number                             5.732749e-08  2.868652e-07
## pedestrian_crossing_human_control1            -1.417520e-05 -2.795678e-07
## pedestrian_crossing_human_control2            -4.249021e-05  3.742400e-05
## pedestrian_crossing_physical_facilities1      -5.228420e-04 -3.822359e-05
## pedestrian_crossing_physical_facilities4      -1.483107e-04  1.778656e-04
## pedestrian_crossing_physical_facilities5       5.062914e-05  2.423078e-04
## pedestrian_crossing_physical_facilities7      -1.217584e-05  1.980894e-06
## pedestrian_crossing_physical_facilities8      -2.004433e-05  1.480810e-05
## light_conditions4                              3.685951e-05  2.239431e-04
## light_conditions5                             -3.720682e-06  3.348277e-06
## light_conditions6                              9.487252e-05 -2.644072e-05
## light_conditions7                             -9.566984e-06 -1.045864e-05
## weather_conditions2                           -9.965870e-06  6.233125e-05
## weather_conditions3                            4.207342e-06 -7.381699e-07
## weather_conditions4                            3.321433e-06  3.025955e-06
## weather_conditions5                            3.370038e-06 -2.201691e-06
## weather_conditions6                            1.550810e-06 -9.324359e-07
## weather_conditions7                            1.295850e-06 -1.264115e-06
## weather_conditions8                           -1.565405e-05 -1.081486e-05
## road_surface_conditions2                       5.221363e-05  6.540907e-05
## road_surface_conditions3                       6.835259e-07 -1.168432e-06
## road_surface_conditions4                      -3.644309e-06 -9.350655e-07
## road_surface_conditions5                       6.780017e-07  2.724365e-07
## special_conditions_at_site1                   -1.833483e-06  2.197358e-06
## special_conditions_at_site2                    6.790653e-08  2.107637e-07
## special_conditions_at_site3                    2.025078e-06 -2.018041e-06
## special_conditions_at_site4                   -3.715645e-06  5.316805e-06
## special_conditions_at_site5                   -1.742560e-07 -6.481691e-07
## special_conditions_at_site6                   -1.443598e-06  2.793092e-07
## special_conditions_at_site7                   -2.230238e-06 -1.675501e-06
## carriageway_hazards1                          -4.182360e-06  2.633084e-06
## carriageway_hazards2                           4.837639e-06 -5.071663e-06
## carriageway_hazards3                           4.149717e-06  2.212466e-06
## carriageway_hazards6                          -9.614368e-06 -1.208515e-06
## carriageway_hazards7                           1.305460e-06  6.693966e-07
## did_police_officer_attend_scene_of_collision1 -6.020997e-04  4.387679e-04
## 1|2                                            2.311555e-04 -8.007921e-05
## 2|3                                           -8.007922e-05  7.782795e-03
#👸store the coefficients and p-values into one new dataframe
full_test2.coef <- data.frame(coef(summary(full_test2)))
full_test2.coef
##                                                       Value   Std..Error
## police_force                                   3.230595e-03 1.373585e-03
## number_of_vehicles                             4.265101e-01 4.155237e-02
## number_of_casualties                          -8.422624e-02 3.421859e-02
## day_of_week                                   -1.037475e-02 1.223468e-02
## first_road_class                               4.844015e-03 1.933777e-02
## first_road_number                             -2.125853e-05 2.072712e-05
## road_type2                                     2.485913e-01 5.641744e-02
## road_type3                                     5.334475e-02 8.557896e-02
## road_type6                                    -2.105413e-02 6.546775e-02
## road_type7                                    -1.119921e-01 2.936768e-02
## speed_limit                                   -1.027694e-02 2.208917e-03
## junction_detail1                               3.643206e-01 8.594962e-02
## junction_detail2                               1.712716e-01 3.047423e-02
## junction_detail5                              -9.276249e-02 2.405273e-02
## junction_detail6                              -4.698872e-02 6.814328e-02
## junction_detail7                               2.827486e-01 1.770464e-02
## junction_detail8                               9.584854e-02 1.215361e-01
## junction_detail9                               1.726160e-01 7.905967e-02
## junction_control1                              6.180706e-01 3.352450e-03
## junction_control2                              2.910535e-01 7.854581e-02
## junction_control3                              5.518884e-02 5.145758e-03
## second_road_class                             -6.095171e-02 2.317174e-02
## second_road_number                            -4.870301e-05 2.875283e-05
## pedestrian_crossing_human_control1             5.624002e-01 2.321910e-03
## pedestrian_crossing_human_control2             2.864052e-01 1.208853e-02
## pedestrian_crossing_physical_facilities1       2.317927e-01 1.085146e-01
## pedestrian_crossing_physical_facilities4      -4.873031e-02 8.582157e-02
## pedestrian_crossing_physical_facilities5      -7.346324e-02 8.316488e-02
## pedestrian_crossing_physical_facilities7      -1.572874e-03 1.448924e-03
## pedestrian_crossing_physical_facilities8      -1.405312e-01 8.585613e-02
## light_conditions4                             -2.300793e-01 5.795571e-02
## light_conditions5                             -7.831407e-01 1.628151e-03
## light_conditions6                              5.327328e-02 1.442372e-02
## light_conditions7                              3.421531e-01 1.813784e-03
## weather_conditions2                            9.196373e-02 9.978474e-02
## weather_conditions3                           -6.675492e-02 3.219935e-03
## weather_conditions4                           -1.123286e-01 4.873776e-03
## weather_conditions5                           -1.247158e-01 1.024380e-02
## weather_conditions6                            2.304587e-01 4.507887e-04
## weather_conditions7                            2.807177e-01 1.534522e-03
## weather_conditions8                            2.403537e-03 2.448874e-02
## road_surface_conditions2                       1.861046e-01 7.123883e-02
## road_surface_conditions3                       8.091304e-01 2.860129e-04
## road_surface_conditions4                       4.564709e-01 2.168251e-03
## road_surface_conditions5                       1.218938e-01 3.203473e-04
## special_conditions_at_site1                    1.149044e+00 3.198556e-04
## special_conditions_at_site2                   -8.860794e-01 2.477089e-04
## special_conditions_at_site3                   -1.810893e-01 9.392374e-04
## special_conditions_at_site4                   -1.144464e-02 2.242366e-03
## special_conditions_at_site5                    5.277993e-01 6.564248e-04
## special_conditions_at_site6                    1.071381e+00 2.453307e-04
## special_conditions_at_site7                   -1.133183e+00 9.169879e-04
## carriageway_hazards1                          -3.496611e-01 7.490099e-04
## carriageway_hazards2                          -2.249431e-02 2.628279e-03
## carriageway_hazards3                          -6.123622e-01 6.455854e-04
## carriageway_hazards6                           2.408518e-01 1.085590e-03
## carriageway_hazards7                          -4.971114e-01 6.342787e-04
## did_police_officer_attend_scene_of_collision1 -9.057968e-01 8.026315e-02
## 1|2                                           -5.239448e+00 1.520380e-02
## 2|3                                           -1.780145e+00 8.822015e-02
##                                                     t.value
## police_force                                   2.351943e+00
## number_of_vehicles                             1.026440e+01
## number_of_casualties                          -2.461417e+00
## day_of_week                                   -8.479791e-01
## first_road_class                               2.504950e-01
## first_road_number                             -1.025638e+00
## road_type2                                     4.406285e+00
## road_type3                                     6.233395e-01
## road_type6                                    -3.215954e-01
## road_type7                                    -3.813445e+00
## speed_limit                                   -4.652481e+00
## junction_detail1                               4.238769e+00
## junction_detail2                               5.620210e+00
## junction_detail5                              -3.856630e+00
## junction_detail6                              -6.895577e-01
## junction_detail7                               1.597031e+01
## junction_detail8                               7.886426e-01
## junction_detail9                               2.183363e+00
## junction_control1                              1.843638e+02
## junction_control2                              3.705525e+00
## junction_control3                              1.072511e+01
## second_road_class                             -2.630433e+00
## second_road_number                            -1.693851e+00
## pedestrian_crossing_human_control1             2.422144e+02
## pedestrian_crossing_human_control2             2.369232e+01
## pedestrian_crossing_physical_facilities1       2.136051e+00
## pedestrian_crossing_physical_facilities4      -5.678097e-01
## pedestrian_crossing_physical_facilities5      -8.833445e-01
## pedestrian_crossing_physical_facilities7      -1.085546e+00
## pedestrian_crossing_physical_facilities8      -1.636822e+00
## light_conditions4                             -3.969916e+00
## light_conditions5                             -4.810000e+02
## light_conditions6                              3.693449e+00
## light_conditions7                              1.886405e+02
## weather_conditions2                            9.216212e-01
## weather_conditions3                           -2.073176e+01
## weather_conditions4                           -2.304756e+01
## weather_conditions5                           -1.217476e+01
## weather_conditions6                            5.112343e+02
## weather_conditions7                            1.829350e+02
## weather_conditions8                            9.814868e-02
## road_surface_conditions2                       2.612404e+00
## road_surface_conditions3                       2.829000e+03
## road_surface_conditions4                       2.105250e+02
## road_surface_conditions5                       3.805050e+02
## special_conditions_at_site1                    3.592385e+03
## special_conditions_at_site2                   -3.577099e+03
## special_conditions_at_site3                   -1.928046e+02
## special_conditions_at_site4                   -5.103824e+00
## special_conditions_at_site5                    8.040515e+02
## special_conditions_at_site6                    4.367089e+03
## special_conditions_at_site7                   -1.235767e+03
## carriageway_hazards1                          -4.668310e+02
## carriageway_hazards2                          -8.558573e+00
## carriageway_hazards3                          -9.485379e+02
## carriageway_hazards6                           2.218626e+02
## carriageway_hazards7                          -7.837429e+02
## did_police_officer_attend_scene_of_collision1 -1.128534e+01
## 1|2                                           -3.446144e+02
## 2|3                                           -2.017844e+01
view(full_test2.coef) 
full_test2.coef$pval <- round((pnorm(abs(full_test2.coef$t.value), lower.tail = FALSE) * 2),2)
full_test2.coef  
##                                                       Value   Std..Error
## police_force                                   3.230595e-03 1.373585e-03
## number_of_vehicles                             4.265101e-01 4.155237e-02
## number_of_casualties                          -8.422624e-02 3.421859e-02
## day_of_week                                   -1.037475e-02 1.223468e-02
## first_road_class                               4.844015e-03 1.933777e-02
## first_road_number                             -2.125853e-05 2.072712e-05
## road_type2                                     2.485913e-01 5.641744e-02
## road_type3                                     5.334475e-02 8.557896e-02
## road_type6                                    -2.105413e-02 6.546775e-02
## road_type7                                    -1.119921e-01 2.936768e-02
## speed_limit                                   -1.027694e-02 2.208917e-03
## junction_detail1                               3.643206e-01 8.594962e-02
## junction_detail2                               1.712716e-01 3.047423e-02
## junction_detail5                              -9.276249e-02 2.405273e-02
## junction_detail6                              -4.698872e-02 6.814328e-02
## junction_detail7                               2.827486e-01 1.770464e-02
## junction_detail8                               9.584854e-02 1.215361e-01
## junction_detail9                               1.726160e-01 7.905967e-02
## junction_control1                              6.180706e-01 3.352450e-03
## junction_control2                              2.910535e-01 7.854581e-02
## junction_control3                              5.518884e-02 5.145758e-03
## second_road_class                             -6.095171e-02 2.317174e-02
## second_road_number                            -4.870301e-05 2.875283e-05
## pedestrian_crossing_human_control1             5.624002e-01 2.321910e-03
## pedestrian_crossing_human_control2             2.864052e-01 1.208853e-02
## pedestrian_crossing_physical_facilities1       2.317927e-01 1.085146e-01
## pedestrian_crossing_physical_facilities4      -4.873031e-02 8.582157e-02
## pedestrian_crossing_physical_facilities5      -7.346324e-02 8.316488e-02
## pedestrian_crossing_physical_facilities7      -1.572874e-03 1.448924e-03
## pedestrian_crossing_physical_facilities8      -1.405312e-01 8.585613e-02
## light_conditions4                             -2.300793e-01 5.795571e-02
## light_conditions5                             -7.831407e-01 1.628151e-03
## light_conditions6                              5.327328e-02 1.442372e-02
## light_conditions7                              3.421531e-01 1.813784e-03
## weather_conditions2                            9.196373e-02 9.978474e-02
## weather_conditions3                           -6.675492e-02 3.219935e-03
## weather_conditions4                           -1.123286e-01 4.873776e-03
## weather_conditions5                           -1.247158e-01 1.024380e-02
## weather_conditions6                            2.304587e-01 4.507887e-04
## weather_conditions7                            2.807177e-01 1.534522e-03
## weather_conditions8                            2.403537e-03 2.448874e-02
## road_surface_conditions2                       1.861046e-01 7.123883e-02
## road_surface_conditions3                       8.091304e-01 2.860129e-04
## road_surface_conditions4                       4.564709e-01 2.168251e-03
## road_surface_conditions5                       1.218938e-01 3.203473e-04
## special_conditions_at_site1                    1.149044e+00 3.198556e-04
## special_conditions_at_site2                   -8.860794e-01 2.477089e-04
## special_conditions_at_site3                   -1.810893e-01 9.392374e-04
## special_conditions_at_site4                   -1.144464e-02 2.242366e-03
## special_conditions_at_site5                    5.277993e-01 6.564248e-04
## special_conditions_at_site6                    1.071381e+00 2.453307e-04
## special_conditions_at_site7                   -1.133183e+00 9.169879e-04
## carriageway_hazards1                          -3.496611e-01 7.490099e-04
## carriageway_hazards2                          -2.249431e-02 2.628279e-03
## carriageway_hazards3                          -6.123622e-01 6.455854e-04
## carriageway_hazards6                           2.408518e-01 1.085590e-03
## carriageway_hazards7                          -4.971114e-01 6.342787e-04
## did_police_officer_attend_scene_of_collision1 -9.057968e-01 8.026315e-02
## 1|2                                           -5.239448e+00 1.520380e-02
## 2|3                                           -1.780145e+00 8.822015e-02
##                                                     t.value pval
## police_force                                   2.351943e+00 0.02
## number_of_vehicles                             1.026440e+01 0.00
## number_of_casualties                          -2.461417e+00 0.01
## day_of_week                                   -8.479791e-01 0.40
## first_road_class                               2.504950e-01 0.80
## first_road_number                             -1.025638e+00 0.31
## road_type2                                     4.406285e+00 0.00
## road_type3                                     6.233395e-01 0.53
## road_type6                                    -3.215954e-01 0.75
## road_type7                                    -3.813445e+00 0.00
## speed_limit                                   -4.652481e+00 0.00
## junction_detail1                               4.238769e+00 0.00
## junction_detail2                               5.620210e+00 0.00
## junction_detail5                              -3.856630e+00 0.00
## junction_detail6                              -6.895577e-01 0.49
## junction_detail7                               1.597031e+01 0.00
## junction_detail8                               7.886426e-01 0.43
## junction_detail9                               2.183363e+00 0.03
## junction_control1                              1.843638e+02 0.00
## junction_control2                              3.705525e+00 0.00
## junction_control3                              1.072511e+01 0.00
## second_road_class                             -2.630433e+00 0.01
## second_road_number                            -1.693851e+00 0.09
## pedestrian_crossing_human_control1             2.422144e+02 0.00
## pedestrian_crossing_human_control2             2.369232e+01 0.00
## pedestrian_crossing_physical_facilities1       2.136051e+00 0.03
## pedestrian_crossing_physical_facilities4      -5.678097e-01 0.57
## pedestrian_crossing_physical_facilities5      -8.833445e-01 0.38
## pedestrian_crossing_physical_facilities7      -1.085546e+00 0.28
## pedestrian_crossing_physical_facilities8      -1.636822e+00 0.10
## light_conditions4                             -3.969916e+00 0.00
## light_conditions5                             -4.810000e+02 0.00
## light_conditions6                              3.693449e+00 0.00
## light_conditions7                              1.886405e+02 0.00
## weather_conditions2                            9.216212e-01 0.36
## weather_conditions3                           -2.073176e+01 0.00
## weather_conditions4                           -2.304756e+01 0.00
## weather_conditions5                           -1.217476e+01 0.00
## weather_conditions6                            5.112343e+02 0.00
## weather_conditions7                            1.829350e+02 0.00
## weather_conditions8                            9.814868e-02 0.92
## road_surface_conditions2                       2.612404e+00 0.01
## road_surface_conditions3                       2.829000e+03 0.00
## road_surface_conditions4                       2.105250e+02 0.00
## road_surface_conditions5                       3.805050e+02 0.00
## special_conditions_at_site1                    3.592385e+03 0.00
## special_conditions_at_site2                   -3.577099e+03 0.00
## special_conditions_at_site3                   -1.928046e+02 0.00
## special_conditions_at_site4                   -5.103824e+00 0.00
## special_conditions_at_site5                    8.040515e+02 0.00
## special_conditions_at_site6                    4.367089e+03 0.00
## special_conditions_at_site7                   -1.235767e+03 0.00
## carriageway_hazards1                          -4.668310e+02 0.00
## carriageway_hazards2                          -8.558573e+00 0.00
## carriageway_hazards3                          -9.485379e+02 0.00
## carriageway_hazards6                           2.218626e+02 0.00
## carriageway_hazards7                          -7.837429e+02 0.00
## did_police_officer_attend_scene_of_collision1 -1.128534e+01 0.00
## 1|2                                           -3.446144e+02 0.00
## 2|3                                           -2.017844e+01 0.00
view(full_test2.coef)
#Select the row names corresponding to all values less than 0.05 in the full_model2.coef$pval column
significant_rows <- rownames(full_test2.coef[full_test2.coef$pval < 0.05, ])
significant_rows       #16 predictors
##  [1] "police_force"                                 
##  [2] "number_of_vehicles"                           
##  [3] "number_of_casualties"                         
##  [4] "road_type2"                                   
##  [5] "road_type7"                                   
##  [6] "speed_limit"                                  
##  [7] "junction_detail1"                             
##  [8] "junction_detail2"                             
##  [9] "junction_detail5"                             
## [10] "junction_detail7"                             
## [11] "junction_detail9"                             
## [12] "junction_control1"                            
## [13] "junction_control2"                            
## [14] "junction_control3"                            
## [15] "second_road_class"                            
## [16] "pedestrian_crossing_human_control1"           
## [17] "pedestrian_crossing_human_control2"           
## [18] "pedestrian_crossing_physical_facilities1"     
## [19] "light_conditions4"                            
## [20] "light_conditions5"                            
## [21] "light_conditions6"                            
## [22] "light_conditions7"                            
## [23] "weather_conditions3"                          
## [24] "weather_conditions4"                          
## [25] "weather_conditions5"                          
## [26] "weather_conditions6"                          
## [27] "weather_conditions7"                          
## [28] "road_surface_conditions2"                     
## [29] "road_surface_conditions3"                     
## [30] "road_surface_conditions4"                     
## [31] "road_surface_conditions5"                     
## [32] "special_conditions_at_site1"                  
## [33] "special_conditions_at_site2"                  
## [34] "special_conditions_at_site3"                  
## [35] "special_conditions_at_site4"                  
## [36] "special_conditions_at_site5"                  
## [37] "special_conditions_at_site6"                  
## [38] "special_conditions_at_site7"                  
## [39] "carriageway_hazards1"                         
## [40] "carriageway_hazards2"                         
## [41] "carriageway_hazards3"                         
## [42] "carriageway_hazards6"                         
## [43] "carriageway_hazards7"                         
## [44] "did_police_officer_attend_scene_of_collision1"
## [45] "1|2"                                          
## [46] "2|3"
#💛1_2. Run a Ordered logit shorted model       💜8
#16 predictors
#different from Mutinomial Logit model(Baseline=3), who has 17 predictors in shorted_test
library(MASS)
unique(data4$legacy_collision_severity)
## [1] 3 2 1
## Levels: 1 < 2 < 3
data4$pedestrian_crossing_human_control[1]
## [1] 2
## Levels: 0 1 2
data4$did_police_officer_attend_scene_of_collision[1]
## [1] 1
## Levels: 2 1
shorted_test2 <- polr(legacy_collision_severity ~ police_force + number_of_vehicles + number_of_casualties + road_type + speed_limit + junction_detail + junction_control + second_road_class + pedestrian_crossing_human_control + pedestrian_crossing_physical_facilities + light_conditions + weather_conditions + road_surface_conditions + special_conditions_at_site + carriageway_hazards + did_police_officer_attend_scene_of_collision, data = data4, Hess = TRUE)  
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
summary(shorted_test2) ## Residual Deviance: 11222.24  AIC: 11334.24
## Call:
## polr(formula = legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + road_type + speed_limit + junction_detail + 
##     junction_control + second_road_class + pedestrian_crossing_human_control + 
##     pedestrian_crossing_physical_facilities + light_conditions + 
##     weather_conditions + road_surface_conditions + special_conditions_at_site + 
##     carriageway_hazards + did_police_officer_attend_scene_of_collision, 
##     data = data4, Hess = TRUE)
## 
## Coefficients:
##                                                   Value Std. Error   t value
## police_force                                   0.003124   0.001378   2.26803
## number_of_vehicles                             0.422805   0.043065   9.81773
## number_of_casualties                          -0.085610   0.034300  -2.49593
## road_type2                                     0.248876   0.210676   1.18132
## road_type3                                     0.059759   0.147936   0.40395
## road_type6                                    -0.015504   0.140402  -0.11042
## road_type7                                    -0.103355   0.236646  -0.43675
## speed_limit                                   -0.010363   0.002445  -4.23785
## junction_detail1                               0.371461   0.124393   2.98619
## junction_detail2                               0.171106   0.173149   0.98820
## junction_detail5                              -0.071809   0.185078  -0.38800
## junction_detail6                              -0.049840   0.071378  -0.69826
## junction_detail7                               0.289727   0.161753   1.79117
## junction_detail8                               0.093108   0.126259   0.73744
## junction_detail9                               0.169208   0.081595   2.07376
## junction_control1                              0.628161   0.244009   2.57433
## junction_control2                              0.280064   0.090546   3.09304
## junction_control3                              0.034801   0.221404   0.15718
## second_road_class                             -0.034215   0.024166  -1.41587
## pedestrian_crossing_human_control1             0.556194   0.372127   1.49463
## pedestrian_crossing_human_control2             0.292387   0.182981   1.59791
## pedestrian_crossing_physical_facilities1       0.227436   0.119254   1.90716
## pedestrian_crossing_physical_facilities4      -0.055211   0.096804  -0.57034
## pedestrian_crossing_physical_facilities5      -0.076243   0.103332  -0.73785
## pedestrian_crossing_physical_facilities7       0.013914   0.513460   0.02710
## pedestrian_crossing_physical_facilities8      -0.158123   0.128919  -1.22653
## light_conditions4                             -0.230997   0.058892  -3.92235
## light_conditions5                             -0.765910   0.280402  -2.73147
## light_conditions6                              0.052363   0.156833   0.33388
## light_conditions7                              0.336535   0.292684   1.14982
## weather_conditions2                            0.084699   0.107555   0.78749
## weather_conditions3                           -0.069150   0.425169  -0.16264
## weather_conditions4                           -0.113436   0.247994  -0.45741
## weather_conditions5                           -0.127221   0.286234  -0.44447
## weather_conditions6                            0.266776   1.156513   0.23067
## weather_conditions7                            0.308954   0.513517   0.60164
## weather_conditions8                           -0.007836   0.155574  -0.05037
## road_surface_conditions2                       0.183387   0.078502   2.33607
## road_surface_conditions3                       0.804214   0.663814   1.21151
## road_surface_conditions4                       0.450437   0.216709   2.07853
## road_surface_conditions5                       0.088535   1.238909   0.07146
## special_conditions_at_site1                    1.134081   0.537110   2.11145
## special_conditions_at_site2                   -0.900822   1.385359  -0.65024
## special_conditions_at_site3                   -0.206853   0.512145  -0.40390
## special_conditions_at_site4                   -0.009406   0.234767  -0.04007
## special_conditions_at_site5                    0.510398   0.657044   0.77681
## special_conditions_at_site6                    1.072193   1.075558   0.99687
## special_conditions_at_site7                   -1.114194   0.593731  -1.87660
## carriageway_hazards1                          -0.362486   0.459623  -0.78866
## carriageway_hazards2                          -0.013291   0.243083  -0.05468
## carriageway_hazards3                          -0.598150   0.577652  -1.03549
## carriageway_hazards6                           0.253309   0.521053   0.48615
## carriageway_hazards7                          -0.487794   0.595727  -0.81882
## did_police_officer_attend_scene_of_collision1 -0.895064   0.086451 -10.35344
## 
## Intercepts:
##     Value    Std. Error t value 
## 1|2  -5.0398   0.2598   -19.4014
## 2|3  -1.5818   0.2412    -6.5589
## 
## Residual Deviance: 11222.24 
## AIC: 11334.24
summary(shorted_test2)$coef
##                                                      Value  Std. Error
## police_force                                   0.003124304 0.001377543
## number_of_vehicles                             0.422805134 0.043065470
## number_of_casualties                          -0.085609689 0.034299765
## road_type2                                     0.248876439 0.210676376
## road_type3                                     0.059759213 0.147936114
## road_type6                                    -0.015503708 0.140402161
## road_type7                                    -0.103355186 0.236645679
## speed_limit                                   -0.010363247 0.002445403
## junction_detail1                               0.371461192 0.124393146
## junction_detail2                               0.171105773 0.173148612
## junction_detail5                              -0.071809241 0.185077506
## junction_detail6                              -0.049840334 0.071377513
## junction_detail7                               0.289726644 0.161752851
## junction_detail8                               0.093108462 0.126258596
## junction_detail9                               0.169207963 0.081594682
## junction_control1                              0.628160839 0.244009328
## junction_control2                              0.280064142 0.090546421
## junction_control3                              0.034800957 0.221404411
## second_road_class                             -0.034215346 0.024165527
## pedestrian_crossing_human_control1             0.556193848 0.372126950
## pedestrian_crossing_human_control2             0.292387239 0.182980590
## pedestrian_crossing_physical_facilities1       0.227436005 0.119253841
## pedestrian_crossing_physical_facilities4      -0.055210638 0.096803768
## pedestrian_crossing_physical_facilities5      -0.076243488 0.103332494
## pedestrian_crossing_physical_facilities7       0.013913691 0.513459515
## pedestrian_crossing_physical_facilities8      -0.158123355 0.128918864
## light_conditions4                             -0.230996966 0.058892446
## light_conditions5                             -0.765910191 0.280401697
## light_conditions6                              0.052363298 0.156833022
## light_conditions7                              0.336534733 0.292684150
## weather_conditions2                            0.084698697 0.107555387
## weather_conditions3                           -0.069150255 0.425168781
## weather_conditions4                           -0.113436148 0.247994274
## weather_conditions5                           -0.127221134 0.286234248
## weather_conditions6                            0.266775546 1.156513098
## weather_conditions7                            0.308953671 0.513517428
## weather_conditions8                           -0.007836116 0.155573849
## road_surface_conditions2                       0.183387058 0.078502320
## road_surface_conditions3                       0.804214236 0.663813610
## road_surface_conditions4                       0.450437467 0.216709482
## road_surface_conditions5                       0.088534624 1.238909124
## special_conditions_at_site1                    1.134080638 0.537109782
## special_conditions_at_site2                   -0.900821632 1.385359393
## special_conditions_at_site3                   -0.206853355 0.512145038
## special_conditions_at_site4                   -0.009406264 0.234767432
## special_conditions_at_site5                    0.510397582 0.657043574
## special_conditions_at_site6                    1.072192500 1.075557662
## special_conditions_at_site7                   -1.114194034 0.593731062
## carriageway_hazards1                          -0.362486169 0.459622530
## carriageway_hazards2                          -0.013291183 0.243083105
## carriageway_hazards3                          -0.598149796 0.577651698
## carriageway_hazards6                           0.253309263 0.521052870
## carriageway_hazards7                          -0.487794450 0.595726771
## did_police_officer_attend_scene_of_collision1 -0.895063552 0.086450819
## 1|2                                           -5.039825999 0.259766243
## 2|3                                           -1.581776891 0.241164136
##                                                    t value
## police_force                                    2.26802670
## number_of_vehicles                              9.81772944
## number_of_casualties                           -2.49592640
## road_type2                                      1.18132106
## road_type3                                      0.40395283
## road_type6                                     -0.11042357
## road_type7                                     -0.43675078
## speed_limit                                    -4.23784886
## junction_detail1                                2.98618697
## junction_detail2                                0.98820182
## junction_detail5                               -0.38799551
## junction_detail6                               -0.69826381
## junction_detail7                                1.79116870
## junction_detail8                                0.73744255
## junction_detail9                                2.07376213
## junction_control1                               2.57433126
## junction_control2                               3.09304487
## junction_control3                               0.15718276
## second_road_class                              -1.41587419
## pedestrian_crossing_human_control1              1.49463469
## pedestrian_crossing_human_control2              1.59791396
## pedestrian_crossing_physical_facilities1        1.90715873
## pedestrian_crossing_physical_facilities4       -0.57033563
## pedestrian_crossing_physical_facilities5       -0.73784621
## pedestrian_crossing_physical_facilities7        0.02709793
## pedestrian_crossing_physical_facilities8       -1.22653389
## light_conditions4                              -3.92235304
## light_conditions5                              -2.73147488
## light_conditions6                               0.33387929
## light_conditions7                               1.14982220
## weather_conditions2                             0.78748912
## weather_conditions3                            -0.16264189
## weather_conditions4                            -0.45741438
## weather_conditions5                            -0.44446510
## weather_conditions6                             0.23067231
## weather_conditions7                             0.60164204
## weather_conditions8                            -0.05036911
## road_surface_conditions2                        2.33607183
## road_surface_conditions3                        1.21150610
## road_surface_conditions4                        2.07853142
## road_surface_conditions5                        0.07146176
## special_conditions_at_site1                     2.11145035
## special_conditions_at_site2                    -0.65024400
## special_conditions_at_site3                    -0.40389605
## special_conditions_at_site4                    -0.04006631
## special_conditions_at_site5                     0.77680934
## special_conditions_at_site6                     0.99687124
## special_conditions_at_site7                    -1.87659718
## carriageway_hazards1                           -0.78866057
## carriageway_hazards2                           -0.05467753
## carriageway_hazards3                           -1.03548522
## carriageway_hazards6                            0.48614887
## carriageway_hazards7                           -0.81882244
## did_police_officer_attend_scene_of_collision1 -10.35344208
## 1|2                                           -19.40138924
## 2|3                                            -6.55892256
coef(shorted_test2)   # the values of Log odds ratio
##                                  police_force 
##                                   0.003124304 
##                            number_of_vehicles 
##                                   0.422805134 
##                          number_of_casualties 
##                                  -0.085609689 
##                                    road_type2 
##                                   0.248876439 
##                                    road_type3 
##                                   0.059759213 
##                                    road_type6 
##                                  -0.015503708 
##                                    road_type7 
##                                  -0.103355186 
##                                   speed_limit 
##                                  -0.010363247 
##                              junction_detail1 
##                                   0.371461192 
##                              junction_detail2 
##                                   0.171105773 
##                              junction_detail5 
##                                  -0.071809241 
##                              junction_detail6 
##                                  -0.049840334 
##                              junction_detail7 
##                                   0.289726644 
##                              junction_detail8 
##                                   0.093108462 
##                              junction_detail9 
##                                   0.169207963 
##                             junction_control1 
##                                   0.628160839 
##                             junction_control2 
##                                   0.280064142 
##                             junction_control3 
##                                   0.034800957 
##                             second_road_class 
##                                  -0.034215346 
##            pedestrian_crossing_human_control1 
##                                   0.556193848 
##            pedestrian_crossing_human_control2 
##                                   0.292387239 
##      pedestrian_crossing_physical_facilities1 
##                                   0.227436005 
##      pedestrian_crossing_physical_facilities4 
##                                  -0.055210638 
##      pedestrian_crossing_physical_facilities5 
##                                  -0.076243488 
##      pedestrian_crossing_physical_facilities7 
##                                   0.013913691 
##      pedestrian_crossing_physical_facilities8 
##                                  -0.158123355 
##                             light_conditions4 
##                                  -0.230996966 
##                             light_conditions5 
##                                  -0.765910191 
##                             light_conditions6 
##                                   0.052363298 
##                             light_conditions7 
##                                   0.336534733 
##                           weather_conditions2 
##                                   0.084698697 
##                           weather_conditions3 
##                                  -0.069150255 
##                           weather_conditions4 
##                                  -0.113436148 
##                           weather_conditions5 
##                                  -0.127221134 
##                           weather_conditions6 
##                                   0.266775546 
##                           weather_conditions7 
##                                   0.308953671 
##                           weather_conditions8 
##                                  -0.007836116 
##                      road_surface_conditions2 
##                                   0.183387058 
##                      road_surface_conditions3 
##                                   0.804214236 
##                      road_surface_conditions4 
##                                   0.450437467 
##                      road_surface_conditions5 
##                                   0.088534624 
##                   special_conditions_at_site1 
##                                   1.134080638 
##                   special_conditions_at_site2 
##                                  -0.900821632 
##                   special_conditions_at_site3 
##                                  -0.206853355 
##                   special_conditions_at_site4 
##                                  -0.009406264 
##                   special_conditions_at_site5 
##                                   0.510397582 
##                   special_conditions_at_site6 
##                                   1.072192500 
##                   special_conditions_at_site7 
##                                  -1.114194034 
##                          carriageway_hazards1 
##                                  -0.362486169 
##                          carriageway_hazards2 
##                                  -0.013291183 
##                          carriageway_hazards3 
##                                  -0.598149796 
##                          carriageway_hazards6 
##                                   0.253309263 
##                          carriageway_hazards7 
##                                  -0.487794450 
## did_police_officer_attend_scene_of_collision1 
##                                  -0.895063552
vcov(shorted_test2) 
##                                                police_force number_of_vehicles
## police_force                                   1.897624e-06       8.025984e-07
## number_of_vehicles                             8.025984e-07       1.854635e-03
## number_of_casualties                          -1.166492e-06      -2.718963e-04
## road_type2                                     6.214179e-06       4.424354e-04
## road_type3                                     9.208133e-06       8.753852e-05
## road_type6                                    -3.281872e-06       1.398520e-04
## road_type7                                     6.510711e-06       2.145770e-04
## speed_limit                                   -1.077285e-06      -7.583540e-06
## junction_detail1                              -8.256375e-06       1.439843e-04
## junction_detail2                              -9.748954e-06      -3.114591e-05
## junction_detail5                               1.009901e-05       1.757577e-04
## junction_detail6                               3.446518e-06      -1.227443e-04
## junction_detail7                               1.144584e-05      -2.369430e-05
## junction_detail8                               2.948437e-06      -1.093915e-04
## junction_detail9                               8.965782e-06       5.154829e-05
## junction_control1                             -1.443899e-05       6.365947e-05
## junction_control2                              3.741435e-06      -5.852332e-05
## junction_control3                              5.893550e-06      -1.444113e-04
## second_road_class                             -2.440834e-06       4.595822e-06
## pedestrian_crossing_human_control1             5.591302e-06       3.059586e-04
## pedestrian_crossing_human_control2             9.880561e-06       1.404411e-04
## pedestrian_crossing_physical_facilities1       9.360524e-06       3.305766e-04
## pedestrian_crossing_physical_facilities4       5.834943e-07       1.955126e-04
## pedestrian_crossing_physical_facilities5      -1.438665e-06       2.785219e-04
## pedestrian_crossing_physical_facilities7      -1.240338e-05       6.949352e-05
## pedestrian_crossing_physical_facilities8      -3.816750e-06       2.546977e-04
## light_conditions4                              2.748314e-06       6.586602e-05
## light_conditions5                             -2.695962e-06      -8.890554e-05
## light_conditions6                             -3.698647e-06       5.240249e-04
## light_conditions7                             -4.650401e-06       4.129255e-04
## weather_conditions2                            5.368980e-06       6.612076e-05
## weather_conditions3                            9.789859e-06       1.999227e-04
## weather_conditions4                            1.623597e-06       9.804878e-05
## weather_conditions5                           -1.443245e-07       7.777018e-05
## weather_conditions6                            4.556588e-05       4.026250e-04
## weather_conditions7                           -4.911409e-06       2.472542e-05
## weather_conditions8                            5.994749e-06       8.293645e-05
## road_surface_conditions2                      -4.905571e-06       7.817709e-06
## road_surface_conditions3                      -3.196201e-06      -2.173558e-04
## road_surface_conditions4                      -8.154648e-06       4.922549e-05
## road_surface_conditions5                      -2.580389e-05       1.191380e-03
## special_conditions_at_site1                   -7.272675e-07       8.714675e-05
## special_conditions_at_site2                    1.462736e-05       1.698752e-04
## special_conditions_at_site3                   -3.287575e-07       3.131704e-04
## special_conditions_at_site4                    8.496634e-06       1.476858e-04
## special_conditions_at_site5                    7.139577e-06       6.050104e-04
## special_conditions_at_site6                    1.275415e-05       7.047035e-04
## special_conditions_at_site7                    5.252832e-09       7.022984e-04
## carriageway_hazards1                           1.062817e-05      -3.032485e-04
## carriageway_hazards2                           1.142972e-05       3.173973e-04
## carriageway_hazards3                           7.157866e-06      -4.406857e-04
## carriageway_hazards6                           1.558998e-05       7.874682e-04
## carriageway_hazards7                          -1.336979e-06       1.055727e-03
## did_police_officer_attend_scene_of_collision1  8.300320e-07      -1.171484e-04
## 1|2                                           -5.056130e-06       2.775128e-03
## 2|3                                           -4.397034e-06       2.865688e-03
##                                               number_of_casualties
## police_force                                         -1.166492e-06
## number_of_vehicles                                   -2.718963e-04
## number_of_casualties                                  1.176474e-03
## road_type2                                            3.982038e-05
## road_type3                                           -3.243110e-05
## road_type6                                           -9.354539e-06
## road_type7                                           -7.619911e-05
## speed_limit                                          -9.850909e-06
## junction_detail1                                      1.179088e-04
## junction_detail2                                     -1.273445e-05
## junction_detail5                                     -9.950491e-07
## junction_detail6                                     -1.096320e-04
## junction_detail7                                     -2.728590e-05
## junction_detail8                                      2.286728e-05
## junction_detail9                                     -5.508376e-06
## junction_control1                                    -1.140968e-04
## junction_control2                                    -5.075707e-07
## junction_control3                                    -1.252369e-05
## second_road_class                                     9.108229e-06
## pedestrian_crossing_human_control1                   -6.562656e-05
## pedestrian_crossing_human_control2                    5.671635e-05
## pedestrian_crossing_physical_facilities1              6.033465e-05
## pedestrian_crossing_physical_facilities4             -1.556625e-05
## pedestrian_crossing_physical_facilities5             -2.658804e-07
## pedestrian_crossing_physical_facilities7              1.683366e-04
## pedestrian_crossing_physical_facilities8             -5.082271e-05
## light_conditions4                                    -5.027184e-05
## light_conditions5                                     3.347068e-05
## light_conditions6                                    -6.002179e-05
## light_conditions7                                     1.311347e-04
## weather_conditions2                                  -6.453136e-05
## weather_conditions3                                  -4.209503e-05
## weather_conditions4                                   5.453756e-05
## weather_conditions5                                   2.717027e-05
## weather_conditions6                                  -3.786211e-04
## weather_conditions7                                  -1.748535e-04
## weather_conditions8                                  -2.827528e-05
## road_surface_conditions2                              2.270092e-05
## road_surface_conditions3                             -1.852760e-04
## road_surface_conditions4                              1.160612e-04
## road_surface_conditions5                             -9.145523e-04
## special_conditions_at_site1                          -6.318951e-05
## special_conditions_at_site2                          -1.758362e-03
## special_conditions_at_site3                          -1.844841e-04
## special_conditions_at_site4                           1.124180e-04
## special_conditions_at_site5                           1.240782e-04
## special_conditions_at_site6                          -8.490112e-05
## special_conditions_at_site7                          -1.643479e-04
## carriageway_hazards1                                 -1.933438e-04
## carriageway_hazards2                                 -1.166335e-04
## carriageway_hazards3                                  1.373269e-04
## carriageway_hazards6                                 -1.841422e-04
## carriageway_hazards7                                  2.510767e-04
## did_police_officer_attend_scene_of_collision1        -1.200215e-04
## 1|2                                                   6.273449e-04
## 2|3                                                   6.027295e-04
##                                                  road_type2    road_type3
## police_force                                   6.214179e-06  9.208133e-06
## number_of_vehicles                             4.424354e-04  8.753852e-05
## number_of_casualties                           3.982038e-05 -3.243110e-05
## road_type2                                     4.438454e-02  1.751005e-02
## road_type3                                     1.751005e-02  2.188509e-02
## road_type6                                     1.897573e-02  1.736820e-02
## road_type7                                     1.668530e-02  1.645796e-02
## speed_limit                                    2.461894e-05 -2.966464e-05
## junction_detail1                               1.161520e-02  9.768796e-03
## junction_detail2                               9.016391e-03  7.978880e-03
## junction_detail5                               1.454202e-03 -5.866122e-04
## junction_detail6                               1.788151e-05 -6.076633e-05
## junction_detail7                               2.768560e-04 -3.737858e-04
## junction_detail8                              -2.039016e-04  1.538234e-04
## junction_detail9                              -2.477941e-04 -7.667266e-05
## junction_control1                              7.563444e-04  9.234206e-05
## junction_control2                              4.928681e-04 -5.601390e-04
## junction_control3                              1.188875e-04  1.281629e-04
## second_road_class                              1.030633e-04 -5.366581e-05
## pedestrian_crossing_human_control1             8.775761e-04 -2.503175e-04
## pedestrian_crossing_human_control2            -3.469710e-04  7.673773e-05
## pedestrian_crossing_physical_facilities1      -6.076324e-04 -3.233142e-05
## pedestrian_crossing_physical_facilities4      -5.222486e-05 -4.498120e-04
## pedestrian_crossing_physical_facilities5      -6.847023e-05 -4.749284e-04
## pedestrian_crossing_physical_facilities7       1.405528e-03 -4.200635e-04
## pedestrian_crossing_physical_facilities8       6.034407e-05 -2.098851e-04
## light_conditions4                             -6.149051e-05 -1.948129e-04
## light_conditions5                             -2.737138e-04 -4.053279e-04
## light_conditions6                              2.579836e-04  5.833185e-04
## light_conditions7                              2.956250e-04 -2.237193e-04
## weather_conditions2                           -2.846281e-05 -2.664237e-04
## weather_conditions3                           -8.653859e-05 -1.839748e-04
## weather_conditions4                           -8.131298e-05  2.488681e-04
## weather_conditions5                            1.161230e-04 -2.750454e-04
## weather_conditions6                            3.768606e-04 -7.680330e-04
## weather_conditions7                           -1.485275e-05 -2.936220e-04
## weather_conditions8                           -2.649381e-04 -1.432886e-04
## road_surface_conditions2                      -4.499111e-05 -6.966196e-06
## road_surface_conditions3                      -5.882435e-04 -2.114690e-05
## road_surface_conditions4                       3.628686e-04  1.739785e-04
## road_surface_conditions5                      -1.920407e-03 -1.211223e-03
## special_conditions_at_site1                    7.058798e-04  2.593292e-04
## special_conditions_at_site2                    1.327978e-03 -2.983287e-03
## special_conditions_at_site3                    1.417101e-03  1.396733e-03
## special_conditions_at_site4                   -5.971362e-04  1.537135e-04
## special_conditions_at_site5                    5.963686e-04  2.793193e-05
## special_conditions_at_site6                    4.400235e-03  3.871112e-03
## special_conditions_at_site7                    6.770880e-04 -1.093193e-04
## carriageway_hazards1                           9.696663e-04  8.589464e-04
## carriageway_hazards2                           1.249772e-04  9.158877e-05
## carriageway_hazards3                          -9.998134e-04  9.427656e-04
## carriageway_hazards6                           1.303359e-03  3.477349e-04
## carriageway_hazards7                          -1.327448e-03 -4.705194e-05
## did_police_officer_attend_scene_of_collision1 -1.533964e-04  1.330069e-04
## 1|2                                            2.159303e-02  1.668912e-02
## 2|3                                            2.164604e-02  1.670047e-02
##                                                  road_type6    road_type7
## police_force                                  -3.281872e-06  6.510711e-06
## number_of_vehicles                             1.398520e-04  2.145770e-04
## number_of_casualties                          -9.354539e-06 -7.619911e-05
## road_type2                                     1.897573e-02  1.668530e-02
## road_type3                                     1.736820e-02  1.645796e-02
## road_type6                                     1.971277e-02  1.631876e-02
## road_type7                                     1.631876e-02  5.600118e-02
## speed_limit                                   -2.190565e-06 -1.887061e-05
## junction_detail1                               1.153650e-02  8.839389e-03
## junction_detail2                               8.827152e-03  7.673450e-03
## junction_detail5                               2.144103e-03 -1.109682e-02
## junction_detail6                              -6.778828e-07  9.384708e-06
## junction_detail7                               1.733421e-04 -5.325978e-05
## junction_detail8                              -9.712640e-06 -2.206377e-04
## junction_detail9                               2.531912e-04 -1.928843e-04
## junction_control1                              7.147673e-04  3.423862e-04
## junction_control2                              4.890145e-04  8.658277e-05
## junction_control3                              2.951751e-04 -4.895125e-04
## second_road_class                             -1.266643e-04  2.249805e-04
## pedestrian_crossing_human_control1            -9.593153e-05 -1.420149e-03
## pedestrian_crossing_human_control2             1.188812e-04 -9.130513e-05
## pedestrian_crossing_physical_facilities1       1.498179e-05 -6.089267e-04
## pedestrian_crossing_physical_facilities4      -1.623472e-04 -2.876285e-04
## pedestrian_crossing_physical_facilities5      -9.134883e-05 -1.070627e-05
## pedestrian_crossing_physical_facilities7       1.182413e-03  1.466813e-03
## pedestrian_crossing_physical_facilities8      -1.620676e-04 -2.921010e-05
## light_conditions4                             -1.195266e-05  5.329324e-05
## light_conditions5                             -2.143174e-04 -4.750829e-04
## light_conditions6                              1.876847e-04  2.137344e-04
## light_conditions7                             -6.656146e-05  3.780882e-04
## weather_conditions2                           -4.021740e-05  5.113122e-04
## weather_conditions3                           -1.142441e-04  1.239563e-04
## weather_conditions4                            3.266206e-04  5.651420e-04
## weather_conditions5                           -5.104907e-04 -3.142367e-04
## weather_conditions6                           -1.077001e-04  3.144536e-03
## weather_conditions7                           -4.136371e-05  6.184161e-04
## weather_conditions8                           -8.762487e-05  4.401104e-04
## road_surface_conditions2                      -8.337428e-05 -2.031825e-04
## road_surface_conditions3                       2.864062e-05  1.345627e-03
## road_surface_conditions4                       1.168853e-06 -3.822033e-04
## road_surface_conditions5                      -2.355626e-03 -1.723077e-03
## special_conditions_at_site1                    3.752970e-04  6.689651e-04
## special_conditions_at_site2                    1.536855e-03  5.432975e-04
## special_conditions_at_site3                    8.880946e-04  1.487473e-03
## special_conditions_at_site4                    3.206552e-04  9.831402e-04
## special_conditions_at_site5                   -7.655354e-05  4.200538e-04
## special_conditions_at_site6                    3.920277e-03  4.236945e-03
## special_conditions_at_site7                   -3.984381e-06  5.907402e-04
## carriageway_hazards1                           4.378857e-04  1.006667e-03
## carriageway_hazards2                          -2.540981e-05  3.084665e-04
## carriageway_hazards3                           4.882681e-04  9.330190e-04
## carriageway_hazards6                          -5.381264e-05  1.973508e-03
## carriageway_hazards7                          -4.311293e-04  1.967912e-04
## did_police_officer_attend_scene_of_collision1  2.676129e-04  1.114969e-04
## 1|2                                            1.912045e-02  1.778267e-02
## 2|3                                            1.911971e-02  1.775100e-02
##                                                 speed_limit junction_detail1
## police_force                                  -1.077285e-06    -8.256375e-06
## number_of_vehicles                            -7.583540e-06     1.439843e-04
## number_of_casualties                          -9.850909e-06     1.179088e-04
## road_type2                                     2.461894e-05     1.161520e-02
## road_type3                                    -2.966464e-05     9.768796e-03
## road_type6                                    -2.190565e-06     1.153650e-02
## road_type7                                    -1.887061e-05     8.839389e-03
## speed_limit                                    5.979994e-06    -2.286790e-05
## junction_detail1                              -2.286790e-05     1.547365e-02
## junction_detail2                               1.881809e-05     6.527257e-03
## junction_detail5                              -6.138987e-05     3.923476e-03
## junction_detail6                              -6.106020e-06     1.269510e-03
## junction_detail7                               1.178288e-06     1.568431e-03
## junction_detail8                              -1.308965e-05     8.733311e-04
## junction_detail9                              -8.500348e-07     1.330245e-03
## junction_control1                              1.222578e-05     4.510199e-04
## junction_control2                              8.355301e-06     4.710573e-04
## junction_control3                              7.483500e-06     6.360487e-04
## second_road_class                              7.898563e-06     6.909643e-04
## pedestrian_crossing_human_control1             1.035602e-05     3.860007e-04
## pedestrian_crossing_human_control2            -5.460407e-08    -3.441724e-05
## pedestrian_crossing_physical_facilities1       2.896247e-05    -1.942012e-04
## pedestrian_crossing_physical_facilities4       2.569843e-05     7.545051e-05
## pedestrian_crossing_physical_facilities5       2.436465e-05     5.011824e-04
## pedestrian_crossing_physical_facilities7      -6.802970e-06    -1.611330e-03
## pedestrian_crossing_physical_facilities8       2.171068e-05    -5.728760e-04
## light_conditions4                              1.694989e-05    -2.377277e-04
## light_conditions5                             -4.010030e-06    -1.282368e-04
## light_conditions6                             -7.344690e-05     1.223406e-03
## light_conditions7                             -7.442849e-06    -3.710824e-04
## weather_conditions2                            5.619472e-06    -1.896970e-04
## weather_conditions3                           -4.819899e-06    -1.603962e-05
## weather_conditions4                           -5.885095e-06    -4.558535e-06
## weather_conditions5                           -3.669719e-06     5.294431e-05
## weather_conditions6                           -3.700969e-05     4.296177e-04
## weather_conditions7                           -1.069564e-05    -1.150285e-04
## weather_conditions8                            8.082773e-06    -1.517758e-04
## road_surface_conditions2                      -4.771354e-06     1.028097e-05
## road_surface_conditions3                       9.262917e-06    -1.071535e-03
## road_surface_conditions4                      -1.027053e-05     5.392446e-05
## road_surface_conditions5                      -4.575526e-05    -1.325265e-03
## special_conditions_at_site1                    8.125851e-07     3.633582e-04
## special_conditions_at_site2                   -2.017715e-05     1.033500e-03
## special_conditions_at_site3                   -1.838041e-05     4.274936e-04
## special_conditions_at_site4                   -4.687212e-06    -3.772081e-05
## special_conditions_at_site5                   -2.448622e-05     4.634928e-04
## special_conditions_at_site6                   -5.045741e-05    -6.208574e-04
## special_conditions_at_site7                   -1.401179e-05     6.790915e-04
## carriageway_hazards1                           1.656344e-06    -3.486467e-04
## carriageway_hazards2                           5.601226e-06     3.202427e-04
## carriageway_hazards3                          -2.448636e-05     1.402808e-03
## carriageway_hazards6                           1.412453e-05     7.338070e-05
## carriageway_hazards7                          -1.903962e-05    -1.182865e-03
## did_police_officer_attend_scene_of_collision1 -1.108856e-05     4.252976e-04
## 1|2                                            1.838697e-04     1.621913e-02
## 2|3                                            1.814898e-04     1.627848e-02
##                                               junction_detail2 junction_detail5
## police_force                                     -9.748954e-06     1.009901e-05
## number_of_vehicles                               -3.114591e-05     1.757577e-04
## number_of_casualties                             -1.273445e-05    -9.950491e-07
## road_type2                                        9.016391e-03     1.454202e-03
## road_type3                                        7.978880e-03    -5.866122e-04
## road_type6                                        8.827152e-03     2.144103e-03
## road_type7                                        7.673450e-03    -1.109682e-02
## speed_limit                                       1.881809e-05    -6.138987e-05
## junction_detail1                                  6.527257e-03     3.923476e-03
## junction_detail2                                  2.998044e-02     1.788288e-03
## junction_detail5                                  1.788288e-03     3.425368e-02
## junction_detail6                                  9.899289e-04     1.301257e-03
## junction_detail7                                  1.041140e-03     1.686238e-03
## junction_detail8                                  9.988810e-04     1.098621e-03
## junction_detail9                                  1.204478e-03     1.449519e-03
## junction_control1                                 2.811361e-04     2.041086e-04
## junction_control2                                 6.561931e-04     7.511438e-04
## junction_control3                                 5.599405e-04     5.980924e-04
## second_road_class                                 1.405320e-04     4.468595e-04
## pedestrian_crossing_human_control1                4.072329e-05     1.459791e-04
## pedestrian_crossing_human_control2                3.777954e-05    -1.949970e-04
## pedestrian_crossing_physical_facilities1         -8.049223e-04     1.536721e-04
## pedestrian_crossing_physical_facilities4          5.417355e-05     4.748174e-04
## pedestrian_crossing_physical_facilities5          1.284585e-04     1.523172e-04
## pedestrian_crossing_physical_facilities7          4.456550e-04     1.148698e-03
## pedestrian_crossing_physical_facilities8         -1.215699e-03     1.856288e-04
## light_conditions4                                -1.562904e-04    -5.034426e-04
## light_conditions5                                -4.235079e-04     5.754417e-05
## light_conditions6                                 5.083132e-04    -2.519115e-04
## light_conditions7                                 3.635220e-04    -9.143687e-04
## weather_conditions2                              -3.322964e-04    -3.221377e-04
## weather_conditions3                               5.660002e-04     9.699123e-04
## weather_conditions4                               5.301491e-04     3.166734e-04
## weather_conditions5                               1.502707e-04     2.757588e-04
## weather_conditions6                              -2.088217e-04    -4.249510e-03
## weather_conditions7                               5.368955e-04     1.169426e-03
## weather_conditions8                               1.346052e-04    -4.698085e-04
## road_surface_conditions2                          2.821703e-05     1.201509e-04
## road_surface_conditions3                         -1.070981e-04    -3.598490e-03
## road_surface_conditions4                         -2.581337e-04     2.707105e-04
## road_surface_conditions5                         -7.719971e-03     6.242552e-05
## special_conditions_at_site1                       6.258604e-04     3.057310e-04
## special_conditions_at_site2                       6.228674e-06     2.313610e-03
## special_conditions_at_site3                      -1.000791e-03     1.323559e-04
## special_conditions_at_site4                       5.168919e-04     1.059837e-05
## special_conditions_at_site5                       2.884104e-04     8.107235e-04
## special_conditions_at_site6                       2.391962e-03     5.372547e-04
## special_conditions_at_site7                       5.558655e-04     1.083944e-03
## carriageway_hazards1                             -3.653005e-04     2.105251e-04
## carriageway_hazards2                              1.421408e-04    -2.406128e-04
## carriageway_hazards3                             -1.080855e-03     8.918110e-04
## carriageway_hazards6                              6.254106e-04    -2.971580e-03
## carriageway_hazards7                             -2.075113e-04     5.526488e-04
## did_police_officer_attend_scene_of_collision1     2.710112e-04     2.098139e-04
## 1|2                                               1.118052e-02     4.239949e-03
## 2|3                                               1.121109e-02     4.216072e-03
##                                               junction_detail6 junction_detail7
## police_force                                      3.446518e-06     1.144584e-05
## number_of_vehicles                               -1.227443e-04    -2.369430e-05
## number_of_casualties                             -1.096320e-04    -2.728590e-05
## road_type2                                        1.788151e-05     2.768560e-04
## road_type3                                       -6.076633e-05    -3.737858e-04
## road_type6                                       -6.778828e-07     1.733421e-04
## road_type7                                        9.384708e-06    -5.325978e-05
## speed_limit                                      -6.106020e-06     1.178288e-06
## junction_detail1                                  1.269510e-03     1.568431e-03
## junction_detail2                                  9.899289e-04     1.041140e-03
## junction_detail5                                  1.301257e-03     1.686238e-03
## junction_detail6                                  5.094749e-03     1.977094e-03
## junction_detail7                                  1.977094e-03     2.616398e-02
## junction_detail8                                  9.965913e-04     8.645981e-04
## junction_detail9                                  1.230180e-03     1.371443e-03
## junction_control1                                -6.515735e-05    -2.503562e-04
## junction_control2                                -1.563810e-03    -1.392129e-03
## junction_control3                                -6.028547e-04     3.021601e-04
## second_road_class                                 3.734224e-05     2.174524e-04
## pedestrian_crossing_human_control1                5.204636e-04     7.689686e-04
## pedestrian_crossing_human_control2               -1.062080e-04    -1.332754e-03
## pedestrian_crossing_physical_facilities1         -1.733567e-04    -1.562333e-04
## pedestrian_crossing_physical_facilities4          1.437188e-04     7.007528e-06
## pedestrian_crossing_physical_facilities5         -3.274908e-04    -8.074273e-04
## pedestrian_crossing_physical_facilities7         -2.489622e-04    -1.490098e-04
## pedestrian_crossing_physical_facilities8         -5.169110e-05     2.178067e-04
## light_conditions4                                 4.078398e-05    -2.821773e-05
## light_conditions5                                -1.273020e-04     4.289231e-04
## light_conditions6                                 1.303264e-04     2.218668e-04
## light_conditions7                                -1.121714e-04    -5.554840e-04
## weather_conditions2                              -9.302930e-05    -9.040270e-05
## weather_conditions3                               3.817913e-04     6.454248e-04
## weather_conditions4                              -1.001934e-04     2.041367e-05
## weather_conditions5                               2.137440e-04    -2.113821e-04
## weather_conditions6                              -5.176357e-04     6.282265e-04
## weather_conditions7                              -3.773680e-05    -3.260375e-04
## weather_conditions8                              -1.336609e-04    -3.516752e-04
## road_surface_conditions2                         -1.546711e-05     7.774609e-05
## road_surface_conditions3                         -1.479427e-04    -1.088613e-03
## road_surface_conditions4                          3.701902e-04    -2.743931e-04
## road_surface_conditions5                         -8.020834e-04     3.014752e-04
## special_conditions_at_site1                      -4.865071e-04     1.718751e-04
## special_conditions_at_site2                      -1.845672e-03     2.101209e-03
## special_conditions_at_site3                      -1.778253e-03    -3.090451e-04
## special_conditions_at_site4                      -3.052809e-04     2.926970e-04
## special_conditions_at_site5                      -1.107273e-04     5.080848e-04
## special_conditions_at_site6                       2.260229e-05    -1.484900e-03
## special_conditions_at_site7                       4.020036e-05     2.657670e-04
## carriageway_hazards1                             -5.453178e-04    -2.693708e-04
## carriageway_hazards2                             -1.142046e-04     1.036460e-05
## carriageway_hazards3                              1.563963e-04    -2.200184e-03
## carriageway_hazards6                              4.844973e-04    -7.503678e-04
## carriageway_hazards7                             -2.128657e-04     3.229784e-04
## did_police_officer_attend_scene_of_collision1    -3.751255e-05    -2.988318e-04
## 1|2                                               6.565811e-04     2.207249e-03
## 2|3                                               6.520250e-04     2.244734e-03
##                                               junction_detail8 junction_detail9
## police_force                                      2.948437e-06     8.965782e-06
## number_of_vehicles                               -1.093915e-04     5.154829e-05
## number_of_casualties                              2.286728e-05    -5.508376e-06
## road_type2                                       -2.039016e-04    -2.477941e-04
## road_type3                                        1.538234e-04    -7.667266e-05
## road_type6                                       -9.712640e-06     2.531912e-04
## road_type7                                       -2.206377e-04    -1.928843e-04
## speed_limit                                      -1.308965e-05    -8.500348e-07
## junction_detail1                                  8.733311e-04     1.330245e-03
## junction_detail2                                  9.988810e-04     1.204478e-03
## junction_detail5                                  1.098621e-03     1.449519e-03
## junction_detail6                                  9.965913e-04     1.230180e-03
## junction_detail7                                  8.645981e-04     1.371443e-03
## junction_detail8                                  1.594123e-02     1.080594e-03
## junction_detail9                                  1.080594e-03     6.657692e-03
## junction_control1                                 2.992991e-05     3.334975e-05
## junction_control2                                 1.546272e-04    -1.261134e-04
## junction_control3                                 4.738542e-04    -3.571347e-04
## second_road_class                                -1.940128e-04     2.579251e-05
## pedestrian_crossing_human_control1                1.465451e-04    -1.550390e-04
## pedestrian_crossing_human_control2                6.198377e-05    -5.156935e-04
## pedestrian_crossing_physical_facilities1          3.015101e-04    -6.803497e-05
## pedestrian_crossing_physical_facilities4          4.367375e-05    -1.091948e-05
## pedestrian_crossing_physical_facilities5         -2.750773e-05     1.267227e-04
## pedestrian_crossing_physical_facilities7         -3.135202e-05    -4.690840e-04
## pedestrian_crossing_physical_facilities8          2.756872e-04    -2.489674e-04
## light_conditions4                                 1.245938e-04    -6.648772e-06
## light_conditions5                                -2.054208e-04    -1.945943e-04
## light_conditions6                                 3.731900e-05     4.860903e-05
## light_conditions7                                 1.364093e-04    -1.333479e-04
## weather_conditions2                              -1.047924e-04     2.364895e-05
## weather_conditions3                              -2.592778e-04     2.979037e-04
## weather_conditions4                              -1.076822e-04    -2.105091e-04
## weather_conditions5                              -6.393930e-04    -1.541796e-04
## weather_conditions6                              -2.587339e-03     5.275964e-04
## weather_conditions7                               3.582783e-04     3.647925e-04
## weather_conditions8                               8.771211e-05    -4.232007e-04
## road_surface_conditions2                          6.837807e-05    -2.322594e-06
## road_surface_conditions3                          3.255830e-04    -4.561176e-04
## road_surface_conditions4                          1.074543e-05     1.973031e-04
## road_surface_conditions5                          2.764035e-04    -2.044819e-03
## special_conditions_at_site1                       3.335571e-04    -2.818482e-04
## special_conditions_at_site2                      -1.730173e-04     2.984483e-04
## special_conditions_at_site3                       4.131078e-04     3.084421e-04
## special_conditions_at_site4                      -8.402246e-05    -2.089564e-05
## special_conditions_at_site5                      -1.424886e-03    -4.413336e-04
## special_conditions_at_site6                       4.746352e-04    -5.788310e-04
## special_conditions_at_site7                      -7.958580e-04    -9.035520e-04
## carriageway_hazards1                              4.363337e-04     1.177510e-04
## carriageway_hazards2                             -4.109376e-04     1.521191e-05
## carriageway_hazards3                             -2.672402e-04    -5.892884e-05
## carriageway_hazards6                              4.013363e-04    -5.218505e-04
## carriageway_hazards7                             -9.181339e-04    -8.033003e-04
## did_police_officer_attend_scene_of_collision1    -2.964465e-05    -7.798085e-05
## 1|2                                              -4.739398e-04     1.611439e-03
## 2|3                                              -4.458505e-04     1.645349e-03
##                                               junction_control1
## police_force                                      -1.443899e-05
## number_of_vehicles                                 6.365947e-05
## number_of_casualties                              -1.140968e-04
## road_type2                                         7.563444e-04
## road_type3                                         9.234206e-05
## road_type6                                         7.147673e-04
## road_type7                                         3.423862e-04
## speed_limit                                        1.222578e-05
## junction_detail1                                   4.510199e-04
## junction_detail2                                   2.811361e-04
## junction_detail5                                   2.041086e-04
## junction_detail6                                  -6.515735e-05
## junction_detail7                                  -2.503562e-04
## junction_detail8                                   2.992991e-05
## junction_detail9                                   3.334975e-05
## junction_control1                                  5.954055e-02
## junction_control2                                  1.256862e-03
## junction_control3                                  7.721504e-04
## second_road_class                                 -6.013359e-05
## pedestrian_crossing_human_control1                -1.074049e-03
## pedestrian_crossing_human_control2                -2.002120e-03
## pedestrian_crossing_physical_facilities1           4.775006e-05
## pedestrian_crossing_physical_facilities4          -2.619791e-04
## pedestrian_crossing_physical_facilities5          -6.771631e-04
## pedestrian_crossing_physical_facilities7           4.422022e-04
## pedestrian_crossing_physical_facilities8           3.138679e-05
## light_conditions4                                 -1.506916e-04
## light_conditions5                                 -7.994109e-06
## light_conditions6                                 -6.797496e-05
## light_conditions7                                  1.318191e-04
## weather_conditions2                                1.904733e-04
## weather_conditions3                                3.506290e-04
## weather_conditions4                                3.219488e-04
## weather_conditions5                                1.059759e-04
## weather_conditions6                                1.041047e-04
## weather_conditions7                                4.824266e-04
## weather_conditions8                               -7.430450e-07
## road_surface_conditions2                           3.000379e-04
## road_surface_conditions3                           3.072578e-04
## road_surface_conditions4                           7.543003e-04
## road_surface_conditions5                           6.759683e-04
## special_conditions_at_site1                        7.976359e-04
## special_conditions_at_site2                        6.761184e-04
## special_conditions_at_site3                        5.702722e-04
## special_conditions_at_site4                        4.590319e-04
## special_conditions_at_site5                        4.434712e-04
## special_conditions_at_site6                        5.654219e-04
## special_conditions_at_site7                        4.845807e-04
## carriageway_hazards1                              -5.108832e-03
## carriageway_hazards2                              -2.579181e-04
## carriageway_hazards3                               5.208245e-04
## carriageway_hazards6                               7.039663e-04
## carriageway_hazards7                               5.731288e-04
## did_police_officer_attend_scene_of_collision1     -3.545453e-04
## 1|2                                                6.732911e-04
## 2|3                                                7.683471e-04
##                                               junction_control2
## police_force                                       3.741435e-06
## number_of_vehicles                                -5.852332e-05
## number_of_casualties                              -5.075707e-07
## road_type2                                         4.928681e-04
## road_type3                                        -5.601390e-04
## road_type6                                         4.890145e-04
## road_type7                                         8.658277e-05
## speed_limit                                        8.355301e-06
## junction_detail1                                   4.710573e-04
## junction_detail2                                   6.561931e-04
## junction_detail5                                   7.511438e-04
## junction_detail6                                  -1.563810e-03
## junction_detail7                                  -1.392129e-03
## junction_detail8                                   1.546272e-04
## junction_detail9                                  -1.261134e-04
## junction_control1                                  1.256862e-03
## junction_control2                                  8.198654e-03
## junction_control3                                  1.335105e-03
## second_road_class                                  4.380685e-04
## pedestrian_crossing_human_control1                -3.839096e-04
## pedestrian_crossing_human_control2                -3.858813e-04
## pedestrian_crossing_physical_facilities1           5.854876e-05
## pedestrian_crossing_physical_facilities4          -2.015458e-03
## pedestrian_crossing_physical_facilities5          -4.971563e-03
## pedestrian_crossing_physical_facilities7          -1.952301e-03
## pedestrian_crossing_physical_facilities8          -3.208810e-04
## light_conditions4                                 -2.114915e-04
## light_conditions5                                 -4.050332e-05
## light_conditions6                                  1.133338e-04
## light_conditions7                                  5.161262e-04
## weather_conditions2                               -2.137028e-05
## weather_conditions3                               -1.274346e-04
## weather_conditions4                                2.693739e-04
## weather_conditions5                                1.567703e-04
## weather_conditions6                                5.531710e-04
## weather_conditions7                                4.732030e-04
## weather_conditions8                                3.232384e-04
## road_surface_conditions2                           7.764811e-05
## road_surface_conditions3                           3.115660e-05
## road_surface_conditions4                          -1.357558e-04
## road_surface_conditions5                          -6.634911e-04
## special_conditions_at_site1                       -6.730240e-04
## special_conditions_at_site2                        6.724218e-06
## special_conditions_at_site3                        5.688055e-04
## special_conditions_at_site4                       -4.924581e-04
## special_conditions_at_site5                       -9.047888e-04
## special_conditions_at_site6                        6.442919e-04
## special_conditions_at_site7                        2.792726e-04
## carriageway_hazards1                              -8.324528e-04
## carriageway_hazards2                               5.253903e-04
## carriageway_hazards3                               3.363968e-04
## carriageway_hazards6                               2.393807e-04
## carriageway_hazards7                              -1.535258e-04
## did_police_officer_attend_scene_of_collision1      1.169854e-04
## 1|2                                                3.437625e-03
## 2|3                                                3.484383e-03
##                                               junction_control3
## police_force                                       5.893550e-06
## number_of_vehicles                                -1.444113e-04
## number_of_casualties                              -1.252369e-05
## road_type2                                         1.188875e-04
## road_type3                                         1.281629e-04
## road_type6                                         2.951751e-04
## road_type7                                        -4.895125e-04
## speed_limit                                        7.483500e-06
## junction_detail1                                   6.360487e-04
## junction_detail2                                   5.599405e-04
## junction_detail5                                   5.980924e-04
## junction_detail6                                  -6.028547e-04
## junction_detail7                                   3.021601e-04
## junction_detail8                                   4.738542e-04
## junction_detail9                                  -3.571347e-04
## junction_control1                                  7.721504e-04
## junction_control2                                  1.335105e-03
## junction_control3                                  4.901991e-02
## second_road_class                                  1.123618e-04
## pedestrian_crossing_human_control1                -6.680046e-04
## pedestrian_crossing_human_control2                -9.898462e-04
## pedestrian_crossing_physical_facilities1           4.920325e-04
## pedestrian_crossing_physical_facilities4           9.596834e-05
## pedestrian_crossing_physical_facilities5          -3.272652e-04
## pedestrian_crossing_physical_facilities7          -1.818830e-03
## pedestrian_crossing_physical_facilities8           2.831152e-04
## light_conditions4                                  1.155272e-04
## light_conditions5                                 -1.255254e-03
## light_conditions6                                 -1.817153e-04
## light_conditions7                                  2.487535e-04
## weather_conditions2                                2.731061e-05
## weather_conditions3                                1.064178e-03
## weather_conditions4                                5.280649e-05
## weather_conditions5                                6.094390e-04
## weather_conditions6                                9.757797e-04
## weather_conditions7                               -1.022809e-03
## weather_conditions8                               -3.420760e-05
## road_surface_conditions2                           5.477760e-05
## road_surface_conditions3                          -1.618346e-03
## road_surface_conditions4                           5.116140e-04
## road_surface_conditions5                           1.157274e-04
## special_conditions_at_site1                        5.580000e-04
## special_conditions_at_site2                        6.454125e-04
## special_conditions_at_site3                       -7.958514e-03
## special_conditions_at_site4                       -4.021722e-04
## special_conditions_at_site5                       -2.493771e-03
## special_conditions_at_site6                        3.340305e-04
## special_conditions_at_site7                        6.899647e-04
## carriageway_hazards1                               3.410900e-04
## carriageway_hazards2                              -1.133536e-03
## carriageway_hazards3                               5.760966e-04
## carriageway_hazards6                               5.595488e-04
## carriageway_hazards7                              -2.625078e-03
## did_police_officer_attend_scene_of_collision1      5.826382e-05
## 1|2                                                1.781821e-03
## 2|3                                                1.784519e-03
##                                               second_road_class
## police_force                                      -2.440834e-06
## number_of_vehicles                                 4.595822e-06
## number_of_casualties                               9.108229e-06
## road_type2                                         1.030633e-04
## road_type3                                        -5.366581e-05
## road_type6                                        -1.266643e-04
## road_type7                                         2.249805e-04
## speed_limit                                        7.898563e-06
## junction_detail1                                   6.909643e-04
## junction_detail2                                   1.405320e-04
## junction_detail5                                   4.468595e-04
## junction_detail6                                   3.734224e-05
## junction_detail7                                   2.174524e-04
## junction_detail8                                  -1.940128e-04
## junction_detail9                                   2.579251e-05
## junction_control1                                 -6.013359e-05
## junction_control2                                  4.380685e-04
## junction_control3                                  1.123618e-04
## second_road_class                                  5.839727e-04
## pedestrian_crossing_human_control1                -1.114888e-04
## pedestrian_crossing_human_control2                -4.506226e-05
## pedestrian_crossing_physical_facilities1           3.867482e-06
## pedestrian_crossing_physical_facilities4           5.184243e-05
## pedestrian_crossing_physical_facilities5           9.137876e-05
## pedestrian_crossing_physical_facilities7           1.639650e-04
## pedestrian_crossing_physical_facilities8           1.212330e-04
## light_conditions4                                  1.565148e-05
## light_conditions5                                 -2.515128e-05
## light_conditions6                                  3.278632e-05
## light_conditions7                                  4.127617e-05
## weather_conditions2                               -8.624938e-06
## weather_conditions3                               -2.164020e-04
## weather_conditions4                               -9.247236e-06
## weather_conditions5                                6.463390e-05
## weather_conditions6                                1.832445e-04
## weather_conditions7                                3.442524e-05
## weather_conditions8                                1.306204e-05
## road_surface_conditions2                           1.442078e-05
## road_surface_conditions3                          -6.743798e-05
## road_surface_conditions4                          -7.036255e-05
## road_surface_conditions5                          -1.496769e-04
## special_conditions_at_site1                        1.855860e-05
## special_conditions_at_site2                       -6.009680e-05
## special_conditions_at_site3                       -8.591409e-05
## special_conditions_at_site4                        5.780040e-05
## special_conditions_at_site5                       -8.033753e-05
## special_conditions_at_site6                       -2.416362e-04
## special_conditions_at_site7                        1.198336e-04
## carriageway_hazards1                              -7.200061e-05
## carriageway_hazards2                               2.628471e-05
## carriageway_hazards3                               2.865062e-04
## carriageway_hazards6                               4.556375e-05
## carriageway_hazards7                              -1.295122e-04
## did_police_officer_attend_scene_of_collision1      1.952975e-05
## 1|2                                                3.471926e-03
## 2|3                                                3.463670e-03
##                                               pedestrian_crossing_human_control1
## police_force                                                        5.591302e-06
## number_of_vehicles                                                  3.059586e-04
## number_of_casualties                                               -6.562656e-05
## road_type2                                                          8.775761e-04
## road_type3                                                         -2.503175e-04
## road_type6                                                         -9.593153e-05
## road_type7                                                         -1.420149e-03
## speed_limit                                                         1.035602e-05
## junction_detail1                                                    3.860007e-04
## junction_detail2                                                    4.072329e-05
## junction_detail5                                                    1.459791e-04
## junction_detail6                                                    5.204636e-04
## junction_detail7                                                    7.689686e-04
## junction_detail8                                                    1.465451e-04
## junction_detail9                                                   -1.550390e-04
## junction_control1                                                  -1.074049e-03
## junction_control2                                                  -3.839096e-04
## junction_control3                                                  -6.680046e-04
## second_road_class                                                  -1.114888e-04
## pedestrian_crossing_human_control1                                  1.384785e-01
## pedestrian_crossing_human_control2                                  1.492162e-03
## pedestrian_crossing_physical_facilities1                           -2.683520e-03
## pedestrian_crossing_physical_facilities4                           -1.053554e-03
## pedestrian_crossing_physical_facilities5                           -5.910232e-04
## pedestrian_crossing_physical_facilities7                           -6.073167e-03
## pedestrian_crossing_physical_facilities8                           -1.232873e-04
## light_conditions4                                                   4.423108e-04
## light_conditions5                                                  -2.696731e-03
## light_conditions6                                                   4.641323e-05
## light_conditions7                                                   6.696835e-04
## weather_conditions2                                                 2.371192e-04
## weather_conditions3                                                -1.461240e-03
## weather_conditions4                                                -1.817673e-03
## weather_conditions5                                                 7.785497e-04
## weather_conditions6                                                -9.325934e-05
## weather_conditions7                                                 1.595827e-05
## weather_conditions8                                                -3.646770e-04
## road_surface_conditions2                                           -2.137465e-04
## road_surface_conditions3                                            1.783851e-03
## road_surface_conditions4                                            6.541847e-04
## road_surface_conditions5                                            3.150900e-04
## special_conditions_at_site1                                         8.352532e-04
## special_conditions_at_site2                                         9.840658e-04
## special_conditions_at_site3                                         6.918585e-04
## special_conditions_at_site4                                        -2.219916e-04
## special_conditions_at_site5                                         5.893904e-04
## special_conditions_at_site6                                         4.493882e-04
## special_conditions_at_site7                                         9.478051e-04
## carriageway_hazards1                                               -3.438006e-03
## carriageway_hazards2                                               -3.041642e-04
## carriageway_hazards3                                                5.516223e-05
## carriageway_hazards6                                               -2.809340e-03
## carriageway_hazards7                                                4.632956e-04
## did_police_officer_attend_scene_of_collision1                      -3.627500e-05
## 1|2                                                                 5.314560e-04
## 2|3                                                                 6.234667e-04
##                                               pedestrian_crossing_human_control2
## police_force                                                        9.880561e-06
## number_of_vehicles                                                  1.404411e-04
## number_of_casualties                                                5.671635e-05
## road_type2                                                         -3.469710e-04
## road_type3                                                          7.673773e-05
## road_type6                                                          1.188812e-04
## road_type7                                                         -9.130513e-05
## speed_limit                                                        -5.460407e-08
## junction_detail1                                                   -3.441724e-05
## junction_detail2                                                    3.777954e-05
## junction_detail5                                                   -1.949970e-04
## junction_detail6                                                   -1.062080e-04
## junction_detail7                                                   -1.332754e-03
## junction_detail8                                                    6.198377e-05
## junction_detail9                                                   -5.156935e-04
## junction_control1                                                  -2.002120e-03
## junction_control2                                                  -3.858813e-04
## junction_control3                                                  -9.898462e-04
## second_road_class                                                  -4.506226e-05
## pedestrian_crossing_human_control1                                  1.492162e-03
## pedestrian_crossing_human_control2                                  3.348190e-02
## pedestrian_crossing_physical_facilities1                           -1.263385e-03
## pedestrian_crossing_physical_facilities4                           -2.231094e-03
## pedestrian_crossing_physical_facilities5                           -1.488108e-03
## pedestrian_crossing_physical_facilities7                           -1.434983e-03
## pedestrian_crossing_physical_facilities8                           -1.398349e-04
## light_conditions4                                                   1.005189e-04
## light_conditions5                                                  -3.908942e-04
## light_conditions6                                                   1.591149e-04
## light_conditions7                                                   1.767032e-04
## weather_conditions2                                                 1.253686e-04
## weather_conditions3                                                 5.189317e-04
## weather_conditions4                                                -9.565543e-04
## weather_conditions5                                                -1.057764e-03
## weather_conditions6                                                 3.627714e-04
## weather_conditions7                                                 8.403411e-05
## weather_conditions8                                                -1.164314e-03
## road_surface_conditions2                                           -2.041029e-04
## road_surface_conditions3                                           -1.845996e-04
## road_surface_conditions4                                            1.340884e-04
## road_surface_conditions5                                            1.287979e-03
## special_conditions_at_site1                                        -5.769511e-05
## special_conditions_at_site2                                         1.927773e-03
## special_conditions_at_site3                                         4.704642e-04
## special_conditions_at_site4                                        -2.774125e-04
## special_conditions_at_site5                                        -1.287392e-03
## special_conditions_at_site6                                        -1.067728e-03
## special_conditions_at_site7                                         4.777775e-04
## carriageway_hazards1                                                8.414950e-04
## carriageway_hazards2                                               -7.692407e-04
## carriageway_hazards3                                               -1.751094e-03
## carriageway_hazards6                                               -1.774620e-03
## carriageway_hazards7                                               -2.112910e-03
## did_police_officer_attend_scene_of_collision1                      -2.542124e-04
## 1|2                                                                 7.584129e-05
## 2|3                                                                 1.235596e-04
##                                               pedestrian_crossing_physical_facilities1
## police_force                                                              9.360524e-06
## number_of_vehicles                                                        3.305766e-04
## number_of_casualties                                                      6.033465e-05
## road_type2                                                               -6.076324e-04
## road_type3                                                               -3.233142e-05
## road_type6                                                                1.498179e-05
## road_type7                                                               -6.089267e-04
## speed_limit                                                               2.896247e-05
## junction_detail1                                                         -1.942012e-04
## junction_detail2                                                         -8.049223e-04
## junction_detail5                                                          1.536721e-04
## junction_detail6                                                         -1.733567e-04
## junction_detail7                                                         -1.562333e-04
## junction_detail8                                                          3.015101e-04
## junction_detail9                                                         -6.803497e-05
## junction_control1                                                         4.775006e-05
## junction_control2                                                         5.854876e-05
## junction_control3                                                         4.920325e-04
## second_road_class                                                         3.867482e-06
## pedestrian_crossing_human_control1                                       -2.683520e-03
## pedestrian_crossing_human_control2                                       -1.263385e-03
## pedestrian_crossing_physical_facilities1                                  1.422148e-02
## pedestrian_crossing_physical_facilities4                                  1.218486e-03
## pedestrian_crossing_physical_facilities5                                  1.210281e-03
## pedestrian_crossing_physical_facilities7                                  8.645160e-04
## pedestrian_crossing_physical_facilities8                                  1.043964e-03
## light_conditions4                                                        -9.276686e-05
## light_conditions5                                                        -5.008887e-05
## light_conditions6                                                         1.783126e-04
## light_conditions7                                                        -4.607297e-06
## weather_conditions2                                                      -2.346926e-05
## weather_conditions3                                                       6.379281e-04
## weather_conditions4                                                       4.152848e-04
## weather_conditions5                                                      -2.657786e-04
## weather_conditions6                                                       3.173555e-04
## weather_conditions7                                                       3.259630e-04
## weather_conditions8                                                       1.565300e-04
## road_surface_conditions2                                                  1.402369e-05
## road_surface_conditions3                                                 -3.349721e-04
## road_surface_conditions4                                                 -3.569125e-04
## road_surface_conditions5                                                  4.640924e-04
## special_conditions_at_site1                                              -3.258605e-04
## special_conditions_at_site2                                              -4.909568e-04
## special_conditions_at_site3                                              -7.505765e-04
## special_conditions_at_site4                                               1.275244e-04
## special_conditions_at_site5                                              -1.303642e-04
## special_conditions_at_site6                                              -1.374949e-03
## special_conditions_at_site7                                              -1.793634e-03
## carriageway_hazards1                                                     -5.176559e-04
## carriageway_hazards2                                                      3.939720e-04
## carriageway_hazards3                                                      6.530190e-04
## carriageway_hazards6                                                     -1.397830e-03
## carriageway_hazards7                                                      6.254526e-04
## did_police_officer_attend_scene_of_collision1                            -2.808521e-04
## 1|2                                                                       2.355778e-03
## 2|3                                                                       2.400536e-03
##                                               pedestrian_crossing_physical_facilities4
## police_force                                                              5.834943e-07
## number_of_vehicles                                                        1.955126e-04
## number_of_casualties                                                     -1.556625e-05
## road_type2                                                               -5.222486e-05
## road_type3                                                               -4.498120e-04
## road_type6                                                               -1.623472e-04
## road_type7                                                               -2.876285e-04
## speed_limit                                                               2.569843e-05
## junction_detail1                                                          7.545051e-05
## junction_detail2                                                          5.417355e-05
## junction_detail5                                                          4.748174e-04
## junction_detail6                                                          1.437188e-04
## junction_detail7                                                          7.007528e-06
## junction_detail8                                                          4.367375e-05
## junction_detail9                                                         -1.091948e-05
## junction_control1                                                        -2.619791e-04
## junction_control2                                                        -2.015458e-03
## junction_control3                                                         9.596834e-05
## second_road_class                                                         5.184243e-05
## pedestrian_crossing_human_control1                                       -1.053554e-03
## pedestrian_crossing_human_control2                                       -2.231094e-03
## pedestrian_crossing_physical_facilities1                                  1.218486e-03
## pedestrian_crossing_physical_facilities4                                  9.370970e-03
## pedestrian_crossing_physical_facilities5                                  2.722540e-03
## pedestrian_crossing_physical_facilities7                                  1.610113e-03
## pedestrian_crossing_physical_facilities8                                  1.087744e-03
## light_conditions4                                                        -1.723883e-04
## light_conditions5                                                        -3.752441e-05
## light_conditions6                                                         1.663608e-04
## light_conditions7                                                         4.865562e-06
## weather_conditions2                                                      -7.523282e-05
## weather_conditions3                                                       1.676468e-04
## weather_conditions4                                                       8.917630e-05
## weather_conditions5                                                       9.932714e-06
## weather_conditions6                                                       1.048227e-04
## weather_conditions7                                                       3.937815e-05
## weather_conditions8                                                       2.226851e-04
## road_surface_conditions2                                                  7.087366e-05
## road_surface_conditions3                                                  1.585226e-04
## road_surface_conditions4                                                 -7.439608e-05
## road_surface_conditions5                                                  3.587755e-04
## special_conditions_at_site1                                               1.688123e-04
## special_conditions_at_site2                                               5.185463e-05
## special_conditions_at_site3                                               3.681137e-04
## special_conditions_at_site4                                               1.553700e-04
## special_conditions_at_site5                                               4.021592e-04
## special_conditions_at_site6                                              -5.952441e-04
## special_conditions_at_site7                                               3.561431e-04
## carriageway_hazards1                                                      3.137408e-04
## carriageway_hazards2                                                     -1.361421e-05
## carriageway_hazards3                                                      6.051540e-04
## carriageway_hazards6                                                      3.298645e-04
## carriageway_hazards7                                                      5.952675e-04
## did_police_officer_attend_scene_of_collision1                            -1.651015e-04
## 1|2                                                                       1.903690e-03
## 2|3                                                                       1.890421e-03
##                                               pedestrian_crossing_physical_facilities5
## police_force                                                             -1.438665e-06
## number_of_vehicles                                                        2.785219e-04
## number_of_casualties                                                     -2.658804e-07
## road_type2                                                               -6.847023e-05
## road_type3                                                               -4.749284e-04
## road_type6                                                               -9.134883e-05
## road_type7                                                               -1.070627e-05
## speed_limit                                                               2.436465e-05
## junction_detail1                                                          5.011824e-04
## junction_detail2                                                          1.284585e-04
## junction_detail5                                                          1.523172e-04
## junction_detail6                                                         -3.274908e-04
## junction_detail7                                                         -8.074273e-04
## junction_detail8                                                         -2.750773e-05
## junction_detail9                                                          1.267227e-04
## junction_control1                                                        -6.771631e-04
## junction_control2                                                        -4.971563e-03
## junction_control3                                                        -3.272652e-04
## second_road_class                                                         9.137876e-05
## pedestrian_crossing_human_control1                                       -5.910232e-04
## pedestrian_crossing_human_control2                                       -1.488108e-03
## pedestrian_crossing_physical_facilities1                                  1.210281e-03
## pedestrian_crossing_physical_facilities4                                  2.722540e-03
## pedestrian_crossing_physical_facilities5                                  1.067760e-02
## pedestrian_crossing_physical_facilities7                                  2.585227e-03
## pedestrian_crossing_physical_facilities8                                  1.224323e-03
## light_conditions4                                                        -1.722647e-04
## light_conditions5                                                         1.184904e-04
## light_conditions6                                                         1.489059e-04
## light_conditions7                                                        -1.457467e-04
## weather_conditions2                                                       3.843077e-05
## weather_conditions3                                                      -3.760176e-04
## weather_conditions4                                                      -2.934447e-06
## weather_conditions5                                                      -7.125437e-05
## weather_conditions6                                                      -4.820704e-04
## weather_conditions7                                                      -5.213942e-05
## weather_conditions8                                                      -1.127561e-05
## road_surface_conditions2                                                  1.623345e-05
## road_surface_conditions3                                                  8.510097e-04
## road_surface_conditions4                                                  1.126786e-04
## road_surface_conditions5                                                 -1.336540e-03
## special_conditions_at_site1                                              -4.537648e-04
## special_conditions_at_site2                                              -4.640050e-03
## special_conditions_at_site3                                               1.502462e-04
## special_conditions_at_site4                                               5.165243e-04
## special_conditions_at_site5                                               1.163031e-03
## special_conditions_at_site6                                              -2.521467e-04
## special_conditions_at_site7                                               2.135756e-04
## carriageway_hazards1                                                      8.906014e-04
## carriageway_hazards2                                                     -1.986872e-04
## carriageway_hazards3                                                     -6.421995e-04
## carriageway_hazards6                                                     -8.645038e-04
## carriageway_hazards7                                                     -4.310374e-04
## did_police_officer_attend_scene_of_collision1                            -2.539137e-04
## 1|2                                                                       1.943859e-03
## 2|3                                                                       1.930110e-03
##                                               pedestrian_crossing_physical_facilities7
## police_force                                                             -1.240338e-05
## number_of_vehicles                                                        6.949352e-05
## number_of_casualties                                                      1.683366e-04
## road_type2                                                                1.405528e-03
## road_type3                                                               -4.200635e-04
## road_type6                                                                1.182413e-03
## road_type7                                                                1.466813e-03
## speed_limit                                                              -6.802970e-06
## junction_detail1                                                         -1.611330e-03
## junction_detail2                                                          4.456550e-04
## junction_detail5                                                          1.148698e-03
## junction_detail6                                                         -2.489622e-04
## junction_detail7                                                         -1.490098e-04
## junction_detail8                                                         -3.135202e-05
## junction_detail9                                                         -4.690840e-04
## junction_control1                                                         4.422022e-04
## junction_control2                                                        -1.952301e-03
## junction_control3                                                        -1.818830e-03
## second_road_class                                                         1.639650e-04
## pedestrian_crossing_human_control1                                       -6.073167e-03
## pedestrian_crossing_human_control2                                       -1.434983e-03
## pedestrian_crossing_physical_facilities1                                  8.645160e-04
## pedestrian_crossing_physical_facilities4                                  1.610113e-03
## pedestrian_crossing_physical_facilities5                                  2.585227e-03
## pedestrian_crossing_physical_facilities7                                  2.636407e-01
## pedestrian_crossing_physical_facilities8                                  1.184571e-03
## light_conditions4                                                        -2.166249e-04
## light_conditions5                                                         7.538559e-04
## light_conditions6                                                         6.331835e-04
## light_conditions7                                                        -1.920603e-03
## weather_conditions2                                                       8.220439e-05
## weather_conditions3                                                       3.450039e-03
## weather_conditions4                                                       6.667679e-04
## weather_conditions5                                                       6.579252e-05
## weather_conditions6                                                       1.810554e-03
## weather_conditions7                                                       1.829371e-04
## weather_conditions8                                                      -3.078051e-03
## road_surface_conditions2                                                  1.911352e-04
## road_surface_conditions3                                                 -8.907432e-03
## road_surface_conditions4                                                  1.087833e-03
## road_surface_conditions5                                                  1.357431e-03
## special_conditions_at_site1                                               7.253440e-04
## special_conditions_at_site2                                               1.106951e-03
## special_conditions_at_site3                                               6.076173e-04
## special_conditions_at_site4                                              -2.553980e-03
## special_conditions_at_site5                                               7.413680e-04
## special_conditions_at_site6                                               1.227144e-03
## special_conditions_at_site7                                               2.239091e-04
## carriageway_hazards1                                                      1.022165e-03
## carriageway_hazards2                                                      6.369690e-04
## carriageway_hazards3                                                      2.147629e-04
## carriageway_hazards6                                                      2.684333e-04
## carriageway_hazards7                                                      9.399592e-04
## did_police_officer_attend_scene_of_collision1                            -3.069229e-04
## 1|2                                                                       1.780425e-03
## 2|3                                                                       1.751328e-03
##                                               pedestrian_crossing_physical_facilities8
## police_force                                                             -3.816750e-06
## number_of_vehicles                                                        2.546977e-04
## number_of_casualties                                                     -5.082271e-05
## road_type2                                                                6.034407e-05
## road_type3                                                               -2.098851e-04
## road_type6                                                               -1.620676e-04
## road_type7                                                               -2.921010e-05
## speed_limit                                                               2.171068e-05
## junction_detail1                                                         -5.728760e-04
## junction_detail2                                                         -1.215699e-03
## junction_detail5                                                          1.856288e-04
## junction_detail6                                                         -5.169110e-05
## junction_detail7                                                          2.178067e-04
## junction_detail8                                                          2.756872e-04
## junction_detail9                                                         -2.489674e-04
## junction_control1                                                         3.138679e-05
## junction_control2                                                        -3.208810e-04
## junction_control3                                                         2.831152e-04
## second_road_class                                                         1.212330e-04
## pedestrian_crossing_human_control1                                       -1.232873e-04
## pedestrian_crossing_human_control2                                       -1.398349e-04
## pedestrian_crossing_physical_facilities1                                  1.043964e-03
## pedestrian_crossing_physical_facilities4                                  1.087744e-03
## pedestrian_crossing_physical_facilities5                                  1.224323e-03
## pedestrian_crossing_physical_facilities7                                  1.184571e-03
## pedestrian_crossing_physical_facilities8                                  1.662007e-02
## light_conditions4                                                         8.174300e-07
## light_conditions5                                                         3.000402e-04
## light_conditions6                                                         4.789200e-04
## light_conditions7                                                         9.079969e-05
## weather_conditions2                                                      -6.359889e-05
## weather_conditions3                                                       1.149521e-04
## weather_conditions4                                                      -5.093554e-04
## weather_conditions5                                                      -3.804380e-05
## weather_conditions6                                                       3.655274e-05
## weather_conditions7                                                      -3.373898e-04
## weather_conditions8                                                       9.160245e-05
## road_surface_conditions2                                                  1.983575e-05
## road_surface_conditions3                                                  4.821669e-05
## road_surface_conditions4                                                  8.152129e-05
## road_surface_conditions5                                                  9.420800e-04
## special_conditions_at_site1                                              -3.201332e-04
## special_conditions_at_site2                                              -8.881318e-05
## special_conditions_at_site3                                               5.809397e-04
## special_conditions_at_site4                                              -1.776596e-04
## special_conditions_at_site5                                              -9.116228e-04
## special_conditions_at_site6                                              -2.465769e-03
## special_conditions_at_site7                                               4.155573e-04
## carriageway_hazards1                                                      6.563009e-04
## carriageway_hazards2                                                      6.258123e-04
## carriageway_hazards3                                                     -6.000012e-04
## carriageway_hazards6                                                      5.597872e-04
## carriageway_hazards7                                                     -4.326400e-04
## did_police_officer_attend_scene_of_collision1                            -6.029574e-05
## 1|2                                                                       2.255299e-03
## 2|3                                                                       2.218277e-03
##                                               light_conditions4
## police_force                                       2.748314e-06
## number_of_vehicles                                 6.586602e-05
## number_of_casualties                              -5.027184e-05
## road_type2                                        -6.149051e-05
## road_type3                                        -1.948129e-04
## road_type6                                        -1.195266e-05
## road_type7                                         5.329324e-05
## speed_limit                                        1.694989e-05
## junction_detail1                                  -2.377277e-04
## junction_detail2                                  -1.562904e-04
## junction_detail5                                  -5.034426e-04
## junction_detail6                                   4.078398e-05
## junction_detail7                                  -2.821773e-05
## junction_detail8                                   1.245938e-04
## junction_detail9                                  -6.648772e-06
## junction_control1                                 -1.506916e-04
## junction_control2                                 -2.114915e-04
## junction_control3                                  1.155272e-04
## second_road_class                                  1.565148e-05
## pedestrian_crossing_human_control1                 4.423108e-04
## pedestrian_crossing_human_control2                 1.005189e-04
## pedestrian_crossing_physical_facilities1          -9.276686e-05
## pedestrian_crossing_physical_facilities4          -1.723883e-04
## pedestrian_crossing_physical_facilities5          -1.722647e-04
## pedestrian_crossing_physical_facilities7          -2.166249e-04
## pedestrian_crossing_physical_facilities8           8.174300e-07
## light_conditions4                                  3.468320e-03
## light_conditions5                                  1.046119e-03
## light_conditions6                                  6.718837e-04
## light_conditions7                                  9.066540e-04
## weather_conditions2                               -3.393111e-05
## weather_conditions3                                1.048952e-04
## weather_conditions4                                8.613320e-05
## weather_conditions5                               -1.960151e-04
## weather_conditions6                                4.678942e-04
## weather_conditions7                               -1.497153e-04
## weather_conditions8                               -1.207937e-04
## road_surface_conditions2                          -7.197940e-04
## road_surface_conditions3                          -2.328191e-04
## road_surface_conditions4                          -4.730801e-04
## road_surface_conditions5                          -5.102599e-04
## special_conditions_at_site1                       -2.762035e-04
## special_conditions_at_site2                        1.144244e-03
## special_conditions_at_site3                        7.698278e-05
## special_conditions_at_site4                       -1.410689e-04
## special_conditions_at_site5                        5.534026e-05
## special_conditions_at_site6                        7.487394e-04
## special_conditions_at_site7                        7.350706e-04
## carriageway_hazards1                              -6.493003e-04
## carriageway_hazards2                              -1.684992e-04
## carriageway_hazards3                              -2.471117e-04
## carriageway_hazards6                               1.519863e-04
## carriageway_hazards7                              -4.472179e-04
## did_police_officer_attend_scene_of_collision1     -9.238489e-05
## 1|2                                                1.314715e-03
## 2|3                                                1.263997e-03
##                                               light_conditions5
## police_force                                      -2.695962e-06
## number_of_vehicles                                -8.890554e-05
## number_of_casualties                               3.347068e-05
## road_type2                                        -2.737138e-04
## road_type3                                        -4.053279e-04
## road_type6                                        -2.143174e-04
## road_type7                                        -4.750829e-04
## speed_limit                                       -4.010030e-06
## junction_detail1                                  -1.282368e-04
## junction_detail2                                  -4.235079e-04
## junction_detail5                                   5.754417e-05
## junction_detail6                                  -1.273020e-04
## junction_detail7                                   4.289231e-04
## junction_detail8                                  -2.054208e-04
## junction_detail9                                  -1.945943e-04
## junction_control1                                 -7.994109e-06
## junction_control2                                 -4.050332e-05
## junction_control3                                 -1.255254e-03
## second_road_class                                 -2.515128e-05
## pedestrian_crossing_human_control1                -2.696731e-03
## pedestrian_crossing_human_control2                -3.908942e-04
## pedestrian_crossing_physical_facilities1          -5.008887e-05
## pedestrian_crossing_physical_facilities4          -3.752441e-05
## pedestrian_crossing_physical_facilities5           1.184904e-04
## pedestrian_crossing_physical_facilities7           7.538559e-04
## pedestrian_crossing_physical_facilities8           3.000402e-04
## light_conditions4                                  1.046119e-03
## light_conditions5                                  7.862511e-02
## light_conditions6                                  1.167773e-03
## light_conditions7                                  1.019196e-03
## weather_conditions2                               -7.409023e-04
## weather_conditions3                               -2.472670e-03
## weather_conditions4                                6.556358e-04
## weather_conditions5                               -2.533832e-03
## weather_conditions6                               -3.669763e-05
## weather_conditions7                                3.849097e-04
## weather_conditions8                               -8.605687e-04
## road_surface_conditions2                          -9.848734e-04
## road_surface_conditions3                           2.386824e-03
## road_surface_conditions4                           2.951723e-04
## road_surface_conditions5                           1.634234e-03
## special_conditions_at_site1                        4.525278e-04
## special_conditions_at_site2                        6.832355e-04
## special_conditions_at_site3                       -4.145652e-03
## special_conditions_at_site4                        3.982313e-04
## special_conditions_at_site5                        5.600130e-04
## special_conditions_at_site6                        8.136654e-04
## special_conditions_at_site7                        8.582119e-04
## carriageway_hazards1                               5.052685e-04
## carriageway_hazards2                               5.809117e-04
## carriageway_hazards3                               6.646992e-04
## carriageway_hazards6                               4.483582e-04
## carriageway_hazards7                               3.280446e-04
## did_police_officer_attend_scene_of_collision1     -4.702882e-05
## 1|2                                                5.961430e-05
## 2|3                                               -2.123247e-04
##                                               light_conditions6
## police_force                                      -3.698647e-06
## number_of_vehicles                                 5.240249e-04
## number_of_casualties                              -6.002179e-05
## road_type2                                         2.579836e-04
## road_type3                                         5.833185e-04
## road_type6                                         1.876847e-04
## road_type7                                         2.137344e-04
## speed_limit                                       -7.344690e-05
## junction_detail1                                   1.223406e-03
## junction_detail2                                   5.083132e-04
## junction_detail5                                  -2.519115e-04
## junction_detail6                                   1.303264e-04
## junction_detail7                                   2.218668e-04
## junction_detail8                                   3.731900e-05
## junction_detail9                                   4.860903e-05
## junction_control1                                 -6.797496e-05
## junction_control2                                  1.133338e-04
## junction_control3                                 -1.817153e-04
## second_road_class                                  3.278632e-05
## pedestrian_crossing_human_control1                 4.641323e-05
## pedestrian_crossing_human_control2                 1.591149e-04
## pedestrian_crossing_physical_facilities1           1.783126e-04
## pedestrian_crossing_physical_facilities4           1.663608e-04
## pedestrian_crossing_physical_facilities5           1.489059e-04
## pedestrian_crossing_physical_facilities7           6.331835e-04
## pedestrian_crossing_physical_facilities8           4.789200e-04
## light_conditions4                                  6.718837e-04
## light_conditions5                                  1.167773e-03
## light_conditions6                                  2.459660e-02
## light_conditions7                                  1.237948e-03
## weather_conditions2                                3.539418e-04
## weather_conditions3                                1.067314e-03
## weather_conditions4                               -8.514659e-05
## weather_conditions5                               -2.139731e-03
## weather_conditions6                               -1.019251e-02
## weather_conditions7                               -6.775440e-03
## weather_conditions8                               -6.911371e-04
## road_surface_conditions2                          -8.111877e-04
## road_surface_conditions3                          -2.103547e-03
## road_surface_conditions4                          -1.814801e-03
## road_surface_conditions5                           2.048218e-03
## special_conditions_at_site1                        8.521184e-04
## special_conditions_at_site2                        5.258247e-04
## special_conditions_at_site3                        1.038556e-03
## special_conditions_at_site4                       -4.309803e-04
## special_conditions_at_site5                       -2.905434e-03
## special_conditions_at_site6                        1.323500e-03
## special_conditions_at_site7                       -4.643751e-03
## carriageway_hazards1                              -9.650496e-04
## carriageway_hazards2                              -7.228322e-04
## carriageway_hazards3                               8.164603e-04
## carriageway_hazards6                               4.650742e-04
## carriageway_hazards7                              -7.217730e-03
## did_police_officer_attend_scene_of_collision1     -3.122888e-04
## 1|2                                               -7.496482e-04
## 2|3                                               -7.351993e-04
##                                               light_conditions7
## police_force                                      -4.650401e-06
## number_of_vehicles                                 4.129255e-04
## number_of_casualties                               1.311347e-04
## road_type2                                         2.956250e-04
## road_type3                                        -2.237193e-04
## road_type6                                        -6.656146e-05
## road_type7                                         3.780882e-04
## speed_limit                                       -7.442849e-06
## junction_detail1                                  -3.710824e-04
## junction_detail2                                   3.635220e-04
## junction_detail5                                  -9.143687e-04
## junction_detail6                                  -1.121714e-04
## junction_detail7                                  -5.554840e-04
## junction_detail8                                   1.364093e-04
## junction_detail9                                  -1.333479e-04
## junction_control1                                  1.318191e-04
## junction_control2                                  5.161262e-04
## junction_control3                                  2.487535e-04
## second_road_class                                  4.127617e-05
## pedestrian_crossing_human_control1                 6.696835e-04
## pedestrian_crossing_human_control2                 1.767032e-04
## pedestrian_crossing_physical_facilities1          -4.607297e-06
## pedestrian_crossing_physical_facilities4           4.865562e-06
## pedestrian_crossing_physical_facilities5          -1.457467e-04
## pedestrian_crossing_physical_facilities7          -1.920603e-03
## pedestrian_crossing_physical_facilities8           9.079969e-05
## light_conditions4                                  9.066540e-04
## light_conditions5                                  1.019196e-03
## light_conditions6                                  1.237948e-03
## light_conditions7                                  8.566401e-02
## weather_conditions2                               -3.399290e-04
## weather_conditions3                                6.356180e-04
## weather_conditions4                                5.729813e-04
## weather_conditions5                               -4.072321e-04
## weather_conditions6                                5.334453e-04
## weather_conditions7                                5.450267e-04
## weather_conditions8                               -1.363212e-03
## road_surface_conditions2                          -3.592329e-04
## road_surface_conditions3                           5.871710e-06
## road_surface_conditions4                          -3.828177e-04
## road_surface_conditions5                           1.127821e-03
## special_conditions_at_site1                        5.595062e-04
## special_conditions_at_site2                        2.515433e-04
## special_conditions_at_site3                        5.374557e-04
## special_conditions_at_site4                        5.742093e-04
## special_conditions_at_site5                       -2.866353e-03
## special_conditions_at_site6                        1.288186e-03
## special_conditions_at_site7                        1.109945e-03
## carriageway_hazards1                              -3.384908e-03
## carriageway_hazards2                              -5.531559e-04
## carriageway_hazards3                               2.833100e-04
## carriageway_hazards6                               7.533289e-04
## carriageway_hazards7                               5.447964e-04
## did_police_officer_attend_scene_of_collision1      6.672968e-04
## 1|2                                                1.972010e-03
## 2|3                                                2.018503e-03
##                                               weather_conditions2
## police_force                                         5.368980e-06
## number_of_vehicles                                   6.612076e-05
## number_of_casualties                                -6.453136e-05
## road_type2                                          -2.846281e-05
## road_type3                                          -2.664237e-04
## road_type6                                          -4.021740e-05
## road_type7                                           5.113122e-04
## speed_limit                                          5.619472e-06
## junction_detail1                                    -1.896970e-04
## junction_detail2                                    -3.322964e-04
## junction_detail5                                    -3.221377e-04
## junction_detail6                                    -9.302930e-05
## junction_detail7                                    -9.040270e-05
## junction_detail8                                    -1.047924e-04
## junction_detail9                                     2.364895e-05
## junction_control1                                    1.904733e-04
## junction_control2                                   -2.137028e-05
## junction_control3                                    2.731061e-05
## second_road_class                                   -8.624938e-06
## pedestrian_crossing_human_control1                   2.371192e-04
## pedestrian_crossing_human_control2                   1.253686e-04
## pedestrian_crossing_physical_facilities1            -2.346926e-05
## pedestrian_crossing_physical_facilities4            -7.523282e-05
## pedestrian_crossing_physical_facilities5             3.843077e-05
## pedestrian_crossing_physical_facilities7             8.220439e-05
## pedestrian_crossing_physical_facilities8            -6.359889e-05
## light_conditions4                                   -3.393111e-05
## light_conditions5                                   -7.409023e-04
## light_conditions6                                    3.539418e-04
## light_conditions7                                   -3.399290e-04
## weather_conditions2                                  1.156816e-02
## weather_conditions3                                  4.422105e-03
## weather_conditions4                                  2.006222e-03
## weather_conditions5                                  5.122696e-03
## weather_conditions6                                  4.482406e-03
## weather_conditions7                                  2.929563e-03
## weather_conditions8                                  2.197662e-03
## road_surface_conditions2                            -5.047659e-03
## road_surface_conditions3                            -4.087218e-03
## road_surface_conditions4                            -8.468274e-04
## road_surface_conditions5                            -6.403034e-03
## special_conditions_at_site1                          1.325762e-04
## special_conditions_at_site2                          4.603058e-04
## special_conditions_at_site3                          1.393149e-03
## special_conditions_at_site4                          2.138411e-04
## special_conditions_at_site5                         -1.085737e-04
## special_conditions_at_site6                         -5.123657e-04
## special_conditions_at_site7                          2.073807e-04
## carriageway_hazards1                                 1.913325e-04
## carriageway_hazards2                                -9.984283e-05
## carriageway_hazards3                                -7.642648e-04
## carriageway_hazards6                                 3.302976e-04
## carriageway_hazards7                                -1.174420e-03
## did_police_officer_attend_scene_of_collision1       -8.160727e-05
## 1|2                                                  2.056471e-04
## 2|3                                                  2.169771e-04
##                                               weather_conditions3
## police_force                                         9.789859e-06
## number_of_vehicles                                   1.999227e-04
## number_of_casualties                                -4.209503e-05
## road_type2                                          -8.653859e-05
## road_type3                                          -1.839748e-04
## road_type6                                          -1.142441e-04
## road_type7                                           1.239563e-04
## speed_limit                                         -4.819899e-06
## junction_detail1                                    -1.603962e-05
## junction_detail2                                     5.660002e-04
## junction_detail5                                     9.699123e-04
## junction_detail6                                     3.817913e-04
## junction_detail7                                     6.454248e-04
## junction_detail8                                    -2.592778e-04
## junction_detail9                                     2.979037e-04
## junction_control1                                    3.506290e-04
## junction_control2                                   -1.274346e-04
## junction_control3                                    1.064178e-03
## second_road_class                                   -2.164020e-04
## pedestrian_crossing_human_control1                  -1.461240e-03
## pedestrian_crossing_human_control2                   5.189317e-04
## pedestrian_crossing_physical_facilities1             6.379281e-04
## pedestrian_crossing_physical_facilities4             1.676468e-04
## pedestrian_crossing_physical_facilities5            -3.760176e-04
## pedestrian_crossing_physical_facilities7             3.450039e-03
## pedestrian_crossing_physical_facilities8             1.149521e-04
## light_conditions4                                    1.048952e-04
## light_conditions5                                   -2.472670e-03
## light_conditions6                                    1.067314e-03
## light_conditions7                                    6.356180e-04
## weather_conditions2                                  4.422105e-03
## weather_conditions3                                  1.807685e-01
## weather_conditions4                                  1.858014e-03
## weather_conditions5                                  4.472006e-03
## weather_conditions6                                  3.930952e-02
## weather_conditions7                                  3.573164e-03
## weather_conditions8                                  2.315192e-03
## road_surface_conditions2                            -4.471309e-03
## road_surface_conditions3                            -1.596522e-01
## road_surface_conditions4                            -5.235169e-03
## road_surface_conditions5                            -3.672847e-03
## special_conditions_at_site1                          3.850775e-04
## special_conditions_at_site2                          4.621284e-04
## special_conditions_at_site3                          1.088079e-03
## special_conditions_at_site4                          5.415675e-04
## special_conditions_at_site5                          6.189389e-04
## special_conditions_at_site6                          1.251515e-03
## special_conditions_at_site7                          1.466712e-03
## carriageway_hazards1                                 6.633121e-04
## carriageway_hazards2                                 5.288085e-04
## carriageway_hazards3                                -6.001018e-05
## carriageway_hazards6                                 7.739596e-04
## carriageway_hazards7                                -1.501325e-04
## did_police_officer_attend_scene_of_collision1        4.551529e-04
## 1|2                                                 -1.772710e-04
## 2|3                                                 -1.878494e-04
##                                               weather_conditions4
## police_force                                         1.623597e-06
## number_of_vehicles                                   9.804878e-05
## number_of_casualties                                 5.453756e-05
## road_type2                                          -8.131298e-05
## road_type3                                           2.488681e-04
## road_type6                                           3.266206e-04
## road_type7                                           5.651420e-04
## speed_limit                                         -5.885095e-06
## junction_detail1                                    -4.558535e-06
## junction_detail2                                     5.301491e-04
## junction_detail5                                     3.166734e-04
## junction_detail6                                    -1.001934e-04
## junction_detail7                                     2.041367e-05
## junction_detail8                                    -1.076822e-04
## junction_detail9                                    -2.105091e-04
## junction_control1                                    3.219488e-04
## junction_control2                                    2.693739e-04
## junction_control3                                    5.280649e-05
## second_road_class                                   -9.247236e-06
## pedestrian_crossing_human_control1                  -1.817673e-03
## pedestrian_crossing_human_control2                  -9.565543e-04
## pedestrian_crossing_physical_facilities1             4.152848e-04
## pedestrian_crossing_physical_facilities4             8.917630e-05
## pedestrian_crossing_physical_facilities5            -2.934447e-06
## pedestrian_crossing_physical_facilities7             6.667679e-04
## pedestrian_crossing_physical_facilities8            -5.093554e-04
## light_conditions4                                    8.613320e-05
## light_conditions5                                    6.556358e-04
## light_conditions6                                   -8.514659e-05
## light_conditions7                                    5.729813e-04
## weather_conditions2                                  2.006222e-03
## weather_conditions3                                  1.858014e-03
## weather_conditions4                                  6.150116e-02
## weather_conditions5                                  2.160329e-03
## weather_conditions6                                  2.035348e-03
## weather_conditions7                                  1.695193e-03
## weather_conditions8                                  1.267508e-03
## road_surface_conditions2                            -1.590110e-03
## road_surface_conditions3                            -1.274194e-03
## road_surface_conditions4                            -8.432944e-04
## road_surface_conditions5                            -1.413684e-03
## special_conditions_at_site1                         -1.685020e-04
## special_conditions_at_site2                          3.520774e-04
## special_conditions_at_site3                          8.277965e-04
## special_conditions_at_site4                         -6.499754e-05
## special_conditions_at_site5                          7.965896e-04
## special_conditions_at_site6                          1.888801e-03
## special_conditions_at_site7                          9.194371e-04
## carriageway_hazards1                                 5.068099e-04
## carriageway_hazards2                                -2.668530e-04
## carriageway_hazards3                                -4.451626e-03
## carriageway_hazards6                                 6.608512e-04
## carriageway_hazards7                                -5.317431e-03
## did_police_officer_attend_scene_of_collision1       -3.454315e-04
## 1|2                                                  5.592780e-04
## 2|3                                                  5.225715e-04
##                                               weather_conditions5
## police_force                                        -1.443245e-07
## number_of_vehicles                                   7.777018e-05
## number_of_casualties                                 2.717027e-05
## road_type2                                           1.161230e-04
## road_type3                                          -2.750454e-04
## road_type6                                          -5.104907e-04
## road_type7                                          -3.142367e-04
## speed_limit                                         -3.669719e-06
## junction_detail1                                     5.294431e-05
## junction_detail2                                     1.502707e-04
## junction_detail5                                     2.757588e-04
## junction_detail6                                     2.137440e-04
## junction_detail7                                    -2.113821e-04
## junction_detail8                                    -6.393930e-04
## junction_detail9                                    -1.541796e-04
## junction_control1                                    1.059759e-04
## junction_control2                                    1.567703e-04
## junction_control3                                    6.094390e-04
## second_road_class                                    6.463390e-05
## pedestrian_crossing_human_control1                   7.785497e-04
## pedestrian_crossing_human_control2                  -1.057764e-03
## pedestrian_crossing_physical_facilities1            -2.657786e-04
## pedestrian_crossing_physical_facilities4             9.932714e-06
## pedestrian_crossing_physical_facilities5            -7.125437e-05
## pedestrian_crossing_physical_facilities7             6.579252e-05
## pedestrian_crossing_physical_facilities8            -3.804380e-05
## light_conditions4                                   -1.960151e-04
## light_conditions5                                   -2.533832e-03
## light_conditions6                                   -2.139731e-03
## light_conditions7                                   -4.072321e-04
## weather_conditions2                                  5.122696e-03
## weather_conditions3                                  4.472006e-03
## weather_conditions4                                  2.160329e-03
## weather_conditions5                                  8.193004e-02
## weather_conditions6                                  5.700479e-03
## weather_conditions7                                  3.804864e-03
## weather_conditions8                                  2.453241e-03
## road_surface_conditions2                            -5.129024e-03
## road_surface_conditions3                            -4.122890e-03
## road_surface_conditions4                            -5.412088e-04
## road_surface_conditions5                            -2.664260e-02
## special_conditions_at_site1                         -2.214901e-03
## special_conditions_at_site2                         -4.927601e-04
## special_conditions_at_site3                          1.209885e-03
## special_conditions_at_site4                          8.898798e-04
## special_conditions_at_site5                          1.423870e-03
## special_conditions_at_site6                          2.136197e-03
## special_conditions_at_site7                          2.269192e-03
## carriageway_hazards1                                -3.492813e-03
## carriageway_hazards2                                -2.560801e-03
## carriageway_hazards3                                -6.152534e-03
## carriageway_hazards6                                 5.722664e-04
## carriageway_hazards7                                 1.056427e-03
## did_police_officer_attend_scene_of_collision1        1.849467e-04
## 1|2                                                  1.766772e-04
## 2|3                                                  9.842245e-05
##                                               weather_conditions6
## police_force                                         4.556588e-05
## number_of_vehicles                                   4.026250e-04
## number_of_casualties                                -3.786211e-04
## road_type2                                           3.768606e-04
## road_type3                                          -7.680330e-04
## road_type6                                          -1.077001e-04
## road_type7                                           3.144536e-03
## speed_limit                                         -3.700969e-05
## junction_detail1                                     4.296177e-04
## junction_detail2                                    -2.088217e-04
## junction_detail5                                    -4.249510e-03
## junction_detail6                                    -5.176357e-04
## junction_detail7                                     6.282265e-04
## junction_detail8                                    -2.587339e-03
## junction_detail9                                     5.275964e-04
## junction_control1                                    1.041047e-04
## junction_control2                                    5.531710e-04
## junction_control3                                    9.757797e-04
## second_road_class                                    1.832445e-04
## pedestrian_crossing_human_control1                  -9.325934e-05
## pedestrian_crossing_human_control2                   3.627714e-04
## pedestrian_crossing_physical_facilities1             3.173555e-04
## pedestrian_crossing_physical_facilities4             1.048227e-04
## pedestrian_crossing_physical_facilities5            -4.820704e-04
## pedestrian_crossing_physical_facilities7             1.810554e-03
## pedestrian_crossing_physical_facilities8             3.655274e-05
## light_conditions4                                    4.678942e-04
## light_conditions5                                   -3.669763e-05
## light_conditions6                                   -1.019251e-02
## light_conditions7                                    5.334453e-04
## weather_conditions2                                  4.482406e-03
## weather_conditions3                                  3.930952e-02
## weather_conditions4                                  2.035348e-03
## weather_conditions5                                  5.700479e-03
## weather_conditions6                                  1.337523e+00
## weather_conditions7                                  7.434479e-03
## weather_conditions8                                  2.856767e-03
## road_surface_conditions2                            -4.444754e-03
## road_surface_conditions3                            -1.013825e-01
## road_surface_conditions4                            -5.455445e-03
## road_surface_conditions5                            -4.523212e-03
## special_conditions_at_site1                         -1.018254e-04
## special_conditions_at_site2                          2.457662e-03
## special_conditions_at_site3                          1.012403e-03
## special_conditions_at_site4                          1.024873e-03
## special_conditions_at_site5                          2.647261e-03
## special_conditions_at_site6                          1.150136e-03
## special_conditions_at_site7                          4.555851e-03
## carriageway_hazards1                                 1.005204e-03
## carriageway_hazards2                                 1.226115e-03
## carriageway_hazards3                                -6.206646e-05
## carriageway_hazards6                                 1.179648e-03
## carriageway_hazards7                                 3.440675e-03
## did_police_officer_attend_scene_of_collision1        5.030543e-04
## 1|2                                                  1.309785e-03
## 2|3                                                  1.288554e-03
##                                               weather_conditions7
## police_force                                        -4.911409e-06
## number_of_vehicles                                   2.472542e-05
## number_of_casualties                                -1.748535e-04
## road_type2                                          -1.485275e-05
## road_type3                                          -2.936220e-04
## road_type6                                          -4.136371e-05
## road_type7                                           6.184161e-04
## speed_limit                                         -1.069564e-05
## junction_detail1                                    -1.150285e-04
## junction_detail2                                     5.368955e-04
## junction_detail5                                     1.169426e-03
## junction_detail6                                    -3.773680e-05
## junction_detail7                                    -3.260375e-04
## junction_detail8                                     3.582783e-04
## junction_detail9                                     3.647925e-04
## junction_control1                                    4.824266e-04
## junction_control2                                    4.732030e-04
## junction_control3                                   -1.022809e-03
## second_road_class                                    3.442524e-05
## pedestrian_crossing_human_control1                   1.595827e-05
## pedestrian_crossing_human_control2                   8.403411e-05
## pedestrian_crossing_physical_facilities1             3.259630e-04
## pedestrian_crossing_physical_facilities4             3.937815e-05
## pedestrian_crossing_physical_facilities5            -5.213942e-05
## pedestrian_crossing_physical_facilities7             1.829371e-04
## pedestrian_crossing_physical_facilities8            -3.373898e-04
## light_conditions4                                   -1.497153e-04
## light_conditions5                                    3.849097e-04
## light_conditions6                                   -6.775440e-03
## light_conditions7                                    5.450267e-04
## weather_conditions2                                  2.929563e-03
## weather_conditions3                                  3.573164e-03
## weather_conditions4                                  1.695193e-03
## weather_conditions5                                  3.804864e-03
## weather_conditions6                                  7.434479e-03
## weather_conditions7                                  2.637001e-01
## weather_conditions8                                  2.893978e-03
## road_surface_conditions2                            -2.743872e-03
## road_surface_conditions3                            -2.816029e-03
## road_surface_conditions4                            -1.188590e-02
## road_surface_conditions5                            -2.981027e-03
## special_conditions_at_site1                         -5.828614e-05
## special_conditions_at_site2                          4.085982e-04
## special_conditions_at_site3                          1.076393e-03
## special_conditions_at_site4                          7.134908e-04
## special_conditions_at_site5                         -1.177876e-02
## special_conditions_at_site6                          1.693432e-03
## special_conditions_at_site7                          3.535643e-03
## carriageway_hazards1                                 1.099927e-03
## carriageway_hazards2                                 8.740472e-04
## carriageway_hazards3                                -5.605138e-05
## carriageway_hazards6                                 5.061917e-04
## carriageway_hazards7                                 2.338798e-03
## did_police_officer_attend_scene_of_collision1       -1.993368e-04
## 1|2                                                 -5.673585e-04
## 2|3                                                 -4.914968e-04
##                                               weather_conditions8
## police_force                                         5.994749e-06
## number_of_vehicles                                   8.293645e-05
## number_of_casualties                                -2.827528e-05
## road_type2                                          -2.649381e-04
## road_type3                                          -1.432886e-04
## road_type6                                          -8.762487e-05
## road_type7                                           4.401104e-04
## speed_limit                                          8.082773e-06
## junction_detail1                                    -1.517758e-04
## junction_detail2                                     1.346052e-04
## junction_detail5                                    -4.698085e-04
## junction_detail6                                    -1.336609e-04
## junction_detail7                                    -3.516752e-04
## junction_detail8                                     8.771211e-05
## junction_detail9                                    -4.232007e-04
## junction_control1                                   -7.430450e-07
## junction_control2                                    3.232384e-04
## junction_control3                                   -3.420760e-05
## second_road_class                                    1.306204e-05
## pedestrian_crossing_human_control1                  -3.646770e-04
## pedestrian_crossing_human_control2                  -1.164314e-03
## pedestrian_crossing_physical_facilities1             1.565300e-04
## pedestrian_crossing_physical_facilities4             2.226851e-04
## pedestrian_crossing_physical_facilities5            -1.127561e-05
## pedestrian_crossing_physical_facilities7            -3.078051e-03
## pedestrian_crossing_physical_facilities8             9.160245e-05
## light_conditions4                                   -1.207937e-04
## light_conditions5                                   -8.605687e-04
## light_conditions6                                   -6.911371e-04
## light_conditions7                                   -1.363212e-03
## weather_conditions2                                  2.197662e-03
## weather_conditions3                                  2.315192e-03
## weather_conditions4                                  1.267508e-03
## weather_conditions5                                  2.453241e-03
## weather_conditions6                                  2.856767e-03
## weather_conditions7                                  2.893978e-03
## weather_conditions8                                  2.420322e-02
## road_surface_conditions2                            -1.747841e-03
## road_surface_conditions3                            -1.587133e-03
## road_surface_conditions4                            -5.220799e-03
## road_surface_conditions5                            -9.351102e-03
## special_conditions_at_site1                         -4.632259e-04
## special_conditions_at_site2                          2.807616e-04
## special_conditions_at_site3                          8.366927e-04
## special_conditions_at_site4                          3.926497e-04
## special_conditions_at_site5                         -3.374143e-04
## special_conditions_at_site6                          1.015716e-03
## special_conditions_at_site7                         -8.597352e-04
## carriageway_hazards1                                -1.081867e-04
## carriageway_hazards2                                -3.319287e-04
## carriageway_hazards3                                 3.176142e-04
## carriageway_hazards6                                -3.786724e-05
## carriageway_hazards7                                -1.519769e-03
## did_police_officer_attend_scene_of_collision1       -1.243221e-04
## 1|2                                                  7.199819e-04
## 2|3                                                  7.171668e-04
##                                               road_surface_conditions2
## police_force                                             -4.905571e-06
## number_of_vehicles                                        7.817709e-06
## number_of_casualties                                      2.270092e-05
## road_type2                                               -4.499111e-05
## road_type3                                               -6.966196e-06
## road_type6                                               -8.337428e-05
## road_type7                                               -2.031825e-04
## speed_limit                                              -4.771354e-06
## junction_detail1                                          1.028097e-05
## junction_detail2                                          2.821703e-05
## junction_detail5                                          1.201509e-04
## junction_detail6                                         -1.546711e-05
## junction_detail7                                          7.774609e-05
## junction_detail8                                          6.837807e-05
## junction_detail9                                         -2.322594e-06
## junction_control1                                         3.000379e-04
## junction_control2                                         7.764811e-05
## junction_control3                                         5.477760e-05
## second_road_class                                         1.442078e-05
## pedestrian_crossing_human_control1                       -2.137465e-04
## pedestrian_crossing_human_control2                       -2.041029e-04
## pedestrian_crossing_physical_facilities1                  1.402369e-05
## pedestrian_crossing_physical_facilities4                  7.087366e-05
## pedestrian_crossing_physical_facilities5                  1.623345e-05
## pedestrian_crossing_physical_facilities7                  1.911352e-04
## pedestrian_crossing_physical_facilities8                  1.983575e-05
## light_conditions4                                        -7.197940e-04
## light_conditions5                                        -9.848734e-04
## light_conditions6                                        -8.111877e-04
## light_conditions7                                        -3.592329e-04
## weather_conditions2                                      -5.047659e-03
## weather_conditions3                                      -4.471309e-03
## weather_conditions4                                      -1.590110e-03
## weather_conditions5                                      -5.129024e-03
## weather_conditions6                                      -4.444754e-03
## weather_conditions7                                      -2.743872e-03
## weather_conditions8                                      -1.747841e-03
## road_surface_conditions2                                  6.162614e-03
## road_surface_conditions3                                  4.885182e-03
## road_surface_conditions4                                  1.598026e-03
## road_surface_conditions5                                  4.860223e-03
## special_conditions_at_site1                               8.326241e-05
## special_conditions_at_site2                               3.537342e-04
## special_conditions_at_site3                              -7.691623e-04
## special_conditions_at_site4                              -5.075083e-05
## special_conditions_at_site5                              -1.452596e-04
## special_conditions_at_site6                              -9.626491e-04
## special_conditions_at_site7                              -1.103791e-03
## carriageway_hazards1                                     -8.691353e-05
## carriageway_hazards2                                     -1.746963e-05
## carriageway_hazards3                                      4.377966e-04
## carriageway_hazards6                                     -7.945174e-06
## carriageway_hazards7                                      6.757382e-04
## did_police_officer_attend_scene_of_collision1            -2.040250e-04
## 1|2                                                       9.215052e-05
## 2|3                                                       1.304245e-04
##                                               road_surface_conditions3
## police_force                                             -3.196201e-06
## number_of_vehicles                                       -2.173558e-04
## number_of_casualties                                     -1.852760e-04
## road_type2                                               -5.882435e-04
## road_type3                                               -2.114690e-05
## road_type6                                                2.864062e-05
## road_type7                                                1.345627e-03
## speed_limit                                               9.262917e-06
## junction_detail1                                         -1.071535e-03
## junction_detail2                                         -1.070981e-04
## junction_detail5                                         -3.598490e-03
## junction_detail6                                         -1.479427e-04
## junction_detail7                                         -1.088613e-03
## junction_detail8                                          3.255830e-04
## junction_detail9                                         -4.561176e-04
## junction_control1                                         3.072578e-04
## junction_control2                                         3.115660e-05
## junction_control3                                        -1.618346e-03
## second_road_class                                        -6.743798e-05
## pedestrian_crossing_human_control1                        1.783851e-03
## pedestrian_crossing_human_control2                       -1.845996e-04
## pedestrian_crossing_physical_facilities1                 -3.349721e-04
## pedestrian_crossing_physical_facilities4                  1.585226e-04
## pedestrian_crossing_physical_facilities5                  8.510097e-04
## pedestrian_crossing_physical_facilities7                 -8.907432e-03
## pedestrian_crossing_physical_facilities8                  4.821669e-05
## light_conditions4                                        -2.328191e-04
## light_conditions5                                         2.386824e-03
## light_conditions6                                        -2.103547e-03
## light_conditions7                                         5.871710e-06
## weather_conditions2                                      -4.087218e-03
## weather_conditions3                                      -1.596522e-01
## weather_conditions4                                      -1.274194e-03
## weather_conditions5                                      -4.122890e-03
## weather_conditions6                                      -1.013825e-01
## weather_conditions7                                      -2.816029e-03
## weather_conditions8                                      -1.587133e-03
## road_surface_conditions2                                  4.885182e-03
## road_surface_conditions3                                  4.406485e-01
## road_surface_conditions4                                  5.560296e-03
## road_surface_conditions5                                  3.682308e-03
## special_conditions_at_site1                              -9.892815e-05
## special_conditions_at_site2                              -1.038576e-04
## special_conditions_at_site3                              -5.094560e-04
## special_conditions_at_site4                               1.493080e-04
## special_conditions_at_site5                              -1.023808e-04
## special_conditions_at_site6                              -5.938486e-04
## special_conditions_at_site7                              -9.083108e-04
## carriageway_hazards1                                     -9.776856e-05
## carriageway_hazards2                                      2.616234e-05
## carriageway_hazards3                                      2.528241e-04
## carriageway_hazards6                                      3.209810e-05
## carriageway_hazards7                                      9.246427e-04
## did_police_officer_attend_scene_of_collision1             2.287068e-05
## 1|2                                                      -4.349652e-04
## 2|3                                                      -3.304731e-04
##                                               road_surface_conditions4
## police_force                                             -8.154648e-06
## number_of_vehicles                                        4.922549e-05
## number_of_casualties                                      1.160612e-04
## road_type2                                                3.628686e-04
## road_type3                                                1.739785e-04
## road_type6                                                1.168853e-06
## road_type7                                               -3.822033e-04
## speed_limit                                              -1.027053e-05
## junction_detail1                                          5.392446e-05
## junction_detail2                                         -2.581337e-04
## junction_detail5                                          2.707105e-04
## junction_detail6                                          3.701902e-04
## junction_detail7                                         -2.743931e-04
## junction_detail8                                          1.074543e-05
## junction_detail9                                          1.973031e-04
## junction_control1                                         7.543003e-04
## junction_control2                                        -1.357558e-04
## junction_control3                                         5.116140e-04
## second_road_class                                        -7.036255e-05
## pedestrian_crossing_human_control1                        6.541847e-04
## pedestrian_crossing_human_control2                        1.340884e-04
## pedestrian_crossing_physical_facilities1                 -3.569125e-04
## pedestrian_crossing_physical_facilities4                 -7.439608e-05
## pedestrian_crossing_physical_facilities5                  1.126786e-04
## pedestrian_crossing_physical_facilities7                  1.087833e-03
## pedestrian_crossing_physical_facilities8                  8.152129e-05
## light_conditions4                                        -4.730801e-04
## light_conditions5                                         2.951723e-04
## light_conditions6                                        -1.814801e-03
## light_conditions7                                        -3.828177e-04
## weather_conditions2                                      -8.468274e-04
## weather_conditions3                                      -5.235169e-03
## weather_conditions4                                      -8.432944e-04
## weather_conditions5                                      -5.412088e-04
## weather_conditions6                                      -5.455445e-03
## weather_conditions7                                      -1.188590e-02
## weather_conditions8                                      -5.220799e-03
## road_surface_conditions2                                  1.598026e-03
## road_surface_conditions3                                  5.560296e-03
## road_surface_conditions4                                  4.696300e-02
## road_surface_conditions5                                  3.041615e-03
## special_conditions_at_site1                               5.457116e-04
## special_conditions_at_site2                              -2.164938e-04
## special_conditions_at_site3                               7.427231e-05
## special_conditions_at_site4                              -4.038613e-04
## special_conditions_at_site5                              -8.936550e-04
## special_conditions_at_site6                              -3.555171e-03
## special_conditions_at_site7                              -3.525261e-03
## carriageway_hazards1                                     -1.526622e-03
## carriageway_hazards2                                     -2.031827e-04
## carriageway_hazards3                                      5.806520e-04
## carriageway_hazards6                                     -1.664159e-03
## carriageway_hazards7                                      1.604564e-03
## did_police_officer_attend_scene_of_collision1            -7.179689e-05
## 1|2                                                      -2.108627e-04
## 2|3                                                      -1.335965e-04
##                                               road_surface_conditions5
## police_force                                             -2.580389e-05
## number_of_vehicles                                        1.191380e-03
## number_of_casualties                                     -9.145523e-04
## road_type2                                               -1.920407e-03
## road_type3                                               -1.211223e-03
## road_type6                                               -2.355626e-03
## road_type7                                               -1.723077e-03
## speed_limit                                              -4.575526e-05
## junction_detail1                                         -1.325265e-03
## junction_detail2                                         -7.719971e-03
## junction_detail5                                          6.242552e-05
## junction_detail6                                         -8.020834e-04
## junction_detail7                                          3.014752e-04
## junction_detail8                                          2.764035e-04
## junction_detail9                                         -2.044819e-03
## junction_control1                                         6.759683e-04
## junction_control2                                        -6.634911e-04
## junction_control3                                         1.157274e-04
## second_road_class                                        -1.496769e-04
## pedestrian_crossing_human_control1                        3.150900e-04
## pedestrian_crossing_human_control2                        1.287979e-03
## pedestrian_crossing_physical_facilities1                  4.640924e-04
## pedestrian_crossing_physical_facilities4                  3.587755e-04
## pedestrian_crossing_physical_facilities5                 -1.336540e-03
## pedestrian_crossing_physical_facilities7                  1.357431e-03
## pedestrian_crossing_physical_facilities8                  9.420800e-04
## light_conditions4                                        -5.102599e-04
## light_conditions5                                         1.634234e-03
## light_conditions6                                         2.048218e-03
## light_conditions7                                         1.127821e-03
## weather_conditions2                                      -6.403034e-03
## weather_conditions3                                      -3.672847e-03
## weather_conditions4                                      -1.413684e-03
## weather_conditions5                                      -2.664260e-02
## weather_conditions6                                      -4.523212e-03
## weather_conditions7                                      -2.981027e-03
## weather_conditions8                                      -9.351102e-03
## road_surface_conditions2                                  4.860223e-03
## road_surface_conditions3                                  3.682308e-03
## road_surface_conditions4                                  3.041615e-03
## road_surface_conditions5                                  1.534896e+00
## special_conditions_at_site1                               1.751798e-03
## special_conditions_at_site2                               2.940984e-03
## special_conditions_at_site3                               2.667897e-04
## special_conditions_at_site4                              -1.609303e-04
## special_conditions_at_site5                               4.219744e-04
## special_conditions_at_site6                              -9.105855e-04
## special_conditions_at_site7                               2.895780e-04
## carriageway_hazards1                                      1.467731e-03
## carriageway_hazards2                                      1.379710e-03
## carriageway_hazards3                                      2.723989e-03
## carriageway_hazards6                                      6.324245e-04
## carriageway_hazards7                                      1.948559e-03
## did_police_officer_attend_scene_of_collision1            -6.080264e-04
## 1|2                                                      -4.781812e-03
## 2|3                                                      -4.818222e-03
##                                               special_conditions_at_site1
## police_force                                                -7.272675e-07
## number_of_vehicles                                           8.714675e-05
## number_of_casualties                                        -6.318951e-05
## road_type2                                                   7.058798e-04
## road_type3                                                   2.593292e-04
## road_type6                                                   3.752970e-04
## road_type7                                                   6.689651e-04
## speed_limit                                                  8.125851e-07
## junction_detail1                                             3.633582e-04
## junction_detail2                                             6.258604e-04
## junction_detail5                                             3.057310e-04
## junction_detail6                                            -4.865071e-04
## junction_detail7                                             1.718751e-04
## junction_detail8                                             3.335571e-04
## junction_detail9                                            -2.818482e-04
## junction_control1                                            7.976359e-04
## junction_control2                                           -6.730240e-04
## junction_control3                                            5.580000e-04
## second_road_class                                            1.855860e-05
## pedestrian_crossing_human_control1                           8.352532e-04
## pedestrian_crossing_human_control2                          -5.769511e-05
## pedestrian_crossing_physical_facilities1                    -3.258605e-04
## pedestrian_crossing_physical_facilities4                     1.688123e-04
## pedestrian_crossing_physical_facilities5                    -4.537648e-04
## pedestrian_crossing_physical_facilities7                     7.253440e-04
## pedestrian_crossing_physical_facilities8                    -3.201332e-04
## light_conditions4                                           -2.762035e-04
## light_conditions5                                            4.525278e-04
## light_conditions6                                            8.521184e-04
## light_conditions7                                            5.595062e-04
## weather_conditions2                                          1.325762e-04
## weather_conditions3                                          3.850775e-04
## weather_conditions4                                         -1.685020e-04
## weather_conditions5                                         -2.214901e-03
## weather_conditions6                                         -1.018254e-04
## weather_conditions7                                         -5.828614e-05
## weather_conditions8                                         -4.632259e-04
## road_surface_conditions2                                     8.326241e-05
## road_surface_conditions3                                    -9.892815e-05
## road_surface_conditions4                                     5.457116e-04
## road_surface_conditions5                                     1.751798e-03
## special_conditions_at_site1                                  2.884869e-01
## special_conditions_at_site2                                  2.121084e-03
## special_conditions_at_site3                                  5.581936e-04
## special_conditions_at_site4                                  5.980944e-04
## special_conditions_at_site5                                  3.204023e-04
## special_conditions_at_site6                                  2.214123e-03
## special_conditions_at_site7                                  6.714328e-05
## carriageway_hazards1                                        -1.330389e-02
## carriageway_hazards2                                         4.620780e-04
## carriageway_hazards3                                        -1.091674e-02
## carriageway_hazards6                                         7.352675e-04
## carriageway_hazards7                                        -1.839883e-02
## did_police_officer_attend_scene_of_collision1               -5.565059e-04
## 1|2                                                          1.793754e-04
## 2|3                                                          3.108543e-04
##                                               special_conditions_at_site2
## police_force                                                 1.462736e-05
## number_of_vehicles                                           1.698752e-04
## number_of_casualties                                        -1.758362e-03
## road_type2                                                   1.327978e-03
## road_type3                                                  -2.983287e-03
## road_type6                                                   1.536855e-03
## road_type7                                                   5.432975e-04
## speed_limit                                                 -2.017715e-05
## junction_detail1                                             1.033500e-03
## junction_detail2                                             6.228674e-06
## junction_detail5                                             2.313610e-03
## junction_detail6                                            -1.845672e-03
## junction_detail7                                             2.101209e-03
## junction_detail8                                            -1.730173e-04
## junction_detail9                                             2.984483e-04
## junction_control1                                            6.761184e-04
## junction_control2                                            6.724218e-06
## junction_control3                                            6.454125e-04
## second_road_class                                           -6.009680e-05
## pedestrian_crossing_human_control1                           9.840658e-04
## pedestrian_crossing_human_control2                           1.927773e-03
## pedestrian_crossing_physical_facilities1                    -4.909568e-04
## pedestrian_crossing_physical_facilities4                     5.185463e-05
## pedestrian_crossing_physical_facilities5                    -4.640050e-03
## pedestrian_crossing_physical_facilities7                     1.106951e-03
## pedestrian_crossing_physical_facilities8                    -8.881318e-05
## light_conditions4                                            1.144244e-03
## light_conditions5                                            6.832355e-04
## light_conditions6                                            5.258247e-04
## light_conditions7                                            2.515433e-04
## weather_conditions2                                          4.603058e-04
## weather_conditions3                                          4.621284e-04
## weather_conditions4                                          3.520774e-04
## weather_conditions5                                         -4.927601e-04
## weather_conditions6                                          2.457662e-03
## weather_conditions7                                          4.085982e-04
## weather_conditions8                                          2.807616e-04
## road_surface_conditions2                                     3.537342e-04
## road_surface_conditions3                                    -1.038576e-04
## road_surface_conditions4                                    -2.164938e-04
## road_surface_conditions5                                     2.940984e-03
## special_conditions_at_site1                                  2.121084e-03
## special_conditions_at_site2                                  1.919221e+00
## special_conditions_at_site3                                  1.321153e-03
## special_conditions_at_site4                                  8.116476e-04
## special_conditions_at_site5                                 -5.551647e-05
## special_conditions_at_site6                                 -7.113553e-05
## special_conditions_at_site7                                  2.936550e-04
## carriageway_hazards1                                         7.431291e-04
## carriageway_hazards2                                         4.385834e-04
## carriageway_hazards3                                         6.384183e-04
## carriageway_hazards6                                         7.349307e-04
## carriageway_hazards7                                        -2.429822e-04
## did_police_officer_attend_scene_of_collision1               -1.565482e-04
## 1|2                                                         -1.155859e-03
## 2|3                                                         -1.444991e-03
##                                               special_conditions_at_site3
## police_force                                                -3.287575e-07
## number_of_vehicles                                           3.131704e-04
## number_of_casualties                                        -1.844841e-04
## road_type2                                                   1.417101e-03
## road_type3                                                   1.396733e-03
## road_type6                                                   8.880946e-04
## road_type7                                                   1.487473e-03
## speed_limit                                                 -1.838041e-05
## junction_detail1                                             4.274936e-04
## junction_detail2                                            -1.000791e-03
## junction_detail5                                             1.323559e-04
## junction_detail6                                            -1.778253e-03
## junction_detail7                                            -3.090451e-04
## junction_detail8                                             4.131078e-04
## junction_detail9                                             3.084421e-04
## junction_control1                                            5.702722e-04
## junction_control2                                            5.688055e-04
## junction_control3                                           -7.958514e-03
## second_road_class                                           -8.591409e-05
## pedestrian_crossing_human_control1                           6.918585e-04
## pedestrian_crossing_human_control2                           4.704642e-04
## pedestrian_crossing_physical_facilities1                    -7.505765e-04
## pedestrian_crossing_physical_facilities4                     3.681137e-04
## pedestrian_crossing_physical_facilities5                     1.502462e-04
## pedestrian_crossing_physical_facilities7                     6.076173e-04
## pedestrian_crossing_physical_facilities8                     5.809397e-04
## light_conditions4                                            7.698278e-05
## light_conditions5                                           -4.145652e-03
## light_conditions6                                            1.038556e-03
## light_conditions7                                            5.374557e-04
## weather_conditions2                                          1.393149e-03
## weather_conditions3                                          1.088079e-03
## weather_conditions4                                          8.277965e-04
## weather_conditions5                                          1.209885e-03
## weather_conditions6                                          1.012403e-03
## weather_conditions7                                          1.076393e-03
## weather_conditions8                                          8.366927e-04
## road_surface_conditions2                                    -7.691623e-04
## road_surface_conditions3                                    -5.094560e-04
## road_surface_conditions4                                     7.427231e-05
## road_surface_conditions5                                     2.667897e-04
## special_conditions_at_site1                                  5.581936e-04
## special_conditions_at_site2                                  1.321153e-03
## special_conditions_at_site3                                  2.622925e-01
## special_conditions_at_site4                                  6.092972e-04
## special_conditions_at_site5                                  8.785170e-04
## special_conditions_at_site6                                  6.838635e-04
## special_conditions_at_site7                                  5.311111e-04
## carriageway_hazards1                                         7.053800e-04
## carriageway_hazards2                                         6.689601e-04
## carriageway_hazards3                                         2.614431e-04
## carriageway_hazards6                                         3.644003e-04
## carriageway_hazards7                                         5.686755e-04
## did_police_officer_attend_scene_of_collision1               -3.636867e-04
## 1|2                                                          2.924616e-04
## 2|3                                                          2.426520e-04
##                                               special_conditions_at_site4
## police_force                                                 8.496634e-06
## number_of_vehicles                                           1.476858e-04
## number_of_casualties                                         1.124180e-04
## road_type2                                                  -5.971362e-04
## road_type3                                                   1.537135e-04
## road_type6                                                   3.206552e-04
## road_type7                                                   9.831402e-04
## speed_limit                                                 -4.687212e-06
## junction_detail1                                            -3.772081e-05
## junction_detail2                                             5.168919e-04
## junction_detail5                                             1.059837e-05
## junction_detail6                                            -3.052809e-04
## junction_detail7                                             2.926970e-04
## junction_detail8                                            -8.402246e-05
## junction_detail9                                            -2.089564e-05
## junction_control1                                            4.590319e-04
## junction_control2                                           -4.924581e-04
## junction_control3                                           -4.021722e-04
## second_road_class                                            5.780040e-05
## pedestrian_crossing_human_control1                          -2.219916e-04
## pedestrian_crossing_human_control2                          -2.774125e-04
## pedestrian_crossing_physical_facilities1                     1.275244e-04
## pedestrian_crossing_physical_facilities4                     1.553700e-04
## pedestrian_crossing_physical_facilities5                     5.165243e-04
## pedestrian_crossing_physical_facilities7                    -2.553980e-03
## pedestrian_crossing_physical_facilities8                    -1.776596e-04
## light_conditions4                                           -1.410689e-04
## light_conditions5                                            3.982313e-04
## light_conditions6                                           -4.309803e-04
## light_conditions7                                            5.742093e-04
## weather_conditions2                                          2.138411e-04
## weather_conditions3                                          5.415675e-04
## weather_conditions4                                         -6.499754e-05
## weather_conditions5                                          8.898798e-04
## weather_conditions6                                          1.024873e-03
## weather_conditions7                                          7.134908e-04
## weather_conditions8                                          3.926497e-04
## road_surface_conditions2                                    -5.075083e-05
## road_surface_conditions3                                     1.493080e-04
## road_surface_conditions4                                    -4.038613e-04
## road_surface_conditions5                                    -1.609303e-04
## special_conditions_at_site1                                  5.980944e-04
## special_conditions_at_site2                                  8.116476e-04
## special_conditions_at_site3                                  6.092972e-04
## special_conditions_at_site4                                  5.511575e-02
## special_conditions_at_site5                                  1.412981e-03
## special_conditions_at_site6                                  9.981783e-04
## special_conditions_at_site7                                  1.086680e-03
## carriageway_hazards1                                         5.503220e-04
## carriageway_hazards2                                        -6.226692e-03
## carriageway_hazards3                                         4.705838e-04
## carriageway_hazards6                                         6.269950e-04
## carriageway_hazards7                                         8.561241e-04
## did_police_officer_attend_scene_of_collision1               -1.044868e-04
## 1|2                                                          1.390533e-03
## 2|3                                                          1.384004e-03
##                                               special_conditions_at_site5
## police_force                                                 7.139577e-06
## number_of_vehicles                                           6.050104e-04
## number_of_casualties                                         1.240782e-04
## road_type2                                                   5.963686e-04
## road_type3                                                   2.793193e-05
## road_type6                                                  -7.655354e-05
## road_type7                                                   4.200538e-04
## speed_limit                                                 -2.448622e-05
## junction_detail1                                             4.634928e-04
## junction_detail2                                             2.884104e-04
## junction_detail5                                             8.107235e-04
## junction_detail6                                            -1.107273e-04
## junction_detail7                                             5.080848e-04
## junction_detail8                                            -1.424886e-03
## junction_detail9                                            -4.413336e-04
## junction_control1                                            4.434712e-04
## junction_control2                                           -9.047888e-04
## junction_control3                                           -2.493771e-03
## second_road_class                                           -8.033753e-05
## pedestrian_crossing_human_control1                           5.893904e-04
## pedestrian_crossing_human_control2                          -1.287392e-03
## pedestrian_crossing_physical_facilities1                    -1.303642e-04
## pedestrian_crossing_physical_facilities4                     4.021592e-04
## pedestrian_crossing_physical_facilities5                     1.163031e-03
## pedestrian_crossing_physical_facilities7                     7.413680e-04
## pedestrian_crossing_physical_facilities8                    -9.116228e-04
## light_conditions4                                            5.534026e-05
## light_conditions5                                            5.600130e-04
## light_conditions6                                           -2.905434e-03
## light_conditions7                                           -2.866353e-03
## weather_conditions2                                         -1.085737e-04
## weather_conditions3                                          6.189389e-04
## weather_conditions4                                          7.965896e-04
## weather_conditions5                                          1.423870e-03
## weather_conditions6                                          2.647261e-03
## weather_conditions7                                         -1.177876e-02
## weather_conditions8                                         -3.374143e-04
## road_surface_conditions2                                    -1.452596e-04
## road_surface_conditions3                                    -1.023808e-04
## road_surface_conditions4                                    -8.936550e-04
## road_surface_conditions5                                     4.219744e-04
## special_conditions_at_site1                                  3.204023e-04
## special_conditions_at_site2                                 -5.551647e-05
## special_conditions_at_site3                                  8.785170e-04
## special_conditions_at_site4                                  1.412981e-03
## special_conditions_at_site5                                  4.317063e-01
## special_conditions_at_site6                                  1.213476e-03
## special_conditions_at_site7                                  2.375686e-03
## carriageway_hazards1                                         5.147989e-04
## carriageway_hazards2                                        -5.506558e-03
## carriageway_hazards3                                         1.931108e-04
## carriageway_hazards6                                         6.426419e-04
## carriageway_hazards7                                         2.297698e-03
## did_police_officer_attend_scene_of_collision1               -5.851357e-04
## 1|2                                                         -1.996613e-04
## 2|3                                                         -1.366006e-04
##                                               special_conditions_at_site6
## police_force                                                 1.275415e-05
## number_of_vehicles                                           7.047035e-04
## number_of_casualties                                        -8.490112e-05
## road_type2                                                   4.400235e-03
## road_type3                                                   3.871112e-03
## road_type6                                                   3.920277e-03
## road_type7                                                   4.236945e-03
## speed_limit                                                 -5.045741e-05
## junction_detail1                                            -6.208574e-04
## junction_detail2                                             2.391962e-03
## junction_detail5                                             5.372547e-04
## junction_detail6                                             2.260229e-05
## junction_detail7                                            -1.484900e-03
## junction_detail8                                             4.746352e-04
## junction_detail9                                            -5.788310e-04
## junction_control1                                            5.654219e-04
## junction_control2                                            6.442919e-04
## junction_control3                                            3.340305e-04
## second_road_class                                           -2.416362e-04
## pedestrian_crossing_human_control1                           4.493882e-04
## pedestrian_crossing_human_control2                          -1.067728e-03
## pedestrian_crossing_physical_facilities1                    -1.374949e-03
## pedestrian_crossing_physical_facilities4                    -5.952441e-04
## pedestrian_crossing_physical_facilities5                    -2.521467e-04
## pedestrian_crossing_physical_facilities7                     1.227144e-03
## pedestrian_crossing_physical_facilities8                    -2.465769e-03
## light_conditions4                                            7.487394e-04
## light_conditions5                                            8.136654e-04
## light_conditions6                                            1.323500e-03
## light_conditions7                                            1.288186e-03
## weather_conditions2                                         -5.123657e-04
## weather_conditions3                                          1.251515e-03
## weather_conditions4                                          1.888801e-03
## weather_conditions5                                          2.136197e-03
## weather_conditions6                                          1.150136e-03
## weather_conditions7                                          1.693432e-03
## weather_conditions8                                          1.015716e-03
## road_surface_conditions2                                    -9.626491e-04
## road_surface_conditions3                                    -5.938486e-04
## road_surface_conditions4                                    -3.555171e-03
## road_surface_conditions5                                    -9.105855e-04
## special_conditions_at_site1                                  2.214123e-03
## special_conditions_at_site2                                 -7.113553e-05
## special_conditions_at_site3                                  6.838635e-04
## special_conditions_at_site4                                  9.981783e-04
## special_conditions_at_site5                                  1.213476e-03
## special_conditions_at_site6                                  1.156824e+00
## special_conditions_at_site7                                  1.616609e-03
## carriageway_hazards1                                         2.085464e-04
## carriageway_hazards2                                        -3.217262e-03
## carriageway_hazards3                                        -5.724221e-02
## carriageway_hazards6                                         9.582885e-04
## carriageway_hazards7                                         6.620294e-04
## did_police_officer_attend_scene_of_collision1               -4.126797e-05
## 1|2                                                          2.220392e-03
## 2|3                                                          2.376872e-03
##                                               special_conditions_at_site7
## police_force                                                 5.252832e-09
## number_of_vehicles                                           7.022984e-04
## number_of_casualties                                        -1.643479e-04
## road_type2                                                   6.770880e-04
## road_type3                                                  -1.093193e-04
## road_type6                                                  -3.984381e-06
## road_type7                                                   5.907402e-04
## speed_limit                                                 -1.401179e-05
## junction_detail1                                             6.790915e-04
## junction_detail2                                             5.558655e-04
## junction_detail5                                             1.083944e-03
## junction_detail6                                             4.020036e-05
## junction_detail7                                             2.657670e-04
## junction_detail8                                            -7.958580e-04
## junction_detail9                                            -9.035520e-04
## junction_control1                                            4.845807e-04
## junction_control2                                            2.792726e-04
## junction_control3                                            6.899647e-04
## second_road_class                                            1.198336e-04
## pedestrian_crossing_human_control1                           9.478051e-04
## pedestrian_crossing_human_control2                           4.777775e-04
## pedestrian_crossing_physical_facilities1                    -1.793634e-03
## pedestrian_crossing_physical_facilities4                     3.561431e-04
## pedestrian_crossing_physical_facilities5                     2.135756e-04
## pedestrian_crossing_physical_facilities7                     2.239091e-04
## pedestrian_crossing_physical_facilities8                     4.155573e-04
## light_conditions4                                            7.350706e-04
## light_conditions5                                            8.582119e-04
## light_conditions6                                           -4.643751e-03
## light_conditions7                                            1.109945e-03
## weather_conditions2                                          2.073807e-04
## weather_conditions3                                          1.466712e-03
## weather_conditions4                                          9.194371e-04
## weather_conditions5                                          2.269192e-03
## weather_conditions6                                          4.555851e-03
## weather_conditions7                                          3.535643e-03
## weather_conditions8                                         -8.597352e-04
## road_surface_conditions2                                    -1.103791e-03
## road_surface_conditions3                                    -9.083108e-04
## road_surface_conditions4                                    -3.525261e-03
## road_surface_conditions5                                     2.895780e-04
## special_conditions_at_site1                                  6.714328e-05
## special_conditions_at_site2                                  2.936550e-04
## special_conditions_at_site3                                  5.311111e-04
## special_conditions_at_site4                                  1.086680e-03
## special_conditions_at_site5                                  2.375686e-03
## special_conditions_at_site6                                  1.616609e-03
## special_conditions_at_site7                                  3.525166e-01
## carriageway_hazards1                                         4.386368e-04
## carriageway_hazards2                                        -3.968582e-03
## carriageway_hazards3                                        -1.118881e-04
## carriageway_hazards6                                         1.008067e-03
## carriageway_hazards7                                         2.526571e-03
## did_police_officer_attend_scene_of_collision1                7.140867e-04
## 1|2                                                          3.041412e-03
## 2|3                                                          2.300325e-03
##                                               carriageway_hazards1
## police_force                                          1.062817e-05
## number_of_vehicles                                   -3.032485e-04
## number_of_casualties                                 -1.933438e-04
## road_type2                                            9.696663e-04
## road_type3                                            8.589464e-04
## road_type6                                            4.378857e-04
## road_type7                                            1.006667e-03
## speed_limit                                           1.656344e-06
## junction_detail1                                     -3.486467e-04
## junction_detail2                                     -3.653005e-04
## junction_detail5                                      2.105251e-04
## junction_detail6                                     -5.453178e-04
## junction_detail7                                     -2.693708e-04
## junction_detail8                                      4.363337e-04
## junction_detail9                                      1.177510e-04
## junction_control1                                    -5.108832e-03
## junction_control2                                    -8.324528e-04
## junction_control3                                     3.410900e-04
## second_road_class                                    -7.200061e-05
## pedestrian_crossing_human_control1                   -3.438006e-03
## pedestrian_crossing_human_control2                    8.414950e-04
## pedestrian_crossing_physical_facilities1             -5.176559e-04
## pedestrian_crossing_physical_facilities4              3.137408e-04
## pedestrian_crossing_physical_facilities5              8.906014e-04
## pedestrian_crossing_physical_facilities7              1.022165e-03
## pedestrian_crossing_physical_facilities8              6.563009e-04
## light_conditions4                                    -6.493003e-04
## light_conditions5                                     5.052685e-04
## light_conditions6                                    -9.650496e-04
## light_conditions7                                    -3.384908e-03
## weather_conditions2                                   1.913325e-04
## weather_conditions3                                   6.633121e-04
## weather_conditions4                                   5.068099e-04
## weather_conditions5                                  -3.492813e-03
## weather_conditions6                                   1.005204e-03
## weather_conditions7                                   1.099927e-03
## weather_conditions8                                  -1.081867e-04
## road_surface_conditions2                             -8.691353e-05
## road_surface_conditions3                             -9.776856e-05
## road_surface_conditions4                             -1.526622e-03
## road_surface_conditions5                              1.467731e-03
## special_conditions_at_site1                          -1.330389e-02
## special_conditions_at_site2                           7.431291e-04
## special_conditions_at_site3                           7.053800e-04
## special_conditions_at_site4                           5.503220e-04
## special_conditions_at_site5                           5.147989e-04
## special_conditions_at_site6                           2.085464e-04
## special_conditions_at_site7                           4.386368e-04
## carriageway_hazards1                                  2.112529e-01
## carriageway_hazards2                                  6.864044e-04
## carriageway_hazards3                                  1.201289e-03
## carriageway_hazards6                                  5.209868e-04
## carriageway_hazards7                                  1.150248e-03
## did_police_officer_attend_scene_of_collision1        -2.405075e-04
## 1|2                                                  -4.125319e-04
## 2|3                                                  -4.618618e-04
##                                               carriageway_hazards2
## police_force                                          1.142972e-05
## number_of_vehicles                                    3.173973e-04
## number_of_casualties                                 -1.166335e-04
## road_type2                                            1.249772e-04
## road_type3                                            9.158877e-05
## road_type6                                           -2.540981e-05
## road_type7                                            3.084665e-04
## speed_limit                                           5.601226e-06
## junction_detail1                                      3.202427e-04
## junction_detail2                                      1.421408e-04
## junction_detail5                                     -2.406128e-04
## junction_detail6                                     -1.142046e-04
## junction_detail7                                      1.036460e-05
## junction_detail8                                     -4.109376e-04
## junction_detail9                                      1.521191e-05
## junction_control1                                    -2.579181e-04
## junction_control2                                     5.253903e-04
## junction_control3                                    -1.133536e-03
## second_road_class                                     2.628471e-05
## pedestrian_crossing_human_control1                   -3.041642e-04
## pedestrian_crossing_human_control2                   -7.692407e-04
## pedestrian_crossing_physical_facilities1              3.939720e-04
## pedestrian_crossing_physical_facilities4             -1.361421e-05
## pedestrian_crossing_physical_facilities5             -1.986872e-04
## pedestrian_crossing_physical_facilities7              6.369690e-04
## pedestrian_crossing_physical_facilities8              6.258123e-04
## light_conditions4                                    -1.684992e-04
## light_conditions5                                     5.809117e-04
## light_conditions6                                    -7.228322e-04
## light_conditions7                                    -5.531559e-04
## weather_conditions2                                  -9.984283e-05
## weather_conditions3                                   5.288085e-04
## weather_conditions4                                  -2.668530e-04
## weather_conditions5                                  -2.560801e-03
## weather_conditions6                                   1.226115e-03
## weather_conditions7                                   8.740472e-04
## weather_conditions8                                  -3.319287e-04
## road_surface_conditions2                             -1.746963e-05
## road_surface_conditions3                              2.616234e-05
## road_surface_conditions4                             -2.031827e-04
## road_surface_conditions5                              1.379710e-03
## special_conditions_at_site1                           4.620780e-04
## special_conditions_at_site2                           4.385834e-04
## special_conditions_at_site3                           6.689601e-04
## special_conditions_at_site4                          -6.226692e-03
## special_conditions_at_site5                          -5.506558e-03
## special_conditions_at_site6                          -3.217262e-03
## special_conditions_at_site7                          -3.968582e-03
## carriageway_hazards1                                  6.864044e-04
## carriageway_hazards2                                  5.908940e-02
## carriageway_hazards3                                  8.741584e-04
## carriageway_hazards6                                  8.907616e-04
## carriageway_hazards7                                  9.890696e-04
## did_police_officer_attend_scene_of_collision1        -6.643964e-05
## 1|2                                                   1.411248e-03
## 2|3                                                   1.428696e-03
##                                               carriageway_hazards3
## police_force                                          7.157866e-06
## number_of_vehicles                                   -4.406857e-04
## number_of_casualties                                  1.373269e-04
## road_type2                                           -9.998134e-04
## road_type3                                            9.427656e-04
## road_type6                                            4.882681e-04
## road_type7                                            9.330190e-04
## speed_limit                                          -2.448636e-05
## junction_detail1                                      1.402808e-03
## junction_detail2                                     -1.080855e-03
## junction_detail5                                      8.918110e-04
## junction_detail6                                      1.563963e-04
## junction_detail7                                     -2.200184e-03
## junction_detail8                                     -2.672402e-04
## junction_detail9                                     -5.892884e-05
## junction_control1                                     5.208245e-04
## junction_control2                                     3.363968e-04
## junction_control3                                     5.760966e-04
## second_road_class                                     2.865062e-04
## pedestrian_crossing_human_control1                    5.516223e-05
## pedestrian_crossing_human_control2                   -1.751094e-03
## pedestrian_crossing_physical_facilities1              6.530190e-04
## pedestrian_crossing_physical_facilities4              6.051540e-04
## pedestrian_crossing_physical_facilities5             -6.421995e-04
## pedestrian_crossing_physical_facilities7              2.147629e-04
## pedestrian_crossing_physical_facilities8             -6.000012e-04
## light_conditions4                                    -2.471117e-04
## light_conditions5                                     6.646992e-04
## light_conditions6                                     8.164603e-04
## light_conditions7                                     2.833100e-04
## weather_conditions2                                  -7.642648e-04
## weather_conditions3                                  -6.001018e-05
## weather_conditions4                                  -4.451626e-03
## weather_conditions5                                  -6.152534e-03
## weather_conditions6                                  -6.206646e-05
## weather_conditions7                                  -5.605138e-05
## weather_conditions8                                   3.176142e-04
## road_surface_conditions2                              4.377966e-04
## road_surface_conditions3                              2.528241e-04
## road_surface_conditions4                              5.806520e-04
## road_surface_conditions5                              2.723989e-03
## special_conditions_at_site1                          -1.091674e-02
## special_conditions_at_site2                           6.384183e-04
## special_conditions_at_site3                           2.614431e-04
## special_conditions_at_site4                           4.705838e-04
## special_conditions_at_site5                           1.931108e-04
## special_conditions_at_site6                          -5.724221e-02
## special_conditions_at_site7                          -1.118881e-04
## carriageway_hazards1                                  1.201289e-03
## carriageway_hazards2                                  8.741584e-04
## carriageway_hazards3                                  3.336815e-01
## carriageway_hazards6                                  4.422784e-04
## carriageway_hazards7                                  1.438060e-03
## did_police_officer_attend_scene_of_collision1        -4.273107e-04
## 1|2                                                   1.146611e-03
## 2|3                                                   9.454955e-04
##                                               carriageway_hazards6
## police_force                                          1.558998e-05
## number_of_vehicles                                    7.874682e-04
## number_of_casualties                                 -1.841422e-04
## road_type2                                            1.303359e-03
## road_type3                                            3.477349e-04
## road_type6                                           -5.381264e-05
## road_type7                                            1.973508e-03
## speed_limit                                           1.412453e-05
## junction_detail1                                      7.338070e-05
## junction_detail2                                      6.254106e-04
## junction_detail5                                     -2.971580e-03
## junction_detail6                                      4.844973e-04
## junction_detail7                                     -7.503678e-04
## junction_detail8                                      4.013363e-04
## junction_detail9                                     -5.218505e-04
## junction_control1                                     7.039663e-04
## junction_control2                                     2.393807e-04
## junction_control3                                     5.595488e-04
## second_road_class                                     4.556375e-05
## pedestrian_crossing_human_control1                   -2.809340e-03
## pedestrian_crossing_human_control2                   -1.774620e-03
## pedestrian_crossing_physical_facilities1             -1.397830e-03
## pedestrian_crossing_physical_facilities4              3.298645e-04
## pedestrian_crossing_physical_facilities5             -8.645038e-04
## pedestrian_crossing_physical_facilities7              2.684333e-04
## pedestrian_crossing_physical_facilities8              5.597872e-04
## light_conditions4                                     1.519863e-04
## light_conditions5                                     4.483582e-04
## light_conditions6                                     4.650742e-04
## light_conditions7                                     7.533289e-04
## weather_conditions2                                   3.302976e-04
## weather_conditions3                                   7.739596e-04
## weather_conditions4                                   6.608512e-04
## weather_conditions5                                   5.722664e-04
## weather_conditions6                                   1.179648e-03
## weather_conditions7                                   5.061917e-04
## weather_conditions8                                  -3.786724e-05
## road_surface_conditions2                             -7.945174e-06
## road_surface_conditions3                              3.209810e-05
## road_surface_conditions4                             -1.664159e-03
## road_surface_conditions5                              6.324245e-04
## special_conditions_at_site1                           7.352675e-04
## special_conditions_at_site2                           7.349307e-04
## special_conditions_at_site3                           3.644003e-04
## special_conditions_at_site4                           6.269950e-04
## special_conditions_at_site5                           6.426419e-04
## special_conditions_at_site6                           9.582885e-04
## special_conditions_at_site7                           1.008067e-03
## carriageway_hazards1                                  5.209868e-04
## carriageway_hazards2                                  8.907616e-04
## carriageway_hazards3                                  4.422784e-04
## carriageway_hazards6                                  2.714961e-01
## carriageway_hazards7                                  7.264422e-04
## did_police_officer_attend_scene_of_collision1        -5.472292e-04
## 1|2                                                   2.272337e-03
## 2|3                                                   2.358868e-03
##                                               carriageway_hazards7
## police_force                                         -1.336979e-06
## number_of_vehicles                                    1.055727e-03
## number_of_casualties                                  2.510767e-04
## road_type2                                           -1.327448e-03
## road_type3                                           -4.705194e-05
## road_type6                                           -4.311293e-04
## road_type7                                            1.967912e-04
## speed_limit                                          -1.903962e-05
## junction_detail1                                     -1.182865e-03
## junction_detail2                                     -2.075113e-04
## junction_detail5                                      5.526488e-04
## junction_detail6                                     -2.128657e-04
## junction_detail7                                      3.229784e-04
## junction_detail8                                     -9.181339e-04
## junction_detail9                                     -8.033003e-04
## junction_control1                                     5.731288e-04
## junction_control2                                    -1.535258e-04
## junction_control3                                    -2.625078e-03
## second_road_class                                    -1.295122e-04
## pedestrian_crossing_human_control1                    4.632956e-04
## pedestrian_crossing_human_control2                   -2.112910e-03
## pedestrian_crossing_physical_facilities1              6.254526e-04
## pedestrian_crossing_physical_facilities4              5.952675e-04
## pedestrian_crossing_physical_facilities5             -4.310374e-04
## pedestrian_crossing_physical_facilities7              9.399592e-04
## pedestrian_crossing_physical_facilities8             -4.326400e-04
## light_conditions4                                    -4.472179e-04
## light_conditions5                                     3.280446e-04
## light_conditions6                                    -7.217730e-03
## light_conditions7                                     5.447964e-04
## weather_conditions2                                  -1.174420e-03
## weather_conditions3                                  -1.501325e-04
## weather_conditions4                                  -5.317431e-03
## weather_conditions5                                   1.056427e-03
## weather_conditions6                                   3.440675e-03
## weather_conditions7                                   2.338798e-03
## weather_conditions8                                  -1.519769e-03
## road_surface_conditions2                              6.757382e-04
## road_surface_conditions3                              9.246427e-04
## road_surface_conditions4                              1.604564e-03
## road_surface_conditions5                              1.948559e-03
## special_conditions_at_site1                          -1.839883e-02
## special_conditions_at_site2                          -2.429822e-04
## special_conditions_at_site3                           5.686755e-04
## special_conditions_at_site4                           8.561241e-04
## special_conditions_at_site5                           2.297698e-03
## special_conditions_at_site6                           6.620294e-04
## special_conditions_at_site7                           2.526571e-03
## carriageway_hazards1                                  1.150248e-03
## carriageway_hazards2                                  9.890696e-04
## carriageway_hazards3                                  1.438060e-03
## carriageway_hazards6                                  7.264422e-04
## carriageway_hazards7                                  3.548904e-01
## did_police_officer_attend_scene_of_collision1        -2.465548e-05
## 1|2                                                   5.408831e-04
## 2|3                                                   3.856980e-04
##                                               did_police_officer_attend_scene_of_collision1
## police_force                                                                   8.300320e-07
## number_of_vehicles                                                            -1.171484e-04
## number_of_casualties                                                          -1.200215e-04
## road_type2                                                                    -1.533964e-04
## road_type3                                                                     1.330069e-04
## road_type6                                                                     2.676129e-04
## road_type7                                                                     1.114969e-04
## speed_limit                                                                   -1.108856e-05
## junction_detail1                                                               4.252976e-04
## junction_detail2                                                               2.710112e-04
## junction_detail5                                                               2.098139e-04
## junction_detail6                                                              -3.751255e-05
## junction_detail7                                                              -2.988318e-04
## junction_detail8                                                              -2.964465e-05
## junction_detail9                                                              -7.798085e-05
## junction_control1                                                             -3.545453e-04
## junction_control2                                                              1.169854e-04
## junction_control3                                                              5.826382e-05
## second_road_class                                                              1.952975e-05
## pedestrian_crossing_human_control1                                            -3.627500e-05
## pedestrian_crossing_human_control2                                            -2.542124e-04
## pedestrian_crossing_physical_facilities1                                      -2.808521e-04
## pedestrian_crossing_physical_facilities4                                      -1.651015e-04
## pedestrian_crossing_physical_facilities5                                      -2.539137e-04
## pedestrian_crossing_physical_facilities7                                      -3.069229e-04
## pedestrian_crossing_physical_facilities8                                      -6.029574e-05
## light_conditions4                                                             -9.238489e-05
## light_conditions5                                                             -4.702882e-05
## light_conditions6                                                             -3.122888e-04
## light_conditions7                                                              6.672968e-04
## weather_conditions2                                                           -8.160727e-05
## weather_conditions3                                                            4.551529e-04
## weather_conditions4                                                           -3.454315e-04
## weather_conditions5                                                            1.849467e-04
## weather_conditions6                                                            5.030543e-04
## weather_conditions7                                                           -1.993368e-04
## weather_conditions8                                                           -1.243221e-04
## road_surface_conditions2                                                      -2.040250e-04
## road_surface_conditions3                                                       2.287068e-05
## road_surface_conditions4                                                      -7.179689e-05
## road_surface_conditions5                                                      -6.080264e-04
## special_conditions_at_site1                                                   -5.565059e-04
## special_conditions_at_site2                                                   -1.565482e-04
## special_conditions_at_site3                                                   -3.636867e-04
## special_conditions_at_site4                                                   -1.044868e-04
## special_conditions_at_site5                                                   -5.851357e-04
## special_conditions_at_site6                                                   -4.126797e-05
## special_conditions_at_site7                                                    7.140867e-04
## carriageway_hazards1                                                          -2.405075e-04
## carriageway_hazards2                                                          -6.643964e-05
## carriageway_hazards3                                                          -4.273107e-04
## carriageway_hazards6                                                          -5.472292e-04
## carriageway_hazards7                                                          -2.465548e-05
## did_police_officer_attend_scene_of_collision1                                  7.473744e-03
## 1|2                                                                            6.451621e-03
## 2|3                                                                            6.335786e-03
##                                                         1|2           2|3
## police_force                                  -5.056130e-06 -4.397034e-06
## number_of_vehicles                             2.775128e-03  2.865688e-03
## number_of_casualties                           6.273449e-04  6.027295e-04
## road_type2                                     2.159303e-02  2.164604e-02
## road_type3                                     1.668912e-02  1.670047e-02
## road_type6                                     1.912045e-02  1.911971e-02
## road_type7                                     1.778267e-02  1.775100e-02
## speed_limit                                    1.838697e-04  1.814898e-04
## junction_detail1                               1.621913e-02  1.627848e-02
## junction_detail2                               1.118052e-02  1.121109e-02
## junction_detail5                               4.239949e-03  4.216072e-03
## junction_detail6                               6.565811e-04  6.520250e-04
## junction_detail7                               2.207249e-03  2.244734e-03
## junction_detail8                              -4.739398e-04 -4.458505e-04
## junction_detail9                               1.611439e-03  1.645349e-03
## junction_control1                              6.732911e-04  7.683471e-04
## junction_control2                              3.437625e-03  3.484383e-03
## junction_control3                              1.781821e-03  1.784519e-03
## second_road_class                              3.471926e-03  3.463670e-03
## pedestrian_crossing_human_control1             5.314560e-04  6.234667e-04
## pedestrian_crossing_human_control2             7.584129e-05  1.235596e-04
## pedestrian_crossing_physical_facilities1       2.355778e-03  2.400536e-03
## pedestrian_crossing_physical_facilities4       1.903690e-03  1.890421e-03
## pedestrian_crossing_physical_facilities5       1.943859e-03  1.930110e-03
## pedestrian_crossing_physical_facilities7       1.780425e-03  1.751328e-03
## pedestrian_crossing_physical_facilities8       2.255299e-03  2.218277e-03
## light_conditions4                              1.314715e-03  1.263997e-03
## light_conditions5                              5.961430e-05 -2.123247e-04
## light_conditions6                             -7.496482e-04 -7.351993e-04
## light_conditions7                              1.972010e-03  2.018503e-03
## weather_conditions2                            2.056471e-04  2.169771e-04
## weather_conditions3                           -1.772710e-04 -1.878494e-04
## weather_conditions4                            5.592780e-04  5.225715e-04
## weather_conditions5                            1.766772e-04  9.842245e-05
## weather_conditions6                            1.309785e-03  1.288554e-03
## weather_conditions7                           -5.673585e-04 -4.914968e-04
## weather_conditions8                            7.199819e-04  7.171668e-04
## road_surface_conditions2                       9.215052e-05  1.304245e-04
## road_surface_conditions3                      -4.349652e-04 -3.304731e-04
## road_surface_conditions4                      -2.108627e-04 -1.335965e-04
## road_surface_conditions5                      -4.781812e-03 -4.818222e-03
## special_conditions_at_site1                    1.793754e-04  3.108543e-04
## special_conditions_at_site2                   -1.155859e-03 -1.444991e-03
## special_conditions_at_site3                    2.924616e-04  2.426520e-04
## special_conditions_at_site4                    1.390533e-03  1.384004e-03
## special_conditions_at_site5                   -1.996613e-04 -1.366006e-04
## special_conditions_at_site6                    2.220392e-03  2.376872e-03
## special_conditions_at_site7                    3.041412e-03  2.300325e-03
## carriageway_hazards1                          -4.125319e-04 -4.618618e-04
## carriageway_hazards2                           1.411248e-03  1.428696e-03
## carriageway_hazards3                           1.146611e-03  9.454955e-04
## carriageway_hazards6                           2.272337e-03  2.358868e-03
## carriageway_hazards7                           5.408831e-04  3.856980e-04
## did_police_officer_attend_scene_of_collision1  6.451621e-03  6.335786e-03
## 1|2                                            6.747850e-02  5.807097e-02
## 2|3                                            5.807097e-02  5.816014e-02
#👸store the coefficients and p-values into one new dataframe
shorted_test2.coef <- data.frame(coef(summary(shorted_test2)))
view(shorted_test2.coef) 
shorted_test2.coef$pval <- round((pnorm(abs(shorted_test2.coef$t.value), lower.tail = FALSE) * 2),3)
view(shorted_test2.coef)
#Select the row names corresponding to all values less than 0.05 in the full_model2.coef$pval column
significant_rows <- rownames(shorted_test2.coef[shorted_test2.coef$pval < 0.05, ])
significant_rows
##  [1] "police_force"                                 
##  [2] "number_of_vehicles"                           
##  [3] "number_of_casualties"                         
##  [4] "speed_limit"                                  
##  [5] "junction_detail1"                             
##  [6] "junction_detail9"                             
##  [7] "junction_control1"                            
##  [8] "junction_control2"                            
##  [9] "light_conditions4"                            
## [10] "light_conditions5"                            
## [11] "road_surface_conditions2"                     
## [12] "road_surface_conditions4"                     
## [13] "special_conditions_at_site1"                  
## [14] "did_police_officer_attend_scene_of_collision1"
## [15] "1|2"                                          
## [16] "2|3"
#💛1_3. Run a Ordered logit reduced model       💜9
#10 predictors
#different from Mutinomial Logit model(Baseline=3), who has 13 predictors in reduced_test
library(MASS)
unique(data4$legacy_collision_severity)
## [1] 3 2 1
## Levels: 1 < 2 < 3
data4$pedestrian_crossing_human_control[1]
## [1] 2
## Levels: 0 1 2
data4$did_police_officer_attend_scene_of_collision[1]
## [1] 1
## Levels: 2 1
reduced_test2 <- polr(legacy_collision_severity ~ police_force + number_of_vehicles + number_of_casualties + speed_limit + junction_detail + junction_control  + light_conditions + road_surface_conditions + special_conditions_at_site + did_police_officer_attend_scene_of_collision, data = data4, Hess = TRUE)  
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
summary(reduced_test2) ## Residual Deviance: 11244.55   AIC: 11308.55
## Call:
## polr(formula = legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + speed_limit + junction_detail + junction_control + 
##     light_conditions + road_surface_conditions + special_conditions_at_site + 
##     did_police_officer_attend_scene_of_collision, data = data4, 
##     Hess = TRUE)
## 
## Coefficients:
##                                                   Value Std. Error   t value
## police_force                                   0.002376   0.001353   1.75568
## number_of_vehicles                             0.415178   0.042580   9.75049
## number_of_casualties                          -0.086315   0.034171  -2.52596
## speed_limit                                   -0.010306   0.002353  -4.37986
## junction_detail1                               0.427796   0.086953   4.91982
## junction_detail2                               0.189953   0.160424   1.18407
## junction_detail5                              -0.022548   0.170081  -0.13257
## junction_detail6                              -0.047127   0.071078  -0.66303
## junction_detail7                               0.316709   0.160506   1.97319
## junction_detail8                               0.074688   0.125734   0.59402
## junction_detail9                               0.183921   0.081143   2.26662
## junction_control1                              0.642544   0.242644   2.64809
## junction_control2                              0.287351   0.071099   4.04155
## junction_control3                              0.049056   0.220850   0.22212
## light_conditions4                             -0.232214   0.058654  -3.95908
## light_conditions5                             -0.744778   0.278727  -2.67207
## light_conditions6                              0.042194   0.154726   0.27270
## light_conditions7                              0.331546   0.291773   1.13631
## road_surface_conditions2                       0.216488   0.061406   3.52555
## road_surface_conditions3                       0.756990   0.545901   1.38668
## road_surface_conditions4                       0.461248   0.212471   2.17088
## road_surface_conditions5                       0.043913   1.238466   0.03546
## special_conditions_at_site1                    1.069794   0.533610   2.00482
## special_conditions_at_site2                   -0.894654   1.386053  -0.64547
## special_conditions_at_site3                   -0.214719   0.511619  -0.41969
## special_conditions_at_site4                    0.011654   0.232629   0.05010
## special_conditions_at_site5                    0.529123   0.653624   0.80952
## special_conditions_at_site6                    0.991735   1.068193   0.92842
## special_conditions_at_site7                   -1.077425   0.592755  -1.81766
## did_police_officer_attend_scene_of_collision1 -0.882287   0.086187 -10.23686
## 
## Intercepts:
##     Value    Std. Error t value 
## 1|2  -4.8580   0.1599   -30.3777
## 2|3  -1.4045   0.1278   -10.9862
## 
## Residual Deviance: 11244.55 
## AIC: 11308.55
summary(reduced_test2)$coef
##                                                      Value  Std. Error
## police_force                                   0.002376036 0.001353340
## number_of_vehicles                             0.415177950 0.042580202
## number_of_casualties                          -0.086315016 0.034171176
## speed_limit                                   -0.010306115 0.002353069
## junction_detail1                               0.427795767 0.086953466
## junction_detail2                               0.189953107 0.160423732
## junction_detail5                              -0.022548012 0.170080663
## junction_detail6                              -0.047126552 0.071077959
## junction_detail7                               0.316709456 0.160505988
## junction_detail8                               0.074688253 0.125733620
## junction_detail9                               0.183920662 0.081143154
## junction_control1                              0.642543754 0.242644059
## junction_control2                              0.287350856 0.071099259
## junction_control3                              0.049055710 0.220850171
## light_conditions4                             -0.232214272 0.058653543
## light_conditions5                             -0.744777856 0.278726998
## light_conditions6                              0.042194211 0.154725692
## light_conditions7                              0.331545961 0.291773290
## road_surface_conditions2                       0.216488415 0.061405622
## road_surface_conditions3                       0.756990460 0.545900804
## road_surface_conditions4                       0.461247866 0.212470582
## road_surface_conditions5                       0.043912553 1.238466422
## special_conditions_at_site1                    1.069793798 0.533609801
## special_conditions_at_site2                   -0.894653915 1.386052981
## special_conditions_at_site3                   -0.214719457 0.511619276
## special_conditions_at_site4                    0.011654379 0.232628932
## special_conditions_at_site5                    0.529122770 0.653623810
## special_conditions_at_site6                    0.991735010 1.068192810
## special_conditions_at_site7                   -1.077424756 0.592754871
## did_police_officer_attend_scene_of_collision1 -0.882286551 0.086187186
## 1|2                                           -4.857981662 0.159919330
## 2|3                                           -1.404524243 0.127844568
##                                                    t value
## police_force                                    1.75568338
## number_of_vehicles                              9.75049271
## number_of_casualties                           -2.52595979
## speed_limit                                    -4.37986042
## junction_detail1                                4.91982422
## junction_detail2                                1.18407111
## junction_detail5                               -0.13257246
## junction_detail6                               -0.66302623
## junction_detail7                                1.97319402
## junction_detail8                                0.59401975
## junction_detail9                                2.26661959
## junction_control1                               2.64809185
## junction_control2                               4.04154503
## junction_control3                               0.22212213
## light_conditions4                              -3.95908347
## light_conditions5                              -2.67206930
## light_conditions6                               0.27270333
## light_conditions7                               1.13631361
## road_surface_conditions2                        3.52554717
## road_surface_conditions3                        1.38668134
## road_surface_conditions4                        2.17087873
## road_surface_conditions5                        0.03545720
## special_conditions_at_site1                     2.00482412
## special_conditions_at_site2                    -0.64546877
## special_conditions_at_site3                    -0.41968602
## special_conditions_at_site4                     0.05009858
## special_conditions_at_site5                     0.80952187
## special_conditions_at_site6                     0.92842322
## special_conditions_at_site7                    -1.81765652
## did_police_officer_attend_scene_of_collision1 -10.23686452
## 1|2                                           -30.37770148
## 2|3                                           -10.98618628
coef(reduced_test2)   # the values of Log odds ratio
##                                  police_force 
##                                   0.002376036 
##                            number_of_vehicles 
##                                   0.415177950 
##                          number_of_casualties 
##                                  -0.086315016 
##                                   speed_limit 
##                                  -0.010306115 
##                              junction_detail1 
##                                   0.427795767 
##                              junction_detail2 
##                                   0.189953107 
##                              junction_detail5 
##                                  -0.022548012 
##                              junction_detail6 
##                                  -0.047126552 
##                              junction_detail7 
##                                   0.316709456 
##                              junction_detail8 
##                                   0.074688253 
##                              junction_detail9 
##                                   0.183920662 
##                             junction_control1 
##                                   0.642543754 
##                             junction_control2 
##                                   0.287350856 
##                             junction_control3 
##                                   0.049055710 
##                             light_conditions4 
##                                  -0.232214272 
##                             light_conditions5 
##                                  -0.744777856 
##                             light_conditions6 
##                                   0.042194211 
##                             light_conditions7 
##                                   0.331545961 
##                      road_surface_conditions2 
##                                   0.216488415 
##                      road_surface_conditions3 
##                                   0.756990460 
##                      road_surface_conditions4 
##                                   0.461247866 
##                      road_surface_conditions5 
##                                   0.043912553 
##                   special_conditions_at_site1 
##                                   1.069793798 
##                   special_conditions_at_site2 
##                                  -0.894653915 
##                   special_conditions_at_site3 
##                                  -0.214719457 
##                   special_conditions_at_site4 
##                                   0.011654379 
##                   special_conditions_at_site5 
##                                   0.529122770 
##                   special_conditions_at_site6 
##                                   0.991735010 
##                   special_conditions_at_site7 
##                                  -1.077424756 
## did_police_officer_attend_scene_of_collision1 
##                                  -0.882286551
vcov(reduced_test2) 
##                                                police_force number_of_vehicles
## police_force                                   1.831529e-06       3.043925e-07
## number_of_vehicles                             3.043925e-07       1.813074e-03
## number_of_casualties                          -1.087896e-06      -2.716462e-04
## speed_limit                                   -1.022821e-06      -9.846321e-06
## junction_detail1                              -2.180107e-06       4.903967e-05
## junction_detail2                              -7.551819e-06      -7.681767e-05
## junction_detail5                               1.990469e-05       1.843558e-04
## junction_detail6                               3.885659e-06      -1.154565e-04
## junction_detail7                               1.407510e-05      -5.938101e-06
## junction_detail8                               1.684013e-06      -1.043450e-04
## junction_detail9                               1.016794e-05       7.123283e-05
## junction_control1                             -1.209848e-05       8.415237e-05
## junction_control2                              7.532131e-06       5.920440e-05
## junction_control3                              6.992260e-06      -1.231708e-04
## light_conditions4                              3.167830e-06       6.930371e-05
## light_conditions5                             -1.754913e-06      -7.825852e-05
## light_conditions6                             -4.291969e-06       5.348549e-04
## light_conditions7                             -4.579974e-06       3.855953e-04
## road_surface_conditions2                      -2.154102e-06       4.365880e-05
## road_surface_conditions3                       6.407535e-06      -2.785198e-05
## road_surface_conditions4                      -6.822409e-06       7.385016e-05
## road_surface_conditions5                      -2.466812e-05       1.279267e-03
## special_conditions_at_site1                    3.345466e-07       9.776141e-05
## special_conditions_at_site2                    2.141141e-05       2.247820e-04
## special_conditions_at_site3                   -2.689756e-06       2.754764e-04
## special_conditions_at_site4                    1.011470e-05       1.693402e-04
## special_conditions_at_site5                    7.348949e-06       6.010089e-04
## special_conditions_at_site6                    1.115475e-05       7.383116e-04
## special_conditions_at_site7                    2.320336e-06       7.101131e-04
## did_police_officer_attend_scene_of_collision1  1.747506e-06      -9.604660e-05
## 1|2                                            1.104288e-05       2.414955e-03
## 2|3                                            1.150789e-05       2.501799e-03
##                                               number_of_casualties
## police_force                                         -1.087896e-06
## number_of_vehicles                                   -2.716462e-04
## number_of_casualties                                  1.167669e-03
## speed_limit                                          -1.005321e-05
## junction_detail1                                      1.122903e-04
## junction_detail2                                     -1.310439e-05
## junction_detail5                                     -4.049735e-05
## junction_detail6                                     -1.067809e-04
## junction_detail7                                     -3.053906e-05
## junction_detail8                                      2.703871e-05
## junction_detail9                                     -2.525120e-06
## junction_control1                                    -1.156057e-04
## junction_control2                                    -1.581154e-05
## junction_control3                                    -1.419462e-05
## light_conditions4                                    -5.054709e-05
## light_conditions5                                     3.352760e-05
## light_conditions6                                    -5.902302e-05
## light_conditions7                                     1.323932e-04
## road_surface_conditions2                             -5.679054e-06
## road_surface_conditions3                             -2.458272e-04
## road_surface_conditions4                              9.501784e-05
## road_surface_conditions5                             -9.539929e-04
## special_conditions_at_site1                          -5.130315e-05
## special_conditions_at_site2                          -1.759949e-03
## special_conditions_at_site3                          -1.662526e-04
## special_conditions_at_site4                           1.052260e-04
## special_conditions_at_site5                           1.042345e-04
## special_conditions_at_site6                          -1.222576e-05
## special_conditions_at_site7                          -1.637625e-04
## did_police_officer_attend_scene_of_collision1        -1.181210e-04
## 1|2                                                   5.734959e-04
## 2|3                                                   5.483793e-04
##                                                 speed_limit junction_detail1
## police_force                                  -1.022821e-06    -2.180107e-06
## number_of_vehicles                            -9.846321e-06     4.903967e-05
## number_of_casualties                          -1.005321e-05     1.122903e-04
## speed_limit                                    5.536935e-06    -3.500363e-05
## junction_detail1                              -3.500363e-05     7.560905e-03
## junction_detail2                               1.935331e-05     1.037212e-03
## junction_detail5                              -8.244242e-05     1.608189e-03
## junction_detail6                              -6.372988e-06     1.216856e-03
## junction_detail7                              -2.729471e-06     1.177367e-03
## junction_detail8                              -1.044998e-05     1.164440e-03
## junction_detail9                              -1.712084e-06     1.093659e-03
## junction_control1                              1.261331e-05     9.238598e-05
## junction_control2                              8.483555e-06    -2.771056e-04
## junction_control3                              4.482216e-06     2.909970e-04
## light_conditions4                              1.660356e-05    -2.573633e-04
## light_conditions5                             -3.556899e-06     3.940041e-05
## light_conditions6                             -7.411260e-05     1.119332e-03
## light_conditions7                             -8.837229e-06    -4.104294e-04
## road_surface_conditions2                      -2.887106e-06    -1.142446e-05
## road_surface_conditions3                       4.107068e-06    -7.340462e-04
## road_surface_conditions4                      -7.342612e-06     1.376983e-04
## road_surface_conditions5                      -3.904378e-05     4.348524e-04
## special_conditions_at_site1                   -9.185312e-07     1.349534e-04
## special_conditions_at_site2                   -3.151750e-05     1.237793e-04
## special_conditions_at_site3                   -1.566256e-05     8.627939e-05
## special_conditions_at_site4                   -5.326034e-06    -2.903628e-04
## special_conditions_at_site5                   -2.459389e-05     5.555064e-04
## special_conditions_at_site6                   -4.412308e-05    -2.579694e-03
## special_conditions_at_site7                   -1.365361e-05     5.159765e-04
## did_police_officer_attend_scene_of_collision1 -9.935154e-06     2.335010e-04
## 1|2                                            1.208160e-04     2.585715e-04
## 2|3                                            1.184877e-04     3.271586e-04
##                                               junction_detail2 junction_detail5
## police_force                                     -7.551819e-06     1.990469e-05
## number_of_vehicles                               -7.681767e-05     1.843558e-04
## number_of_casualties                             -1.310439e-05    -4.049735e-05
## speed_limit                                       1.935331e-05    -8.244242e-05
## junction_detail1                                  1.037212e-03     1.608189e-03
## junction_detail2                                  2.573577e-02     7.933392e-04
## junction_detail5                                  7.933392e-04     2.892743e-02
## junction_detail6                                  9.637351e-04     1.233463e-03
## junction_detail7                                  9.191632e-04     1.209273e-03
## junction_detail8                                  1.102764e-03     1.270445e-03
## junction_detail9                                  1.078089e-03     1.172142e-03
## junction_control1                                -6.888535e-05    -5.105612e-05
## junction_control2                                 4.402633e-04    -9.626012e-05
## junction_control3                                 4.557558e-04     2.078323e-04
## light_conditions4                                -1.593373e-04    -5.408661e-04
## light_conditions5                                -2.954596e-04    -4.602540e-05
## light_conditions6                                 4.816093e-04    -1.511154e-04
## light_conditions7                                 3.816756e-04    -8.316066e-04
## road_surface_conditions2                         -3.965104e-05     1.713528e-05
## road_surface_conditions3                          4.723286e-04    -2.562763e-03
## road_surface_conditions4                         -1.597186e-04     2.696804e-04
## road_surface_conditions5                         -6.381668e-03     7.131992e-04
## special_conditions_at_site1                       3.449181e-04     4.522091e-04
## special_conditions_at_site2                      -4.654075e-04     6.964853e-04
## special_conditions_at_site3                      -1.402312e-03     5.198263e-04
## special_conditions_at_site4                       3.628072e-04     3.249583e-05
## special_conditions_at_site5                       2.441122e-04     1.118749e-03
## special_conditions_at_site6                       2.168917e-04     9.181266e-04
## special_conditions_at_site7                       4.229001e-04     1.056745e-03
## did_police_officer_attend_scene_of_collision1     1.381424e-04     8.829671e-05
## 1|2                                               1.535613e-03    -8.569407e-04
## 2|3                                               1.568202e-03    -8.745097e-04
##                                               junction_detail6 junction_detail7
## police_force                                      3.885659e-06     1.407510e-05
## number_of_vehicles                               -1.154565e-04    -5.938101e-06
## number_of_casualties                             -1.067809e-04    -3.053906e-05
## speed_limit                                      -6.372988e-06    -2.729471e-06
## junction_detail1                                  1.216856e-03     1.177367e-03
## junction_detail2                                  9.637351e-04     9.191632e-04
## junction_detail5                                  1.233463e-03     1.209273e-03
## junction_detail6                                  5.052076e-03     1.910131e-03
## junction_detail7                                  1.910131e-03     2.576217e-02
## junction_detail8                                  1.010076e-03     9.508091e-04
## junction_detail9                                  1.223065e-03     1.312877e-03
## junction_control1                                -9.642462e-05    -4.500633e-04
## junction_control2                                -1.727653e-03    -2.086680e-03
## junction_control3                                -6.251208e-04     1.720622e-04
## light_conditions4                                 2.956543e-05    -7.683768e-05
## light_conditions5                                -1.057121e-04     4.179138e-04
## light_conditions6                                 1.343034e-04     2.420230e-04
## light_conditions7                                -1.336980e-04    -5.899579e-04
## road_surface_conditions2                         -4.919345e-05     2.391570e-05
## road_surface_conditions3                          1.858144e-04    -3.633885e-04
## road_surface_conditions4                          3.575590e-04    -3.118176e-04
## road_surface_conditions5                         -8.397611e-04     1.381859e-04
## special_conditions_at_site1                      -5.394417e-04     9.735835e-05
## special_conditions_at_site2                      -2.057568e-03     1.382897e-03
## special_conditions_at_site3                      -1.765551e-03    -2.028784e-04
## special_conditions_at_site4                      -3.174738e-04     2.373830e-04
## special_conditions_at_site5                      -9.079042e-05     5.911534e-04
## special_conditions_at_site6                       6.173437e-05    -1.837275e-03
## special_conditions_at_site7                      -8.379880e-06     2.057032e-04
## did_police_officer_attend_scene_of_collision1    -5.164508e-05    -3.582666e-04
## 1|2                                               4.592415e-04     7.505921e-04
## 2|3                                               4.541350e-04     7.924603e-04
##                                               junction_detail8 junction_detail9
## police_force                                      1.684013e-06     1.016794e-05
## number_of_vehicles                               -1.043450e-04     7.123283e-05
## number_of_casualties                              2.703871e-05    -2.525120e-06
## speed_limit                                      -1.044998e-05    -1.712084e-06
## junction_detail1                                  1.164440e-03     1.093659e-03
## junction_detail2                                  1.102764e-03     1.078089e-03
## junction_detail5                                  1.270445e-03     1.172142e-03
## junction_detail6                                  1.010076e-03     1.223065e-03
## junction_detail7                                  9.508091e-04     1.312877e-03
## junction_detail8                                  1.580894e-02     1.099606e-03
## junction_detail9                                  1.099606e-03     6.584211e-03
## junction_control1                                 4.070086e-05    -4.660633e-05
## junction_control2                                 3.302412e-04    -1.684372e-04
## junction_control3                                 4.911267e-04    -4.046777e-04
## light_conditions4                                 1.296326e-04    -1.575222e-05
## light_conditions5                                -2.173715e-04    -2.327388e-04
## light_conditions6                                -8.419318e-06     6.426952e-05
## light_conditions7                                 1.760190e-04    -1.490397e-04
## road_surface_conditions2                          6.854772e-06    -3.421518e-06
## road_surface_conditions3                         -1.188336e-04    -1.298593e-04
## road_surface_conditions4                          1.929411e-06     1.549516e-04
## road_surface_conditions5                         -1.440072e-05    -2.103309e-03
## special_conditions_at_site1                       3.099926e-04    -2.785609e-04
## special_conditions_at_site2                      -8.166213e-05     1.810080e-04
## special_conditions_at_site3                       3.916059e-04     3.659908e-04
## special_conditions_at_site4                      -1.556779e-04    -8.408683e-05
## special_conditions_at_site5                      -1.578005e-03    -4.073568e-04
## special_conditions_at_site6                       4.558262e-04    -2.896015e-04
## special_conditions_at_site7                      -7.171299e-04    -8.802036e-04
## did_police_officer_attend_scene_of_collision1    -8.385638e-06    -1.059121e-04
## 1|2                                               7.076430e-04     1.273771e-03
## 2|3                                               7.288486e-04     1.309743e-03
##                                               junction_control1
## police_force                                      -1.209848e-05
## number_of_vehicles                                 8.415237e-05
## number_of_casualties                              -1.156057e-04
## speed_limit                                        1.261331e-05
## junction_detail1                                   9.238598e-05
## junction_detail2                                  -6.888535e-05
## junction_detail5                                  -5.105612e-05
## junction_detail6                                  -9.642462e-05
## junction_detail7                                  -4.500633e-04
## junction_detail8                                   4.070086e-05
## junction_detail9                                  -4.660633e-05
## junction_control1                                  5.887614e-02
## junction_control2                                  7.595578e-04
## junction_control3                                  6.789073e-04
## light_conditions4                                 -1.570781e-04
## light_conditions5                                 -2.284796e-04
## light_conditions6                                 -3.107726e-05
## light_conditions7                                  2.887041e-05
## road_surface_conditions2                           3.844727e-04
## road_surface_conditions3                           6.769149e-04
## road_surface_conditions4                           7.562194e-04
## road_surface_conditions5                           8.947354e-04
## special_conditions_at_site1                        4.540899e-04
## special_conditions_at_site2                        7.931520e-05
## special_conditions_at_site3                        6.348638e-04
## special_conditions_at_site4                        4.465062e-04
## special_conditions_at_site5                        4.398676e-04
## special_conditions_at_site6                        4.494421e-04
## special_conditions_at_site7                        5.174950e-04
## did_police_officer_attend_scene_of_collision1     -3.844957e-04
## 1|2                                                4.512565e-04
## 2|3                                                5.508482e-04
##                                               junction_control2
## police_force                                       7.532131e-06
## number_of_vehicles                                 5.920440e-05
## number_of_casualties                              -1.581154e-05
## speed_limit                                        8.483555e-06
## junction_detail1                                  -2.771056e-04
## junction_detail2                                   4.402633e-04
## junction_detail5                                  -9.626012e-05
## junction_detail6                                  -1.727653e-03
## junction_detail7                                  -2.086680e-03
## junction_detail8                                   3.302412e-04
## junction_detail9                                  -1.684372e-04
## junction_control1                                  7.595578e-04
## junction_control2                                  5.055105e-03
## junction_control3                                  9.946139e-04
## light_conditions4                                 -3.446106e-04
## light_conditions5                                 -4.103804e-05
## light_conditions6                                  2.659023e-04
## light_conditions7                                  3.846597e-04
## road_surface_conditions2                           8.321924e-05
## road_surface_conditions3                           3.699295e-04
## road_surface_conditions4                           1.028940e-04
## road_surface_conditions5                          -7.542155e-04
## special_conditions_at_site1                       -1.009254e-03
## special_conditions_at_site2                       -2.845288e-03
## special_conditions_at_site3                        8.949880e-04
## special_conditions_at_site4                       -2.892563e-04
## special_conditions_at_site5                       -2.543136e-04
## special_conditions_at_site6                        6.602323e-04
## special_conditions_at_site7                        4.233256e-04
## did_police_officer_attend_scene_of_collision1     -6.238607e-05
## 1|2                                                8.610331e-04
## 2|3                                                9.109593e-04
##                                               junction_control3
## police_force                                       6.992260e-06
## number_of_vehicles                                -1.231708e-04
## number_of_casualties                              -1.419462e-05
## speed_limit                                        4.482216e-06
## junction_detail1                                   2.909970e-04
## junction_detail2                                   4.557558e-04
## junction_detail5                                   2.078323e-04
## junction_detail6                                  -6.251208e-04
## junction_detail7                                   1.720622e-04
## junction_detail8                                   4.911267e-04
## junction_detail9                                  -4.046777e-04
## junction_control1                                  6.789073e-04
## junction_control2                                  9.946139e-04
## junction_control3                                  4.877480e-02
## light_conditions4                                  9.316276e-05
## light_conditions5                                 -1.199961e-03
## light_conditions6                                 -2.760207e-04
## light_conditions7                                  2.130164e-04
## road_surface_conditions2                           9.003956e-05
## road_surface_conditions3                          -6.539715e-04
## road_surface_conditions4                           5.400814e-04
## road_surface_conditions5                           3.554213e-04
## special_conditions_at_site1                        4.691044e-04
## special_conditions_at_site2                        4.199372e-04
## special_conditions_at_site3                       -7.794061e-03
## special_conditions_at_site4                       -5.302289e-04
## special_conditions_at_site5                       -2.556591e-03
## special_conditions_at_site6                        3.722995e-04
## special_conditions_at_site7                        6.787154e-04
## did_police_officer_attend_scene_of_collision1      1.050041e-05
## 1|2                                                7.621691e-04
## 2|3                                                7.647968e-04
##                                               light_conditions4
## police_force                                       3.167830e-06
## number_of_vehicles                                 6.930371e-05
## number_of_casualties                              -5.054709e-05
## speed_limit                                        1.660356e-05
## junction_detail1                                  -2.573633e-04
## junction_detail2                                  -1.593373e-04
## junction_detail5                                  -5.408661e-04
## junction_detail6                                   2.956543e-05
## junction_detail7                                  -7.683768e-05
## junction_detail8                                   1.296326e-04
## junction_detail9                                  -1.575222e-05
## junction_control1                                 -1.570781e-04
## junction_control2                                 -3.446106e-04
## junction_control3                                  9.316276e-05
## light_conditions4                                  3.440238e-03
## light_conditions5                                  1.043256e-03
## light_conditions6                                  6.639383e-04
## light_conditions7                                  8.654382e-04
## road_surface_conditions2                          -7.400566e-04
## road_surface_conditions3                          -1.116089e-04
## road_surface_conditions4                          -5.004964e-04
## road_surface_conditions5                          -5.901806e-04
## special_conditions_at_site1                       -3.323394e-04
## special_conditions_at_site2                        9.506835e-04
## special_conditions_at_site3                        9.408595e-05
## special_conditions_at_site4                       -1.521684e-04
## special_conditions_at_site5                        8.124354e-05
## special_conditions_at_site6                        7.159063e-04
## special_conditions_at_site7                        7.176092e-04
## did_police_officer_attend_scene_of_collision1     -1.031140e-04
## 1|2                                                1.259452e-03
## 2|3                                                1.208270e-03
##                                               light_conditions5
## police_force                                      -1.754913e-06
## number_of_vehicles                                -7.825852e-05
## number_of_casualties                               3.352760e-05
## speed_limit                                       -3.556899e-06
## junction_detail1                                   3.940041e-05
## junction_detail2                                  -2.954596e-04
## junction_detail5                                  -4.602540e-05
## junction_detail6                                  -1.057121e-04
## junction_detail7                                   4.179138e-04
## junction_detail8                                  -2.173715e-04
## junction_detail9                                  -2.327388e-04
## junction_control1                                 -2.284796e-04
## junction_control2                                 -4.103804e-05
## junction_control3                                 -1.199961e-03
## light_conditions4                                  1.043256e-03
## light_conditions5                                  7.768874e-02
## light_conditions6                                  1.154284e-03
## light_conditions7                                  9.784221e-04
## road_surface_conditions2                          -1.424565e-03
## road_surface_conditions3                           2.299458e-04
## road_surface_conditions4                           7.514787e-05
## road_surface_conditions5                           3.475481e-04
## special_conditions_at_site1                        4.692904e-04
## special_conditions_at_site2                        6.396824e-04
## special_conditions_at_site3                       -4.028707e-03
## special_conditions_at_site4                        4.995430e-04
## special_conditions_at_site5                        6.604192e-04
## special_conditions_at_site6                        1.075833e-03
## special_conditions_at_site7                        9.328612e-04
## did_police_officer_attend_scene_of_collision1     -2.719033e-05
## 1|2                                                4.915252e-04
## 2|3                                                2.377640e-04
##                                               light_conditions6
## police_force                                      -4.291969e-06
## number_of_vehicles                                 5.348549e-04
## number_of_casualties                              -5.902302e-05
## speed_limit                                       -7.411260e-05
## junction_detail1                                   1.119332e-03
## junction_detail2                                   4.816093e-04
## junction_detail5                                  -1.511154e-04
## junction_detail6                                   1.343034e-04
## junction_detail7                                   2.420230e-04
## junction_detail8                                  -8.419318e-06
## junction_detail9                                   6.426952e-05
## junction_control1                                 -3.107726e-05
## junction_control2                                  2.659023e-04
## junction_control3                                 -2.760207e-04
## light_conditions4                                  6.639383e-04
## light_conditions5                                  1.154284e-03
## light_conditions6                                  2.394004e-02
## light_conditions7                                  1.224381e-03
## road_surface_conditions2                          -7.801698e-04
## road_surface_conditions3                          -1.800848e-03
## road_surface_conditions4                          -2.299826e-03
## road_surface_conditions5                           1.321453e-03
## special_conditions_at_site1                        3.540783e-04
## special_conditions_at_site2                        8.240402e-04
## special_conditions_at_site3                        9.916490e-04
## special_conditions_at_site4                       -4.262986e-04
## special_conditions_at_site5                       -3.369022e-03
## special_conditions_at_site6                        1.684670e-03
## special_conditions_at_site7                       -4.497698e-03
## did_police_officer_attend_scene_of_collision1     -2.958656e-04
## 1|2                                               -1.171870e-03
## 2|3                                               -1.156069e-03
##                                               light_conditions7
## police_force                                      -4.579974e-06
## number_of_vehicles                                 3.855953e-04
## number_of_casualties                               1.323932e-04
## speed_limit                                       -8.837229e-06
## junction_detail1                                  -4.104294e-04
## junction_detail2                                   3.816756e-04
## junction_detail5                                  -8.316066e-04
## junction_detail6                                  -1.336980e-04
## junction_detail7                                  -5.899579e-04
## junction_detail8                                   1.760190e-04
## junction_detail9                                  -1.490397e-04
## junction_control1                                  2.887041e-05
## junction_control2                                  3.846597e-04
## junction_control3                                  2.130164e-04
## light_conditions4                                  8.654382e-04
## light_conditions5                                  9.784221e-04
## light_conditions6                                  1.224381e-03
## light_conditions7                                  8.513165e-02
## road_surface_conditions2                          -5.414212e-04
## road_surface_conditions3                           5.672467e-04
## road_surface_conditions4                          -6.053842e-04
## road_surface_conditions5                           4.359615e-04
## special_conditions_at_site1                        3.257399e-04
## special_conditions_at_site2                        7.696121e-05
## special_conditions_at_site3                        6.223961e-04
## special_conditions_at_site4                        5.262849e-04
## special_conditions_at_site5                       -2.936054e-03
## special_conditions_at_site6                        1.429831e-03
## special_conditions_at_site7                        9.654335e-04
## did_police_officer_attend_scene_of_collision1      6.719193e-04
## 1|2                                                1.727093e-03
## 2|3                                                1.770778e-03
##                                               road_surface_conditions2
## police_force                                             -2.154102e-06
## number_of_vehicles                                        4.365880e-05
## number_of_casualties                                     -5.679054e-06
## speed_limit                                              -2.887106e-06
## junction_detail1                                         -1.142446e-05
## junction_detail2                                         -3.965104e-05
## junction_detail5                                          1.713528e-05
## junction_detail6                                         -4.919345e-05
## junction_detail7                                          2.391570e-05
## junction_detail8                                          6.854772e-06
## junction_detail9                                         -3.421518e-06
## junction_control1                                         3.844727e-04
## junction_control2                                         8.321924e-05
## junction_control3                                         9.003956e-05
## light_conditions4                                        -7.400566e-04
## light_conditions5                                        -1.424565e-03
## light_conditions6                                        -7.801698e-04
## light_conditions7                                        -5.414212e-04
## road_surface_conditions2                                  3.770650e-03
## road_surface_conditions3                                  8.005095e-04
## road_surface_conditions4                                  9.431491e-04
## road_surface_conditions5                                  9.549466e-04
## special_conditions_at_site1                               7.474934e-05
## special_conditions_at_site2                               5.543787e-04
## special_conditions_at_site3                              -7.516397e-05
## special_conditions_at_site4                               6.908251e-05
## special_conditions_at_site5                              -2.660615e-04
## special_conditions_at_site6                              -1.127892e-03
## special_conditions_at_site7                              -9.440536e-04
## did_police_officer_attend_scene_of_collision1            -2.316905e-04
## 1|2                                                       2.517159e-04
## 2|3                                                       2.911763e-04
##                                               road_surface_conditions3
## police_force                                              6.407535e-06
## number_of_vehicles                                       -2.785198e-05
## number_of_casualties                                     -2.458272e-04
## speed_limit                                               4.107068e-06
## junction_detail1                                         -7.340462e-04
## junction_detail2                                          4.723286e-04
## junction_detail5                                         -2.562763e-03
## junction_detail6                                          1.858144e-04
## junction_detail7                                         -3.633885e-04
## junction_detail8                                         -1.188336e-04
## junction_detail9                                         -1.298593e-04
## junction_control1                                         6.769149e-04
## junction_control2                                         3.699295e-04
## junction_control3                                        -6.539715e-04
## light_conditions4                                        -1.116089e-04
## light_conditions5                                         2.299458e-04
## light_conditions6                                        -1.800848e-03
## light_conditions7                                         5.672467e-04
## road_surface_conditions2                                  8.005095e-04
## road_surface_conditions3                                  2.980077e-01
## road_surface_conditions4                                  9.039208e-04
## road_surface_conditions5                                  4.367984e-04
## special_conditions_at_site1                               3.506420e-04
## special_conditions_at_site2                               5.218638e-04
## special_conditions_at_site3                               4.377039e-04
## special_conditions_at_site4                               6.199989e-04
## special_conditions_at_site5                               6.045377e-04
## special_conditions_at_site6                               5.422935e-04
## special_conditions_at_site7                               7.034842e-04
## did_police_officer_attend_scene_of_collision1             4.444376e-04
## 1|2                                                       8.735511e-04
## 2|3                                                       9.657320e-04
##                                               road_surface_conditions4
## police_force                                             -6.822409e-06
## number_of_vehicles                                        7.385016e-05
## number_of_casualties                                      9.501784e-05
## speed_limit                                              -7.342612e-06
## junction_detail1                                          1.376983e-04
## junction_detail2                                         -1.597186e-04
## junction_detail5                                          2.696804e-04
## junction_detail6                                          3.575590e-04
## junction_detail7                                         -3.118176e-04
## junction_detail8                                          1.929411e-06
## junction_detail9                                          1.549516e-04
## junction_control1                                         7.562194e-04
## junction_control2                                         1.028940e-04
## junction_control3                                         5.400814e-04
## light_conditions4                                        -5.004964e-04
## light_conditions5                                         7.514787e-05
## light_conditions6                                        -2.299826e-03
## light_conditions7                                        -6.053842e-04
## road_surface_conditions2                                  9.431491e-04
## road_surface_conditions3                                  9.039208e-04
## road_surface_conditions4                                  4.514375e-02
## road_surface_conditions5                                  8.598182e-04
## special_conditions_at_site1                               4.625783e-04
## special_conditions_at_site2                               3.948536e-05
## special_conditions_at_site3                               2.947686e-04
## special_conditions_at_site4                              -3.076679e-04
## special_conditions_at_site5                              -1.973367e-03
## special_conditions_at_site6                              -3.241014e-03
## special_conditions_at_site7                              -3.523818e-03
## did_police_officer_attend_scene_of_collision1            -9.201484e-05
## 1|2                                                       4.000519e-04
## 2|3                                                       4.795707e-04
##                                               road_surface_conditions5
## police_force                                             -2.466812e-05
## number_of_vehicles                                        1.279267e-03
## number_of_casualties                                     -9.539929e-04
## speed_limit                                              -3.904378e-05
## junction_detail1                                          4.348524e-04
## junction_detail2                                         -6.381668e-03
## junction_detail5                                          7.131992e-04
## junction_detail6                                         -8.397611e-04
## junction_detail7                                          1.381859e-04
## junction_detail8                                         -1.440072e-05
## junction_detail9                                         -2.103309e-03
## junction_control1                                         8.947354e-04
## junction_control2                                        -7.542155e-04
## junction_control3                                         3.554213e-04
## light_conditions4                                        -5.901806e-04
## light_conditions5                                         3.475481e-04
## light_conditions6                                         1.321453e-03
## light_conditions7                                         4.359615e-04
## road_surface_conditions2                                  9.549466e-04
## road_surface_conditions3                                  4.367984e-04
## road_surface_conditions4                                  8.598182e-04
## road_surface_conditions5                                  1.533799e+00
## special_conditions_at_site1                               1.108124e-03
## special_conditions_at_site2                               3.042245e-03
## special_conditions_at_site3                               1.351825e-03
## special_conditions_at_site4                               5.080255e-04
## special_conditions_at_site5                               8.621033e-04
## special_conditions_at_site6                               5.438268e-04
## special_conditions_at_site7                               8.179729e-04
## did_police_officer_attend_scene_of_collision1            -5.538773e-04
## 1|2                                                      -1.165306e-03
## 2|3                                                      -1.225580e-03
##                                               special_conditions_at_site1
## police_force                                                 3.345466e-07
## number_of_vehicles                                           9.776141e-05
## number_of_casualties                                        -5.130315e-05
## speed_limit                                                 -9.185312e-07
## junction_detail1                                             1.349534e-04
## junction_detail2                                             3.449181e-04
## junction_detail5                                             4.522091e-04
## junction_detail6                                            -5.394417e-04
## junction_detail7                                             9.735835e-05
## junction_detail8                                             3.099926e-04
## junction_detail9                                            -2.785609e-04
## junction_control1                                            4.540899e-04
## junction_control2                                           -1.009254e-03
## junction_control3                                            4.691044e-04
## light_conditions4                                           -3.323394e-04
## light_conditions5                                            4.692904e-04
## light_conditions6                                            3.540783e-04
## light_conditions7                                            3.257399e-04
## road_surface_conditions2                                     7.474934e-05
## road_surface_conditions3                                     3.506420e-04
## road_surface_conditions4                                     4.625783e-04
## road_surface_conditions5                                     1.108124e-03
## special_conditions_at_site1                                  2.847394e-01
## special_conditions_at_site2                                  1.978584e-03
## special_conditions_at_site3                                  6.140923e-04
## special_conditions_at_site4                                  7.923861e-04
## special_conditions_at_site5                                  5.681692e-04
## special_conditions_at_site6                                  2.788772e-04
## special_conditions_at_site7                                  2.280731e-04
## did_police_officer_attend_scene_of_collision1               -5.931477e-04
## 1|2                                                         -2.645401e-04
## 2|3                                                         -1.487476e-04
##                                               special_conditions_at_site2
## police_force                                                 2.141141e-05
## number_of_vehicles                                           2.247820e-04
## number_of_casualties                                        -1.759949e-03
## speed_limit                                                 -3.151750e-05
## junction_detail1                                             1.237793e-04
## junction_detail2                                            -4.654075e-04
## junction_detail5                                             6.964853e-04
## junction_detail6                                            -2.057568e-03
## junction_detail7                                             1.382897e-03
## junction_detail8                                            -8.166213e-05
## junction_detail9                                             1.810080e-04
## junction_control1                                            7.931520e-05
## junction_control2                                           -2.845288e-03
## junction_control3                                            4.199372e-04
## light_conditions4                                            9.506835e-04
## light_conditions5                                            6.396824e-04
## light_conditions6                                            8.240402e-04
## light_conditions7                                            7.696121e-05
## road_surface_conditions2                                     5.543787e-04
## road_surface_conditions3                                     5.218638e-04
## road_surface_conditions4                                     3.948536e-05
## road_surface_conditions5                                     3.042245e-03
## special_conditions_at_site1                                  1.978584e-03
## special_conditions_at_site2                                  1.921143e+00
## special_conditions_at_site3                                  1.575288e-03
## special_conditions_at_site4                                  9.765950e-04
## special_conditions_at_site5                                  6.501119e-04
## special_conditions_at_site6                                 -4.256766e-05
## special_conditions_at_site7                                  2.448650e-04
## did_police_officer_attend_scene_of_collision1               -3.152806e-04
## 1|2                                                         -2.286886e-03
## 2|3                                                         -2.560675e-03
##                                               special_conditions_at_site3
## police_force                                                -2.689756e-06
## number_of_vehicles                                           2.754764e-04
## number_of_casualties                                        -1.662526e-04
## speed_limit                                                 -1.566256e-05
## junction_detail1                                             8.627939e-05
## junction_detail2                                            -1.402312e-03
## junction_detail5                                             5.198263e-04
## junction_detail6                                            -1.765551e-03
## junction_detail7                                            -2.028784e-04
## junction_detail8                                             3.916059e-04
## junction_detail9                                             3.659908e-04
## junction_control1                                            6.348638e-04
## junction_control2                                            8.949880e-04
## junction_control3                                           -7.794061e-03
## light_conditions4                                            9.408595e-05
## light_conditions5                                           -4.028707e-03
## light_conditions6                                            9.916490e-04
## light_conditions7                                            6.223961e-04
## road_surface_conditions2                                    -7.516397e-05
## road_surface_conditions3                                     4.377039e-04
## road_surface_conditions4                                     2.947686e-04
## road_surface_conditions5                                     1.351825e-03
## special_conditions_at_site1                                  6.140923e-04
## special_conditions_at_site2                                  1.575288e-03
## special_conditions_at_site3                                  2.617543e-01
## special_conditions_at_site4                                  6.553183e-04
## special_conditions_at_site5                                  9.043563e-04
## special_conditions_at_site6                                  5.940251e-04
## special_conditions_at_site7                                  3.884762e-04
## did_police_officer_attend_scene_of_collision1               -2.943555e-04
## 1|2                                                         -1.386276e-04
## 2|3                                                         -1.886438e-04
##                                               special_conditions_at_site4
## police_force                                                 1.011470e-05
## number_of_vehicles                                           1.693402e-04
## number_of_casualties                                         1.052260e-04
## speed_limit                                                 -5.326034e-06
## junction_detail1                                            -2.903628e-04
## junction_detail2                                             3.628072e-04
## junction_detail5                                             3.249583e-05
## junction_detail6                                            -3.174738e-04
## junction_detail7                                             2.373830e-04
## junction_detail8                                            -1.556779e-04
## junction_detail9                                            -8.408683e-05
## junction_control1                                            4.465062e-04
## junction_control2                                           -2.892563e-04
## junction_control3                                           -5.302289e-04
## light_conditions4                                           -1.521684e-04
## light_conditions5                                            4.995430e-04
## light_conditions6                                           -4.262986e-04
## light_conditions7                                            5.262849e-04
## road_surface_conditions2                                     6.908251e-05
## road_surface_conditions3                                     6.199989e-04
## road_surface_conditions4                                    -3.076679e-04
## road_surface_conditions5                                     5.080255e-04
## special_conditions_at_site1                                  7.923861e-04
## special_conditions_at_site2                                  9.765950e-04
## special_conditions_at_site3                                  6.553183e-04
## special_conditions_at_site4                                  5.411622e-02
## special_conditions_at_site5                                  8.198801e-04
## special_conditions_at_site6                                  6.781651e-04
## special_conditions_at_site7                                  6.562280e-04
## did_police_officer_attend_scene_of_collision1               -1.093581e-04
## 1|2                                                          8.124901e-04
## 2|3                                                          8.148752e-04
##                                               special_conditions_at_site5
## police_force                                                 7.348949e-06
## number_of_vehicles                                           6.010089e-04
## number_of_casualties                                         1.042345e-04
## speed_limit                                                 -2.459389e-05
## junction_detail1                                             5.555064e-04
## junction_detail2                                             2.441122e-04
## junction_detail5                                             1.118749e-03
## junction_detail6                                            -9.079042e-05
## junction_detail7                                             5.911534e-04
## junction_detail8                                            -1.578005e-03
## junction_detail9                                            -4.073568e-04
## junction_control1                                            4.398676e-04
## junction_control2                                           -2.543136e-04
## junction_control3                                           -2.556591e-03
## light_conditions4                                            8.124354e-05
## light_conditions5                                            6.604192e-04
## light_conditions6                                           -3.369022e-03
## light_conditions7                                           -2.936054e-03
## road_surface_conditions2                                    -2.660615e-04
## road_surface_conditions3                                     6.045377e-04
## road_surface_conditions4                                    -1.973367e-03
## road_surface_conditions5                                     8.621033e-04
## special_conditions_at_site1                                  5.681692e-04
## special_conditions_at_site2                                  6.501119e-04
## special_conditions_at_site3                                  9.043563e-04
## special_conditions_at_site4                                  8.198801e-04
## special_conditions_at_site5                                  4.272241e-01
## special_conditions_at_site6                                  8.095814e-04
## special_conditions_at_site7                                  2.161283e-03
## did_police_officer_attend_scene_of_collision1               -5.573626e-04
## 1|2                                                          3.024032e-04
## 2|3                                                          3.734658e-04
##                                               special_conditions_at_site6
## police_force                                                 1.115475e-05
## number_of_vehicles                                           7.383116e-04
## number_of_casualties                                        -1.222576e-05
## speed_limit                                                 -4.412308e-05
## junction_detail1                                            -2.579694e-03
## junction_detail2                                             2.168917e-04
## junction_detail5                                             9.181266e-04
## junction_detail6                                             6.173437e-05
## junction_detail7                                            -1.837275e-03
## junction_detail8                                             4.558262e-04
## junction_detail9                                            -2.896015e-04
## junction_control1                                            4.494421e-04
## junction_control2                                            6.602323e-04
## junction_control3                                            3.722995e-04
## light_conditions4                                            7.159063e-04
## light_conditions5                                            1.075833e-03
## light_conditions6                                            1.684670e-03
## light_conditions7                                            1.429831e-03
## road_surface_conditions2                                    -1.127892e-03
## road_surface_conditions3                                     5.422935e-04
## road_surface_conditions4                                    -3.241014e-03
## road_surface_conditions5                                     5.438268e-04
## special_conditions_at_site1                                  2.788772e-04
## special_conditions_at_site2                                 -4.256766e-05
## special_conditions_at_site3                                  5.940251e-04
## special_conditions_at_site4                                  6.781651e-04
## special_conditions_at_site5                                  8.095814e-04
## special_conditions_at_site6                                  1.141036e+00
## special_conditions_at_site7                                  1.313805e-03
## did_police_officer_attend_scene_of_collision1               -2.074288e-04
## 1|2                                                          1.735914e-04
## 2|3                                                          2.946815e-04
##                                               special_conditions_at_site7
## police_force                                                 2.320336e-06
## number_of_vehicles                                           7.101131e-04
## number_of_casualties                                        -1.637625e-04
## speed_limit                                                 -1.365361e-05
## junction_detail1                                             5.159765e-04
## junction_detail2                                             4.229001e-04
## junction_detail5                                             1.056745e-03
## junction_detail6                                            -8.379880e-06
## junction_detail7                                             2.057032e-04
## junction_detail8                                            -7.171299e-04
## junction_detail9                                            -8.802036e-04
## junction_control1                                            5.174950e-04
## junction_control2                                            4.233256e-04
## junction_control3                                            6.787154e-04
## light_conditions4                                            7.176092e-04
## light_conditions5                                            9.328612e-04
## light_conditions6                                           -4.497698e-03
## light_conditions7                                            9.654335e-04
## road_surface_conditions2                                    -9.440536e-04
## road_surface_conditions3                                     7.034842e-04
## road_surface_conditions4                                    -3.523818e-03
## road_surface_conditions5                                     8.179729e-04
## special_conditions_at_site1                                  2.280731e-04
## special_conditions_at_site2                                  2.448650e-04
## special_conditions_at_site3                                  3.884762e-04
## special_conditions_at_site4                                  6.562280e-04
## special_conditions_at_site5                                  2.161283e-03
## special_conditions_at_site6                                  1.313805e-03
## special_conditions_at_site7                                  3.513583e-01
## did_police_officer_attend_scene_of_collision1                6.766586e-04
## 1|2                                                          2.406290e-03
## 2|3                                                          1.717689e-03
##                                               did_police_officer_attend_scene_of_collision1
## police_force                                                                   1.747506e-06
## number_of_vehicles                                                            -9.604660e-05
## number_of_casualties                                                          -1.181210e-04
## speed_limit                                                                   -9.935154e-06
## junction_detail1                                                               2.335010e-04
## junction_detail2                                                               1.381424e-04
## junction_detail5                                                               8.829671e-05
## junction_detail6                                                              -5.164508e-05
## junction_detail7                                                              -3.582666e-04
## junction_detail8                                                              -8.385638e-06
## junction_detail9                                                              -1.059121e-04
## junction_control1                                                             -3.844957e-04
## junction_control2                                                             -6.238607e-05
## junction_control3                                                              1.050041e-05
## light_conditions4                                                             -1.031140e-04
## light_conditions5                                                             -2.719033e-05
## light_conditions6                                                             -2.958656e-04
## light_conditions7                                                              6.719193e-04
## road_surface_conditions2                                                      -2.316905e-04
## road_surface_conditions3                                                       4.444376e-04
## road_surface_conditions4                                                      -9.201484e-05
## road_surface_conditions5                                                      -5.538773e-04
## special_conditions_at_site1                                                   -5.931477e-04
## special_conditions_at_site2                                                   -3.152806e-04
## special_conditions_at_site3                                                   -2.943555e-04
## special_conditions_at_site4                                                   -1.093581e-04
## special_conditions_at_site5                                                   -5.573626e-04
## special_conditions_at_site6                                                   -2.074288e-04
## special_conditions_at_site7                                                    6.766586e-04
## did_police_officer_attend_scene_of_collision1                                  7.428231e-03
## 1|2                                                                            6.184074e-03
## 2|3                                                                            6.073325e-03
##                                                         1|2           2|3
## police_force                                   1.104288e-05  1.150789e-05
## number_of_vehicles                             2.414955e-03  2.501799e-03
## number_of_casualties                           5.734959e-04  5.483793e-04
## speed_limit                                    1.208160e-04  1.184877e-04
## junction_detail1                               2.585715e-04  3.271586e-04
## junction_detail2                               1.535613e-03  1.568202e-03
## junction_detail5                              -8.569407e-04 -8.745097e-04
## junction_detail6                               4.592415e-04  4.541350e-04
## junction_detail7                               7.505921e-04  7.924603e-04
## junction_detail8                               7.076430e-04  7.288486e-04
## junction_detail9                               1.273771e-03  1.309743e-03
## junction_control1                              4.512565e-04  5.508482e-04
## junction_control2                              8.610331e-04  9.109593e-04
## junction_control3                              7.621691e-04  7.647968e-04
## light_conditions4                              1.259452e-03  1.208270e-03
## light_conditions5                              4.915252e-04  2.377640e-04
## light_conditions6                             -1.171870e-03 -1.156069e-03
## light_conditions7                              1.727093e-03  1.770778e-03
## road_surface_conditions2                       2.517159e-04  2.911763e-04
## road_surface_conditions3                       8.735511e-04  9.657320e-04
## road_surface_conditions4                       4.000519e-04  4.795707e-04
## road_surface_conditions5                      -1.165306e-03 -1.225580e-03
## special_conditions_at_site1                   -2.645401e-04 -1.487476e-04
## special_conditions_at_site2                   -2.286886e-03 -2.560675e-03
## special_conditions_at_site3                   -1.386276e-04 -1.886438e-04
## special_conditions_at_site4                    8.124901e-04  8.148752e-04
## special_conditions_at_site5                    3.024032e-04  3.734658e-04
## special_conditions_at_site6                    1.735914e-04  2.946815e-04
## special_conditions_at_site7                    2.406290e-03  1.717689e-03
## did_police_officer_attend_scene_of_collision1  6.184074e-03  6.073325e-03
## 1|2                                            2.557419e-02  1.621652e-02
## 2|3                                            1.621652e-02  1.634423e-02
#👸store the coefficients and p-values into one new dataframe
reduced_test2.coef <- data.frame(coef(summary(reduced_test2)))
view(reduced_test2.coef) 
reduced_test2.coef$pval <- round((pnorm(abs(reduced_test2.coef$t.value), lower.tail = FALSE) * 2),3)
view(reduced_test2.coef)
#Select the row names corresponding to all values less than 0.05 in the full_model2.coef$pval column
significant_rows <- rownames(reduced_test2.coef[reduced_test2.coef$pval < 0.05, ])
significant_rows
##  [1] "number_of_vehicles"                           
##  [2] "number_of_casualties"                         
##  [3] "speed_limit"                                  
##  [4] "junction_detail1"                             
##  [5] "junction_detail7"                             
##  [6] "junction_detail9"                             
##  [7] "junction_control1"                            
##  [8] "junction_control2"                            
##  [9] "light_conditions4"                            
## [10] "light_conditions5"                            
## [11] "road_surface_conditions2"                     
## [12] "road_surface_conditions4"                     
## [13] "special_conditions_at_site1"                  
## [14] "did_police_officer_attend_scene_of_collision1"
## [15] "1|2"                                          
## [16] "2|3"
#💛1_4. Run a Ordered logit Best stepwise model       💜10
#13 predictors, included 1 more predictor(first_road_number) compared with  step_test in Multinomial model
#13=6 factor + 7 numeric
library(MASS)
unique(data4$legacy_collision_severity)
## [1] 3 2 1
## Levels: 1 < 2 < 3
step_test2 <- stepAIC(full_test2, method = "both") #same as "backward/forward"  here
## Start:  AIC=11333.9
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     road_type + speed_limit + junction_detail + junction_control + 
##     second_road_class + second_road_number + pedestrian_crossing_human_control + 
##     pedestrian_crossing_physical_facilities + light_conditions + 
##     weather_conditions + road_surface_conditions + special_conditions_at_site + 
##     carriageway_hazards + did_police_officer_attend_scene_of_collision
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
##                                                Df   AIC
## - weather_conditions                            7 11322
## - carriageway_hazards                           5 11326
## - road_type                                     4 11330
## - pedestrian_crossing_physical_facilities       5 11330
## - special_conditions_at_site                    7 11332
## - first_road_class                              1 11332
## - day_of_week                                   1 11333
## - first_road_number                             1 11334
## <none>                                            11334
## - pedestrian_crossing_human_control             2 11335
## - second_road_number                            1 11336
## - road_surface_conditions                       4 11336
## - second_road_class                             1 11337
## - police_force                                  1 11337
## - number_of_casualties                          1 11338
## - junction_detail                               7 11338
## - junction_control                              3 11344
## - speed_limit                                   1 11349
## - light_conditions                              4 11350
## - number_of_vehicles                            1 11436
## - did_police_officer_attend_scene_of_collision  1 11459
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## 
## Step:  AIC=11321.6
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     road_type + speed_limit + junction_detail + junction_control + 
##     second_road_class + second_road_number + pedestrian_crossing_human_control + 
##     pedestrian_crossing_physical_facilities + light_conditions + 
##     road_surface_conditions + special_conditions_at_site + carriageway_hazards + 
##     did_police_officer_attend_scene_of_collision
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
##                                                Df   AIC
## - carriageway_hazards                           5 11314
## - road_type                                     4 11318
## - pedestrian_crossing_physical_facilities       5 11318
## - special_conditions_at_site                    7 11320
## - first_road_class                              1 11320
## - day_of_week                                   1 11320
## - first_road_number                             1 11321
## <none>                                            11322
## - pedestrian_crossing_human_control             2 11322
## - second_road_number                            1 11324
## - second_road_class                             1 11324
## - police_force                                  1 11325
## - number_of_casualties                          1 11325
## - junction_detail                               7 11326
## - junction_control                              3 11332
## - road_surface_conditions                       4 11333
## - speed_limit                                   1 11337
## - light_conditions                              4 11337
## - number_of_vehicles                            1 11423
## - did_police_officer_attend_scene_of_collision  1 11447
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## 
## Step:  AIC=11314.19
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     road_type + speed_limit + junction_detail + junction_control + 
##     second_road_class + second_road_number + pedestrian_crossing_human_control + 
##     pedestrian_crossing_physical_facilities + light_conditions + 
##     road_surface_conditions + special_conditions_at_site + did_police_officer_attend_scene_of_collision
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
##                                                Df   AIC
## - road_type                                     4 11310
## - pedestrian_crossing_physical_facilities       5 11311
## - special_conditions_at_site                    7 11311
## - first_road_class                              1 11312
## - day_of_week                                   1 11313
## - first_road_number                             1 11314
## <none>                                            11314
## - pedestrian_crossing_human_control             2 11315
## - second_road_number                            1 11316
## - second_road_class                             1 11317
## - police_force                                  1 11318
## - number_of_casualties                          1 11318
## - junction_detail                               7 11318
## - junction_control                              3 11325
## - road_surface_conditions                       4 11325
## - speed_limit                                   1 11330
## - light_conditions                              4 11330
## - number_of_vehicles                            1 11416
## - did_police_officer_attend_scene_of_collision  1 11439
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## 
## Step:  AIC=11310.1
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     speed_limit + junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     pedestrian_crossing_physical_facilities + light_conditions + 
##     road_surface_conditions + special_conditions_at_site + did_police_officer_attend_scene_of_collision
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
##                                                Df   AIC
## - pedestrian_crossing_physical_facilities       5 11307
## - special_conditions_at_site                    7 11307
## - first_road_class                              1 11308
## - day_of_week                                   1 11309
## - first_road_number                             1 11310
## <none>                                            11310
## - pedestrian_crossing_human_control             2 11311
## - second_road_number                            1 11312
## - police_force                                  1 11313
## - second_road_class                             1 11313
## - number_of_casualties                          1 11314
## - road_surface_conditions                       4 11321
## - junction_control                              3 11322
## - junction_detail                               7 11323
## - light_conditions                              4 11326
## - speed_limit                                   1 11326
## - number_of_vehicles                            1 11411
## - did_police_officer_attend_scene_of_collision  1 11434
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## 
## Step:  AIC=11306.64
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     speed_limit + junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     light_conditions + road_surface_conditions + special_conditions_at_site + 
##     did_police_officer_attend_scene_of_collision
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
##                                                Df   AIC
## - special_conditions_at_site                    7 11304
## - first_road_class                              1 11305
## - day_of_week                                   1 11305
## - first_road_number                             1 11306
## <none>                                            11307
## - pedestrian_crossing_human_control             2 11308
## - police_force                                  1 11309
## - second_road_number                            1 11309
## - second_road_class                             1 11310
## - number_of_casualties                          1 11311
## - road_surface_conditions                       4 11318
## - junction_control                              3 11318
## - junction_detail                               7 11320
## - light_conditions                              4 11322
## - speed_limit                                   1 11324
## - number_of_vehicles                            1 11408
## - did_police_officer_attend_scene_of_collision  1 11430
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## 
## Step:  AIC=11303.65
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_class + first_road_number + 
##     speed_limit + junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
##                                                Df   AIC
## - first_road_class                              1 11302
## - day_of_week                                   1 11302
## - first_road_number                             1 11303
## <none>                                            11304
## - pedestrian_crossing_human_control             2 11305
## - police_force                                  1 11306
## - second_road_number                            1 11306
## - second_road_class                             1 11307
## - number_of_casualties                          1 11308
## - road_surface_conditions                       4 11315
## - junction_control                              3 11316
## - junction_detail                               7 11317
## - light_conditions                              4 11319
## - speed_limit                                   1 11321
## - number_of_vehicles                            1 11406
## - did_police_officer_attend_scene_of_collision  1 11426
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## 
## Step:  AIC=11301.67
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + day_of_week + first_road_number + 
##     speed_limit + junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
##                                                Df   AIC
## - day_of_week                                   1 11300
## <none>                                            11302
## - first_road_number                             1 11302
## - pedestrian_crossing_human_control             2 11303
## - police_force                                  1 11304
## - second_road_number                            1 11304
## - second_road_class                             1 11305
## - number_of_casualties                          1 11306
## - road_surface_conditions                       4 11313
## - junction_control                              3 11314
## - junction_detail                               7 11315
## - light_conditions                              4 11317
## - speed_limit                                   1 11320
## - number_of_vehicles                            1 11404
## - did_police_officer_attend_scene_of_collision  1 11426
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## 
## Step:  AIC=11300.31
## legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + first_road_number + speed_limit + 
##     junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
##                                                Df   AIC
## <none>                                            11300
## - first_road_number                             1 11300
## - pedestrian_crossing_human_control             2 11302
## - police_force                                  1 11303
## - second_road_number                            1 11303
## - second_road_class                             1 11303
## - number_of_casualties                          1 11304
## - road_surface_conditions                       4 11311
## - junction_control                              3 11313
## - junction_detail                               7 11314
## - light_conditions                              4 11316
## - speed_limit                                   1 11318
## - number_of_vehicles                            1 11402
## - did_police_officer_attend_scene_of_collision  1 11424
step_test2  ## Residual Deviance: 11240.31   AIC: 11300.31
## Call:
## polr(formula = legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + first_road_number + speed_limit + 
##     junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision, 
##     data = data4, Hess = TRUE)
## 
## Coefficients:
##                                  police_force 
##                                  2.803911e-03 
##                            number_of_vehicles 
##                                  4.223909e-01 
##                          number_of_casualties 
##                                 -8.624976e-02 
##                             first_road_number 
##                                 -2.160612e-05 
##                                   speed_limit 
##                                 -1.064822e-02 
##                              junction_detail1 
##                                  3.816228e-01 
##                              junction_detail2 
##                                  1.802745e-01 
##                              junction_detail5 
##                                 -8.415701e-02 
##                              junction_detail6 
##                                 -4.358178e-02 
##                              junction_detail7 
##                                  2.872702e-01 
##                              junction_detail8 
##                                  8.503491e-02 
##                              junction_detail9 
##                                  1.785680e-01 
##                             junction_control1 
##                                  6.040942e-01 
##                             junction_control2 
##                                  2.583486e-01 
##                             junction_control3 
##                                  4.060331e-02 
##                             second_road_class 
##                                 -6.021036e-02 
##                            second_road_number 
##                                 -4.883946e-05 
##            pedestrian_crossing_human_control1 
##                                  5.855457e-01 
##            pedestrian_crossing_human_control2 
##                                  2.941869e-01 
##                             light_conditions4 
##                                 -2.276838e-01 
##                             light_conditions5 
##                                 -7.794430e-01 
##                             light_conditions6 
##                                  3.331103e-02 
##                             light_conditions7 
##                                  3.449934e-01 
##                      road_surface_conditions2 
##                                  2.179576e-01 
##                      road_surface_conditions3 
##                                  7.776016e-01 
##                      road_surface_conditions4 
##                                  4.717263e-01 
##                      road_surface_conditions5 
##                                  9.462452e-02 
## did_police_officer_attend_scene_of_collision1 
##                                 -8.942235e-01 
## 
## Intercepts:
##       1|2       2|3 
## -5.221991 -1.767972 
## 
## Residual Deviance: 11240.31 
## AIC: 11300.31
summary(step_test2)
## Call:
## polr(formula = legacy_collision_severity ~ police_force + number_of_vehicles + 
##     number_of_casualties + first_road_number + speed_limit + 
##     junction_detail + junction_control + second_road_class + 
##     second_road_number + pedestrian_crossing_human_control + 
##     light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision, 
##     data = data4, Hess = TRUE)
## 
## Coefficients:
##                                                    Value Std. Error   t value
## police_force                                   2.804e-03  1.349e-03    2.0789
## number_of_vehicles                             4.224e-01  4.138e-02   10.2075
## number_of_casualties                          -8.625e-02  3.409e-02   -2.5298
## first_road_number                             -2.161e-05  1.933e-05   -1.1175
## speed_limit                                   -1.065e-02  2.160e-03   -4.9301
## junction_detail1                               3.816e-01  8.565e-02    4.4556
## junction_detail2                               1.803e-01  1.593e-02   11.3164
## junction_detail5                              -8.416e-02  1.478e-02   -5.6927
## junction_detail6                              -4.358e-02  6.786e-02   -0.6423
## junction_detail7                               2.873e-01  1.895e-02   15.1567
## junction_detail8                               8.503e-02  1.232e-01    0.6904
## junction_detail9                               1.786e-01  7.895e-02    2.2617
## junction_control1                              6.041e-01  1.250e-03  483.1013
## junction_control2                              2.583e-01  6.968e-02    3.7078
## junction_control3                              4.060e-02  3.045e-03   13.3325
## second_road_class                             -6.021e-02  1.901e-02   -3.1678
## second_road_number                            -4.884e-05  2.780e-05   -1.7569
## pedestrian_crossing_human_control1             5.855e-01  5.607e-04 1044.2928
## pedestrian_crossing_human_control2             2.942e-01  4.074e-03   72.2038
## light_conditions4                             -2.277e-01  5.773e-02   -3.9437
## light_conditions5                             -7.794e-01  1.611e-03 -483.9691
## light_conditions6                              3.331e-02  7.572e-03    4.3992
## light_conditions7                              3.450e-01  1.131e-03  305.0754
## road_surface_conditions2                       2.180e-01  6.067e-02    3.5924
## road_surface_conditions3                       7.776e-01  2.714e-04 2864.8771
## road_surface_conditions4                       4.717e-01  1.898e-03  248.5101
## road_surface_conditions5                       9.462e-02  1.275e-04  742.0588
## did_police_officer_attend_scene_of_collision1 -8.942e-01  7.982e-02  -11.2025
## 
## Intercepts:
##     Value     Std. Error t value  
## 1|2   -5.2220    0.0133  -392.3725
## 2|3   -1.7680    0.0862   -20.5012
## 
## Residual Deviance: 11240.31 
## AIC: 11300.31
summary(step_test2)$coef
##                                                       Value   Std. Error
## police_force                                   2.803911e-03 1.348752e-03
## number_of_vehicles                             4.223909e-01 4.138042e-02
## number_of_casualties                          -8.624976e-02 3.409343e-02
## first_road_number                             -2.160612e-05 1.933466e-05
## speed_limit                                   -1.064822e-02 2.159821e-03
## junction_detail1                               3.816228e-01 8.564934e-02
## junction_detail2                               1.802745e-01 1.593033e-02
## junction_detail5                              -8.415701e-02 1.478322e-02
## junction_detail6                              -4.358178e-02 6.785642e-02
## junction_detail7                               2.872702e-01 1.895339e-02
## junction_detail8                               8.503491e-02 1.231661e-01
## junction_detail9                               1.785680e-01 7.895421e-02
## junction_control1                              6.040942e-01 1.250450e-03
## junction_control2                              2.583486e-01 6.967706e-02
## junction_control3                              4.060331e-02 3.045438e-03
## second_road_class                             -6.021036e-02 1.900684e-02
## second_road_number                            -4.883946e-05 2.779943e-05
## pedestrian_crossing_human_control1             5.855457e-01 5.607103e-04
## pedestrian_crossing_human_control2             2.941869e-01 4.074396e-03
## light_conditions4                             -2.276838e-01 5.773384e-02
## light_conditions5                             -7.794430e-01 1.610522e-03
## light_conditions6                              3.331103e-02 7.572059e-03
## light_conditions7                              3.449934e-01 1.130846e-03
## road_surface_conditions2                       2.179576e-01 6.067263e-02
## road_surface_conditions3                       7.776016e-01 2.714258e-04
## road_surface_conditions4                       4.717263e-01 1.898218e-03
## road_surface_conditions5                       9.462452e-02 1.275162e-04
## did_police_officer_attend_scene_of_collision1 -8.942235e-01 7.982335e-02
## 1|2                                           -5.221991e+00 1.330876e-02
## 2|3                                           -1.767972e+00 8.623728e-02
##                                                    t value
## police_force                                     2.0788925
## number_of_vehicles                              10.2075070
## number_of_casualties                            -2.5298061
## first_road_number                               -1.1174810
## speed_limit                                     -4.9301392
## junction_detail1                                 4.4556423
## junction_detail2                                11.3164281
## junction_detail5                                -5.6927402
## junction_detail6                                -0.6422646
## junction_detail7                                15.1566633
## junction_detail8                                 0.6904081
## junction_detail9                                 2.2616649
## junction_control1                              483.1013484
## junction_control2                                3.7078002
## junction_control3                               13.3325044
## second_road_class                               -3.1678266
## second_road_number                              -1.7568514
## pedestrian_crossing_human_control1            1044.2927893
## pedestrian_crossing_human_control2              72.2038037
## light_conditions4                               -3.9436796
## light_conditions5                             -483.9691412
## light_conditions6                                4.3992040
## light_conditions7                              305.0753981
## road_surface_conditions2                         3.5923549
## road_surface_conditions3                      2864.8770634
## road_surface_conditions4                       248.5100689
## road_surface_conditions5                       742.0588304
## did_police_officer_attend_scene_of_collision1  -11.2025302
## 1|2                                           -392.3724609
## 2|3                                            -20.5012455
coef(step_test2)   # the values of Log odds ratio
##                                  police_force 
##                                  2.803911e-03 
##                            number_of_vehicles 
##                                  4.223909e-01 
##                          number_of_casualties 
##                                 -8.624976e-02 
##                             first_road_number 
##                                 -2.160612e-05 
##                                   speed_limit 
##                                 -1.064822e-02 
##                              junction_detail1 
##                                  3.816228e-01 
##                              junction_detail2 
##                                  1.802745e-01 
##                              junction_detail5 
##                                 -8.415701e-02 
##                              junction_detail6 
##                                 -4.358178e-02 
##                              junction_detail7 
##                                  2.872702e-01 
##                              junction_detail8 
##                                  8.503491e-02 
##                              junction_detail9 
##                                  1.785680e-01 
##                             junction_control1 
##                                  6.040942e-01 
##                             junction_control2 
##                                  2.583486e-01 
##                             junction_control3 
##                                  4.060331e-02 
##                             second_road_class 
##                                 -6.021036e-02 
##                            second_road_number 
##                                 -4.883946e-05 
##            pedestrian_crossing_human_control1 
##                                  5.855457e-01 
##            pedestrian_crossing_human_control2 
##                                  2.941869e-01 
##                             light_conditions4 
##                                 -2.276838e-01 
##                             light_conditions5 
##                                 -7.794430e-01 
##                             light_conditions6 
##                                  3.331103e-02 
##                             light_conditions7 
##                                  3.449934e-01 
##                      road_surface_conditions2 
##                                  2.179576e-01 
##                      road_surface_conditions3 
##                                  7.776016e-01 
##                      road_surface_conditions4 
##                                  4.717263e-01 
##                      road_surface_conditions5 
##                                  9.462452e-02 
## did_police_officer_attend_scene_of_collision1 
##                                 -8.942235e-01
#13 significant predictors in best model step_test2 💜10:
#police_force + number_of_vehicles + number_of_casualties + first_road_number + speed_limit + junction_detail + junction_control + second_road_class + second_road_number + pedestrian_crossing_human_control + light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision

#Ordered Logit model:logit(P(Y<=j)) = log(P(Y <= j)/p(Y > j)) = b-sum(kx),
#The equations are: 
#logit(P(Y<=1)) = log(P(Y <= 1)/p(Y > 1)) = -5.2220 + 0.0028*police_force + 0.4224*number_of_vehicles - 0.0863*number_of_casualties - 2.161e-05*first_road_number - 0.0107*speed_limit - 0.3816*junction_detail(1) - 0.1803*junction_detail(2) - 0.0842*junction_detail(5) - 0.0436*junction_detail(6) - 0.2873*junction_detail(7) - 0.0850*junction_detail(8) - 0.1786*junction_detail(9) + 0.6041*junction_control(1) + 0.2583*junction_control(2) + 0.0406*junction_control(3) - 0.0602*second_road_class - 4.883946e-05*second_road_number  + 0.5855*pedestrian_crossing_human_control(1) + 0.2942*pedestrian_crossing_human_control(2) - 0.2277*light_conditions(4) - 0.7794*light_conditions(5) - 0.0333*light_conditions(6) - 0.3450*light_conditions(7) + 0.2180*road_surface_conditions(2)  + 0.7776*road_surface_conditions(3) + 0.4717*road_surface_conditions(4) + 0.0946*road_surface_conditions(5) - 0.8942*did_police_officer_attend_scene_of_collision


#logit(P(Y<=2)) = log(P(Y <= 2)/p(Y > 2)) = -1.7680 + 0.0028*police_force + 0.4224*number_of_vehicles - 0.0863*number_of_casualties - 2.161e-05*first_road_number - 0.0107*speed_limit - 0.3816*junction_detail(1) - 0.1803*junction_detail(2) - 0.0842*junction_detail(5) - 0.0436*junction_detail(6) - 0.2873*junction_detail(7) - 0.0850*junction_detail(8) - 0.1786*junction_detail(9) + 0.6041*junction_control(1) + 0.2583*junction_control(2) + 0.0406*junction_control(3) - 0.060*second_road_class - 4.883946e-05*second_road_number + 0.5855*pedestrian_crossing_human_control(1) + 0.2942*pedestrian_crossing_human_control(2) - 0.2277*light_conditions(4) - 0.7794*light_conditions(5) - 0.0333*light_conditions(6) - 0.3450*light_conditions(7) + 0.2180*road_surface_conditions(2)  + 0.7776*road_surface_conditions(3) + 0.4717*road_surface_conditions(4) + 0.0946*road_surface_conditions(5) - 0.8942*did_police_officer_attend_scene_of_collision


#👸store the coefficients and p-values into one new dataframe
step_test2.coef <- data.frame(coef(summary(step_test2)))
step_test2.coef
##                                                       Value   Std..Error
## police_force                                   2.803911e-03 1.348752e-03
## number_of_vehicles                             4.223909e-01 4.138042e-02
## number_of_casualties                          -8.624976e-02 3.409343e-02
## first_road_number                             -2.160612e-05 1.933466e-05
## speed_limit                                   -1.064822e-02 2.159821e-03
## junction_detail1                               3.816228e-01 8.564934e-02
## junction_detail2                               1.802745e-01 1.593033e-02
## junction_detail5                              -8.415701e-02 1.478322e-02
## junction_detail6                              -4.358178e-02 6.785642e-02
## junction_detail7                               2.872702e-01 1.895339e-02
## junction_detail8                               8.503491e-02 1.231661e-01
## junction_detail9                               1.785680e-01 7.895421e-02
## junction_control1                              6.040942e-01 1.250450e-03
## junction_control2                              2.583486e-01 6.967706e-02
## junction_control3                              4.060331e-02 3.045438e-03
## second_road_class                             -6.021036e-02 1.900684e-02
## second_road_number                            -4.883946e-05 2.779943e-05
## pedestrian_crossing_human_control1             5.855457e-01 5.607103e-04
## pedestrian_crossing_human_control2             2.941869e-01 4.074396e-03
## light_conditions4                             -2.276838e-01 5.773384e-02
## light_conditions5                             -7.794430e-01 1.610522e-03
## light_conditions6                              3.331103e-02 7.572059e-03
## light_conditions7                              3.449934e-01 1.130846e-03
## road_surface_conditions2                       2.179576e-01 6.067263e-02
## road_surface_conditions3                       7.776016e-01 2.714258e-04
## road_surface_conditions4                       4.717263e-01 1.898218e-03
## road_surface_conditions5                       9.462452e-02 1.275162e-04
## did_police_officer_attend_scene_of_collision1 -8.942235e-01 7.982335e-02
## 1|2                                           -5.221991e+00 1.330876e-02
## 2|3                                           -1.767972e+00 8.623728e-02
##                                                    t.value
## police_force                                     2.0788925
## number_of_vehicles                              10.2075070
## number_of_casualties                            -2.5298061
## first_road_number                               -1.1174810
## speed_limit                                     -4.9301392
## junction_detail1                                 4.4556423
## junction_detail2                                11.3164281
## junction_detail5                                -5.6927402
## junction_detail6                                -0.6422646
## junction_detail7                                15.1566633
## junction_detail8                                 0.6904081
## junction_detail9                                 2.2616649
## junction_control1                              483.1013484
## junction_control2                                3.7078002
## junction_control3                               13.3325044
## second_road_class                               -3.1678266
## second_road_number                              -1.7568514
## pedestrian_crossing_human_control1            1044.2927893
## pedestrian_crossing_human_control2              72.2038037
## light_conditions4                               -3.9436796
## light_conditions5                             -483.9691412
## light_conditions6                                4.3992040
## light_conditions7                              305.0753981
## road_surface_conditions2                         3.5923549
## road_surface_conditions3                      2864.8770634
## road_surface_conditions4                       248.5100689
## road_surface_conditions5                       742.0588304
## did_police_officer_attend_scene_of_collision1  -11.2025302
## 1|2                                           -392.3724609
## 2|3                                            -20.5012455
view(step_test2.coef) 
step_test2.coef$pval <- round((pnorm(abs(step_test2.coef$t.value), lower.tail = FALSE) * 2),3)
step_test2.coef  
##                                                       Value   Std..Error
## police_force                                   2.803911e-03 1.348752e-03
## number_of_vehicles                             4.223909e-01 4.138042e-02
## number_of_casualties                          -8.624976e-02 3.409343e-02
## first_road_number                             -2.160612e-05 1.933466e-05
## speed_limit                                   -1.064822e-02 2.159821e-03
## junction_detail1                               3.816228e-01 8.564934e-02
## junction_detail2                               1.802745e-01 1.593033e-02
## junction_detail5                              -8.415701e-02 1.478322e-02
## junction_detail6                              -4.358178e-02 6.785642e-02
## junction_detail7                               2.872702e-01 1.895339e-02
## junction_detail8                               8.503491e-02 1.231661e-01
## junction_detail9                               1.785680e-01 7.895421e-02
## junction_control1                              6.040942e-01 1.250450e-03
## junction_control2                              2.583486e-01 6.967706e-02
## junction_control3                              4.060331e-02 3.045438e-03
## second_road_class                             -6.021036e-02 1.900684e-02
## second_road_number                            -4.883946e-05 2.779943e-05
## pedestrian_crossing_human_control1             5.855457e-01 5.607103e-04
## pedestrian_crossing_human_control2             2.941869e-01 4.074396e-03
## light_conditions4                             -2.276838e-01 5.773384e-02
## light_conditions5                             -7.794430e-01 1.610522e-03
## light_conditions6                              3.331103e-02 7.572059e-03
## light_conditions7                              3.449934e-01 1.130846e-03
## road_surface_conditions2                       2.179576e-01 6.067263e-02
## road_surface_conditions3                       7.776016e-01 2.714258e-04
## road_surface_conditions4                       4.717263e-01 1.898218e-03
## road_surface_conditions5                       9.462452e-02 1.275162e-04
## did_police_officer_attend_scene_of_collision1 -8.942235e-01 7.982335e-02
## 1|2                                           -5.221991e+00 1.330876e-02
## 2|3                                           -1.767972e+00 8.623728e-02
##                                                    t.value  pval
## police_force                                     2.0788925 0.038
## number_of_vehicles                              10.2075070 0.000
## number_of_casualties                            -2.5298061 0.011
## first_road_number                               -1.1174810 0.264
## speed_limit                                     -4.9301392 0.000
## junction_detail1                                 4.4556423 0.000
## junction_detail2                                11.3164281 0.000
## junction_detail5                                -5.6927402 0.000
## junction_detail6                                -0.6422646 0.521
## junction_detail7                                15.1566633 0.000
## junction_detail8                                 0.6904081 0.490
## junction_detail9                                 2.2616649 0.024
## junction_control1                              483.1013484 0.000
## junction_control2                                3.7078002 0.000
## junction_control3                               13.3325044 0.000
## second_road_class                               -3.1678266 0.002
## second_road_number                              -1.7568514 0.079
## pedestrian_crossing_human_control1            1044.2927893 0.000
## pedestrian_crossing_human_control2              72.2038037 0.000
## light_conditions4                               -3.9436796 0.000
## light_conditions5                             -483.9691412 0.000
## light_conditions6                                4.3992040 0.000
## light_conditions7                              305.0753981 0.000
## road_surface_conditions2                         3.5923549 0.000
## road_surface_conditions3                      2864.8770634 0.000
## road_surface_conditions4                       248.5100689 0.000
## road_surface_conditions5                       742.0588304 0.000
## did_police_officer_attend_scene_of_collision1  -11.2025302 0.000
## 1|2                                           -392.3724609 0.000
## 2|3                                            -20.5012455 0.000
view(step_test2.coef)
#Select the row names corresponding to all values less than 0.05 in the full_model2.coef$pval column
significant_rows <- rownames(step_test2.coef[step_test2.coef$pval < 0.05, ])
significant_rows      #first_road_number and second_road_number are not significant, but can not rid these predictors to make predictors into those in step_test
##  [1] "police_force"                                 
##  [2] "number_of_vehicles"                           
##  [3] "number_of_casualties"                         
##  [4] "speed_limit"                                  
##  [5] "junction_detail1"                             
##  [6] "junction_detail2"                             
##  [7] "junction_detail5"                             
##  [8] "junction_detail7"                             
##  [9] "junction_detail9"                             
## [10] "junction_control1"                            
## [11] "junction_control2"                            
## [12] "junction_control3"                            
## [13] "second_road_class"                            
## [14] "pedestrian_crossing_human_control1"           
## [15] "pedestrian_crossing_human_control2"           
## [16] "light_conditions4"                            
## [17] "light_conditions5"                            
## [18] "light_conditions6"                            
## [19] "light_conditions7"                            
## [20] "road_surface_conditions2"                     
## [21] "road_surface_conditions3"                     
## [22] "road_surface_conditions4"                     
## [23] "road_surface_conditions5"                     
## [24] "did_police_officer_attend_scene_of_collision1"
## [25] "1|2"                                          
## [26] "2|3"
####Next, carry analysis for Best model: step_test2 in 💚2 ~ 💚

#💚2 create the coefficient table with p-values column

# store  coefficient table
ctable <- coef(summary(step_test2))     ##same as summary(step_test2)$coefficients
ctable
##                                                       Value   Std. Error
## police_force                                   2.803911e-03 1.348752e-03
## number_of_vehicles                             4.223909e-01 4.138042e-02
## number_of_casualties                          -8.624976e-02 3.409343e-02
## first_road_number                             -2.160612e-05 1.933466e-05
## speed_limit                                   -1.064822e-02 2.159821e-03
## junction_detail1                               3.816228e-01 8.564934e-02
## junction_detail2                               1.802745e-01 1.593033e-02
## junction_detail5                              -8.415701e-02 1.478322e-02
## junction_detail6                              -4.358178e-02 6.785642e-02
## junction_detail7                               2.872702e-01 1.895339e-02
## junction_detail8                               8.503491e-02 1.231661e-01
## junction_detail9                               1.785680e-01 7.895421e-02
## junction_control1                              6.040942e-01 1.250450e-03
## junction_control2                              2.583486e-01 6.967706e-02
## junction_control3                              4.060331e-02 3.045438e-03
## second_road_class                             -6.021036e-02 1.900684e-02
## second_road_number                            -4.883946e-05 2.779943e-05
## pedestrian_crossing_human_control1             5.855457e-01 5.607103e-04
## pedestrian_crossing_human_control2             2.941869e-01 4.074396e-03
## light_conditions4                             -2.276838e-01 5.773384e-02
## light_conditions5                             -7.794430e-01 1.610522e-03
## light_conditions6                              3.331103e-02 7.572059e-03
## light_conditions7                              3.449934e-01 1.130846e-03
## road_surface_conditions2                       2.179576e-01 6.067263e-02
## road_surface_conditions3                       7.776016e-01 2.714258e-04
## road_surface_conditions4                       4.717263e-01 1.898218e-03
## road_surface_conditions5                       9.462452e-02 1.275162e-04
## did_police_officer_attend_scene_of_collision1 -8.942235e-01 7.982335e-02
## 1|2                                           -5.221991e+00 1.330876e-02
## 2|3                                           -1.767972e+00 8.623728e-02
##                                                    t value
## police_force                                     2.0788925
## number_of_vehicles                              10.2075070
## number_of_casualties                            -2.5298061
## first_road_number                               -1.1174810
## speed_limit                                     -4.9301392
## junction_detail1                                 4.4556423
## junction_detail2                                11.3164281
## junction_detail5                                -5.6927402
## junction_detail6                                -0.6422646
## junction_detail7                                15.1566633
## junction_detail8                                 0.6904081
## junction_detail9                                 2.2616649
## junction_control1                              483.1013484
## junction_control2                                3.7078002
## junction_control3                               13.3325044
## second_road_class                               -3.1678266
## second_road_number                              -1.7568514
## pedestrian_crossing_human_control1            1044.2927893
## pedestrian_crossing_human_control2              72.2038037
## light_conditions4                               -3.9436796
## light_conditions5                             -483.9691412
## light_conditions6                                4.3992040
## light_conditions7                              305.0753981
## road_surface_conditions2                         3.5923549
## road_surface_conditions3                      2864.8770634
## road_surface_conditions4                       248.5100689
## road_surface_conditions5                       742.0588304
## did_police_officer_attend_scene_of_collision1  -11.2025302
## 1|2                                           -392.3724609
## 2|3                                            -20.5012455
# calculate and store p values
p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2
p   ##same as (1 - pnorm(abs(coefficients[ ,"t value"]), 0, 1))*2
##                                  police_force 
##                                  3.762723e-02 
##                            number_of_vehicles 
##                                  1.835193e-24 
##                          number_of_casualties 
##                                  1.141256e-02 
##                             first_road_number 
##                                  2.637887e-01 
##                                   speed_limit 
##                                  8.217103e-07 
##                              junction_detail1 
##                                  8.364238e-06 
##                              junction_detail2 
##                                  1.088159e-29 
##                              junction_detail5 
##                                  1.250165e-08 
##                              junction_detail6 
##                                  5.207014e-01 
##                              junction_detail7 
##                                  6.846003e-52 
##                              junction_detail8 
##                                  4.899376e-01 
##                              junction_detail9 
##                                  2.371811e-02 
##                             junction_control1 
##                                  0.000000e+00 
##                             junction_control2 
##                                  2.090675e-04 
##                             junction_control3 
##                                  1.497836e-40 
##                             second_road_class 
##                                  1.535831e-03 
##                            second_road_number 
##                                  7.894314e-02 
##            pedestrian_crossing_human_control1 
##                                  0.000000e+00 
##            pedestrian_crossing_human_control2 
##                                  0.000000e+00 
##                             light_conditions4 
##                                  8.024086e-05 
##                             light_conditions5 
##                                  0.000000e+00 
##                             light_conditions6 
##                                  1.086487e-05 
##                             light_conditions7 
##                                  0.000000e+00 
##                      road_surface_conditions2 
##                                  3.277032e-04 
##                      road_surface_conditions3 
##                                  0.000000e+00 
##                      road_surface_conditions4 
##                                  0.000000e+00 
##                      road_surface_conditions5 
##                                  0.000000e+00 
## did_police_officer_attend_scene_of_collision1 
##                                  3.962518e-29 
##                                           1|2 
##                                  0.000000e+00 
##                                           2|3 
##                                  2.098531e-93
(1 - pnorm(abs(ctable[ ,"t value"]), 0, 1))*2
##                                  police_force 
##                                  3.762723e-02 
##                            number_of_vehicles 
##                                  0.000000e+00 
##                          number_of_casualties 
##                                  1.141256e-02 
##                             first_road_number 
##                                  2.637887e-01 
##                                   speed_limit 
##                                  8.217103e-07 
##                              junction_detail1 
##                                  8.364238e-06 
##                              junction_detail2 
##                                  0.000000e+00 
##                              junction_detail5 
##                                  1.250165e-08 
##                              junction_detail6 
##                                  5.207014e-01 
##                              junction_detail7 
##                                  0.000000e+00 
##                              junction_detail8 
##                                  4.899376e-01 
##                              junction_detail9 
##                                  2.371811e-02 
##                             junction_control1 
##                                  0.000000e+00 
##                             junction_control2 
##                                  2.090675e-04 
##                             junction_control3 
##                                  0.000000e+00 
##                             second_road_class 
##                                  1.535831e-03 
##                            second_road_number 
##                                  7.894314e-02 
##            pedestrian_crossing_human_control1 
##                                  0.000000e+00 
##            pedestrian_crossing_human_control2 
##                                  0.000000e+00 
##                             light_conditions4 
##                                  8.024086e-05 
##                             light_conditions5 
##                                  0.000000e+00 
##                             light_conditions6 
##                                  1.086487e-05 
##                             light_conditions7 
##                                  0.000000e+00 
##                      road_surface_conditions2 
##                                  3.277032e-04 
##                      road_surface_conditions3 
##                                  0.000000e+00 
##                      road_surface_conditions4 
##                                  0.000000e+00 
##                      road_surface_conditions5 
##                                  0.000000e+00 
## did_police_officer_attend_scene_of_collision1 
##                                  0.000000e+00 
##                                           1|2 
##                                  0.000000e+00 
##                                           2|3 
##                                  0.000000e+00
#💛2_1. combined table with p
ctable <- cbind(ctable, "p value" = p)
ctable
##                                                       Value   Std. Error
## police_force                                   2.803911e-03 1.348752e-03
## number_of_vehicles                             4.223909e-01 4.138042e-02
## number_of_casualties                          -8.624976e-02 3.409343e-02
## first_road_number                             -2.160612e-05 1.933466e-05
## speed_limit                                   -1.064822e-02 2.159821e-03
## junction_detail1                               3.816228e-01 8.564934e-02
## junction_detail2                               1.802745e-01 1.593033e-02
## junction_detail5                              -8.415701e-02 1.478322e-02
## junction_detail6                              -4.358178e-02 6.785642e-02
## junction_detail7                               2.872702e-01 1.895339e-02
## junction_detail8                               8.503491e-02 1.231661e-01
## junction_detail9                               1.785680e-01 7.895421e-02
## junction_control1                              6.040942e-01 1.250450e-03
## junction_control2                              2.583486e-01 6.967706e-02
## junction_control3                              4.060331e-02 3.045438e-03
## second_road_class                             -6.021036e-02 1.900684e-02
## second_road_number                            -4.883946e-05 2.779943e-05
## pedestrian_crossing_human_control1             5.855457e-01 5.607103e-04
## pedestrian_crossing_human_control2             2.941869e-01 4.074396e-03
## light_conditions4                             -2.276838e-01 5.773384e-02
## light_conditions5                             -7.794430e-01 1.610522e-03
## light_conditions6                              3.331103e-02 7.572059e-03
## light_conditions7                              3.449934e-01 1.130846e-03
## road_surface_conditions2                       2.179576e-01 6.067263e-02
## road_surface_conditions3                       7.776016e-01 2.714258e-04
## road_surface_conditions4                       4.717263e-01 1.898218e-03
## road_surface_conditions5                       9.462452e-02 1.275162e-04
## did_police_officer_attend_scene_of_collision1 -8.942235e-01 7.982335e-02
## 1|2                                           -5.221991e+00 1.330876e-02
## 2|3                                           -1.767972e+00 8.623728e-02
##                                                    t value      p value
## police_force                                     2.0788925 3.762723e-02
## number_of_vehicles                              10.2075070 1.835193e-24
## number_of_casualties                            -2.5298061 1.141256e-02
## first_road_number                               -1.1174810 2.637887e-01
## speed_limit                                     -4.9301392 8.217103e-07
## junction_detail1                                 4.4556423 8.364238e-06
## junction_detail2                                11.3164281 1.088159e-29
## junction_detail5                                -5.6927402 1.250165e-08
## junction_detail6                                -0.6422646 5.207014e-01
## junction_detail7                                15.1566633 6.846003e-52
## junction_detail8                                 0.6904081 4.899376e-01
## junction_detail9                                 2.2616649 2.371811e-02
## junction_control1                              483.1013484 0.000000e+00
## junction_control2                                3.7078002 2.090675e-04
## junction_control3                               13.3325044 1.497836e-40
## second_road_class                               -3.1678266 1.535831e-03
## second_road_number                              -1.7568514 7.894314e-02
## pedestrian_crossing_human_control1            1044.2927893 0.000000e+00
## pedestrian_crossing_human_control2              72.2038037 0.000000e+00
## light_conditions4                               -3.9436796 8.024086e-05
## light_conditions5                             -483.9691412 0.000000e+00
## light_conditions6                                4.3992040 1.086487e-05
## light_conditions7                              305.0753981 0.000000e+00
## road_surface_conditions2                         3.5923549 3.277032e-04
## road_surface_conditions3                      2864.8770634 0.000000e+00
## road_surface_conditions4                       248.5100689 0.000000e+00
## road_surface_conditions5                       742.0588304 0.000000e+00
## did_police_officer_attend_scene_of_collision1  -11.2025302 3.962518e-29
## 1|2                                           -392.3724609 0.000000e+00
## 2|3                                            -20.5012455 2.098531e-93
view(ctable)   

#💛2_2. get CI for Log Odds

#If the 95% CI does not cross 0, the parameter estimate is statistically significant.
#CI can be obtained either by profiling the likelihood function (#Method 1, not used in this case) or by using the standard errors and assuming a normal distribution (#Method 2). 

#Method 1: ci <- confint(step_test2) # default method gives profiled CIs
#Method 2:
ci <- confint.default(step_test2) # CIs assuming normality
ci    #CI of Log odds
##                                                       2.5 %        97.5 %
## police_force                                   1.604051e-04  5.447416e-03
## number_of_vehicles                             3.412868e-01  5.034950e-01
## number_of_casualties                          -1.530717e-01 -1.942787e-02
## first_road_number                             -5.950136e-05  1.628912e-05
## speed_limit                                   -1.488139e-02 -6.415048e-03
## junction_detail1                               2.137532e-01  5.494924e-01
## junction_detail2                               1.490516e-01  2.114974e-01
## junction_detail5                              -1.131316e-01 -5.518244e-02
## junction_detail6                              -1.765779e-01  8.941436e-02
## junction_detail7                               2.501222e-01  3.244182e-01
## junction_detail8                              -1.563663e-01  3.264361e-01
## junction_detail9                               2.382056e-02  3.333154e-01
## junction_control1                              6.016434e-01  6.065450e-01
## junction_control2                              1.217841e-01  3.949131e-01
## junction_control3                              3.463436e-02  4.657226e-02
## second_road_class                             -9.746308e-02 -2.295765e-02
## second_road_number                            -1.033253e-04  5.646414e-06
## pedestrian_crossing_human_control1             5.844468e-01  5.866447e-01
## pedestrian_crossing_human_control2             2.862012e-01  3.021726e-01
## light_conditions4                             -3.408400e-01 -1.145275e-01
## light_conditions5                             -7.825995e-01 -7.762864e-01
## light_conditions6                              1.847007e-02  4.815199e-02
## light_conditions7                              3.427770e-01  3.472098e-01
## road_surface_conditions2                       9.904145e-02  3.368738e-01
## road_surface_conditions3                       7.770697e-01  7.781336e-01
## road_surface_conditions4                       4.680059e-01  4.754467e-01
## road_surface_conditions5                       9.437459e-02  9.487444e-02
## did_police_officer_attend_scene_of_collision1 -1.050674e+00 -7.377726e-01
summary(step_test2)$coef
##                                                       Value   Std. Error
## police_force                                   2.803911e-03 1.348752e-03
## number_of_vehicles                             4.223909e-01 4.138042e-02
## number_of_casualties                          -8.624976e-02 3.409343e-02
## first_road_number                             -2.160612e-05 1.933466e-05
## speed_limit                                   -1.064822e-02 2.159821e-03
## junction_detail1                               3.816228e-01 8.564934e-02
## junction_detail2                               1.802745e-01 1.593033e-02
## junction_detail5                              -8.415701e-02 1.478322e-02
## junction_detail6                              -4.358178e-02 6.785642e-02
## junction_detail7                               2.872702e-01 1.895339e-02
## junction_detail8                               8.503491e-02 1.231661e-01
## junction_detail9                               1.785680e-01 7.895421e-02
## junction_control1                              6.040942e-01 1.250450e-03
## junction_control2                              2.583486e-01 6.967706e-02
## junction_control3                              4.060331e-02 3.045438e-03
## second_road_class                             -6.021036e-02 1.900684e-02
## second_road_number                            -4.883946e-05 2.779943e-05
## pedestrian_crossing_human_control1             5.855457e-01 5.607103e-04
## pedestrian_crossing_human_control2             2.941869e-01 4.074396e-03
## light_conditions4                             -2.276838e-01 5.773384e-02
## light_conditions5                             -7.794430e-01 1.610522e-03
## light_conditions6                              3.331103e-02 7.572059e-03
## light_conditions7                              3.449934e-01 1.130846e-03
## road_surface_conditions2                       2.179576e-01 6.067263e-02
## road_surface_conditions3                       7.776016e-01 2.714258e-04
## road_surface_conditions4                       4.717263e-01 1.898218e-03
## road_surface_conditions5                       9.462452e-02 1.275162e-04
## did_police_officer_attend_scene_of_collision1 -8.942235e-01 7.982335e-02
## 1|2                                           -5.221991e+00 1.330876e-02
## 2|3                                           -1.767972e+00 8.623728e-02
##                                                    t value
## police_force                                     2.0788925
## number_of_vehicles                              10.2075070
## number_of_casualties                            -2.5298061
## first_road_number                               -1.1174810
## speed_limit                                     -4.9301392
## junction_detail1                                 4.4556423
## junction_detail2                                11.3164281
## junction_detail5                                -5.6927402
## junction_detail6                                -0.6422646
## junction_detail7                                15.1566633
## junction_detail8                                 0.6904081
## junction_detail9                                 2.2616649
## junction_control1                              483.1013484
## junction_control2                                3.7078002
## junction_control3                               13.3325044
## second_road_class                               -3.1678266
## second_road_number                              -1.7568514
## pedestrian_crossing_human_control1            1044.2927893
## pedestrian_crossing_human_control2              72.2038037
## light_conditions4                               -3.9436796
## light_conditions5                             -483.9691412
## light_conditions6                                4.3992040
## light_conditions7                              305.0753981
## road_surface_conditions2                         3.5923549
## road_surface_conditions3                      2864.8770634
## road_surface_conditions4                       248.5100689
## road_surface_conditions5                       742.0588304
## did_police_officer_attend_scene_of_collision1  -11.2025302
## 1|2                                           -392.3724609
## 2|3                                            -20.5012455
exp(8.503491e-02)
## [1] 1.088755
cat("Only the CIs for 'first_road_number', 'second_road_number', 'junction_detail'(6 and 8) do include 0, while all others  don't. It means that for 'junction_detail' going from 3 to 6,  we expect a  0.0436 decrease in the expected value of 'legacy_of_severity' on the log odds scale, given all of the other variables in the model are held constant. for 'junction_detail' going from 3 to 8,  we expect a  0.1487 decrease in the expected value of 'legacy_of_severity'.
Similarly, for one unit increase in 'first_road_number' or 'second_road_number' ', we would expect a 2.161e-05 or -4.883946e-05  insignificant decrease in the expected value of 'legacy_of_severity' in the log odds scale, given that all of the other variables in the model are held constant.")
## Only the CIs for 'first_road_number', 'second_road_number', 'junction_detail'(6 and 8) do include 0, while all others  don't. It means that for 'junction_detail' going from 3 to 6,  we expect a  0.0436 decrease in the expected value of 'legacy_of_severity' on the log odds scale, given all of the other variables in the model are held constant. for 'junction_detail' going from 3 to 8,  we expect a  0.1487 decrease in the expected value of 'legacy_of_severity'.
## Similarly, for one unit increase in 'first_road_number' or 'second_road_number' ', we would expect a 2.161e-05 or -4.883946e-05  insignificant decrease in the expected value of 'legacy_of_severity' in the log odds scale, given that all of the other variables in the model are held constant.
#💛2_3. get odds ratios

step_test2.or <-  exp(coef(step_test2))
step_test2.or  #Odds ratio 
##                                  police_force 
##                                     1.0028078 
##                            number_of_vehicles 
##                                     1.5256048 
##                          number_of_casualties 
##                                     0.9173651 
##                             first_road_number 
##                                     0.9999784 
##                                   speed_limit 
##                                     0.9894083 
##                              junction_detail1 
##                                     1.4646595 
##                              junction_detail2 
##                                     1.1975460 
##                              junction_detail5 
##                                     0.9192869 
##                              junction_detail6 
##                                     0.9573543 
##                              junction_detail7 
##                                     1.3327843 
##                              junction_detail8 
##                                     1.0887551 
##                              junction_detail9 
##                                     1.1955041 
##                             junction_control1 
##                                     1.8295942 
##                             junction_control2 
##                                     1.2947901 
##                             junction_control3 
##                                     1.0414389 
##                             second_road_class 
##                                     0.9415664 
##                            second_road_number 
##                                     0.9999512 
##            pedestrian_crossing_human_control1 
##                                     1.7959708 
##            pedestrian_crossing_human_control2 
##                                     1.3420347 
##                             light_conditions4 
##                                     0.7963761 
##                             light_conditions5 
##                                     0.4586614 
##                             light_conditions6 
##                                     1.0338721 
##                             light_conditions7 
##                                     1.4119806 
##                      road_surface_conditions2 
##                                     1.2435344 
##                      road_surface_conditions3 
##                                     2.1762466 
##                      road_surface_conditions4 
##                                     1.6027586 
##                      road_surface_conditions5 
##                                     1.0992460 
## did_police_officer_attend_scene_of_collision1 
##                                     0.4089250
#For example, the odds ratio for junction_detail(1) is 1.4647, which means that the event is 1.4647 times more likely to occur in 1 : the  Roundabout junction_detail group than in Baseline 3: T or staggered junction_detail group.

#💛2_4. combine odds ratio with coefficient and p_value
ctable <- cbind(ctable, "odds ratio" = step_test2.or)
## Warning in cbind(ctable, `odds ratio` = step_test2.or): number of rows of
## result is not a multiple of vector length (arg 2)
ctable    #Origin of Table 4 in https://www.mdpi.com/2071-1050/14/6/3188
##                                                       Value   Std. Error
## police_force                                   2.803911e-03 1.348752e-03
## number_of_vehicles                             4.223909e-01 4.138042e-02
## number_of_casualties                          -8.624976e-02 3.409343e-02
## first_road_number                             -2.160612e-05 1.933466e-05
## speed_limit                                   -1.064822e-02 2.159821e-03
## junction_detail1                               3.816228e-01 8.564934e-02
## junction_detail2                               1.802745e-01 1.593033e-02
## junction_detail5                              -8.415701e-02 1.478322e-02
## junction_detail6                              -4.358178e-02 6.785642e-02
## junction_detail7                               2.872702e-01 1.895339e-02
## junction_detail8                               8.503491e-02 1.231661e-01
## junction_detail9                               1.785680e-01 7.895421e-02
## junction_control1                              6.040942e-01 1.250450e-03
## junction_control2                              2.583486e-01 6.967706e-02
## junction_control3                              4.060331e-02 3.045438e-03
## second_road_class                             -6.021036e-02 1.900684e-02
## second_road_number                            -4.883946e-05 2.779943e-05
## pedestrian_crossing_human_control1             5.855457e-01 5.607103e-04
## pedestrian_crossing_human_control2             2.941869e-01 4.074396e-03
## light_conditions4                             -2.276838e-01 5.773384e-02
## light_conditions5                             -7.794430e-01 1.610522e-03
## light_conditions6                              3.331103e-02 7.572059e-03
## light_conditions7                              3.449934e-01 1.130846e-03
## road_surface_conditions2                       2.179576e-01 6.067263e-02
## road_surface_conditions3                       7.776016e-01 2.714258e-04
## road_surface_conditions4                       4.717263e-01 1.898218e-03
## road_surface_conditions5                       9.462452e-02 1.275162e-04
## did_police_officer_attend_scene_of_collision1 -8.942235e-01 7.982335e-02
## 1|2                                           -5.221991e+00 1.330876e-02
## 2|3                                           -1.767972e+00 8.623728e-02
##                                                    t value      p value
## police_force                                     2.0788925 3.762723e-02
## number_of_vehicles                              10.2075070 1.835193e-24
## number_of_casualties                            -2.5298061 1.141256e-02
## first_road_number                               -1.1174810 2.637887e-01
## speed_limit                                     -4.9301392 8.217103e-07
## junction_detail1                                 4.4556423 8.364238e-06
## junction_detail2                                11.3164281 1.088159e-29
## junction_detail5                                -5.6927402 1.250165e-08
## junction_detail6                                -0.6422646 5.207014e-01
## junction_detail7                                15.1566633 6.846003e-52
## junction_detail8                                 0.6904081 4.899376e-01
## junction_detail9                                 2.2616649 2.371811e-02
## junction_control1                              483.1013484 0.000000e+00
## junction_control2                                3.7078002 2.090675e-04
## junction_control3                               13.3325044 1.497836e-40
## second_road_class                               -3.1678266 1.535831e-03
## second_road_number                              -1.7568514 7.894314e-02
## pedestrian_crossing_human_control1            1044.2927893 0.000000e+00
## pedestrian_crossing_human_control2              72.2038037 0.000000e+00
## light_conditions4                               -3.9436796 8.024086e-05
## light_conditions5                             -483.9691412 0.000000e+00
## light_conditions6                                4.3992040 1.086487e-05
## light_conditions7                              305.0753981 0.000000e+00
## road_surface_conditions2                         3.5923549 3.277032e-04
## road_surface_conditions3                      2864.8770634 0.000000e+00
## road_surface_conditions4                       248.5100689 0.000000e+00
## road_surface_conditions5                       742.0588304 0.000000e+00
## did_police_officer_attend_scene_of_collision1  -11.2025302 3.962518e-29
## 1|2                                           -392.3724609 0.000000e+00
## 2|3                                            -20.5012455 2.098531e-93
##                                               odds ratio
## police_force                                   1.0028078
## number_of_vehicles                             1.5256048
## number_of_casualties                           0.9173651
## first_road_number                              0.9999784
## speed_limit                                    0.9894083
## junction_detail1                               1.4646595
## junction_detail2                               1.1975460
## junction_detail5                               0.9192869
## junction_detail6                               0.9573543
## junction_detail7                               1.3327843
## junction_detail8                               1.0887551
## junction_detail9                               1.1955041
## junction_control1                              1.8295942
## junction_control2                              1.2947901
## junction_control3                              1.0414389
## second_road_class                              0.9415664
## second_road_number                             0.9999512
## pedestrian_crossing_human_control1             1.7959708
## pedestrian_crossing_human_control2             1.3420347
## light_conditions4                              0.7963761
## light_conditions5                              0.4586614
## light_conditions6                              1.0338721
## light_conditions7                              1.4119806
## road_surface_conditions2                       1.2435344
## road_surface_conditions3                       2.1762466
## road_surface_conditions4                       1.6027586
## road_surface_conditions5                       1.0992460
## did_police_officer_attend_scene_of_collision1  0.4089250
## 1|2                                            1.0028078
## 2|3                                            1.5256048
view(ctable)  

cat(paste("comment:\n","The OR=0.9192 of junction_detail(5) means the '5: Slip road ' junction_detail reduced the probability of severity by approximately 91.92% compared to the '3: T or staggered' junction_detail.\n","The OR=0.4587 of sexmale means the '5: Darkness: street lights present but unlit' light_conditions reduced the probability of severity by approximately 45.87% compared to baseline '1: Daylight' light_conditions."))
## comment:
##  The OR=0.9192 of junction_detail(5) means the '5: Slip road ' junction_detail reduced the probability of severity by approximately 91.92% compared to the '3: T or staggered' junction_detail.
##  The OR=0.4587 of sexmale means the '5: Darkness: street lights present but unlit' light_conditions reduced the probability of severity by approximately 45.87% compared to baseline '1: Daylight' light_conditions.
#Table 4.3
Table4_3 <- ctable[,c(1,5,2,4)]
Table4_3
##                                                       Value odds ratio
## police_force                                   2.803911e-03  1.0028078
## number_of_vehicles                             4.223909e-01  1.5256048
## number_of_casualties                          -8.624976e-02  0.9173651
## first_road_number                             -2.160612e-05  0.9999784
## speed_limit                                   -1.064822e-02  0.9894083
## junction_detail1                               3.816228e-01  1.4646595
## junction_detail2                               1.802745e-01  1.1975460
## junction_detail5                              -8.415701e-02  0.9192869
## junction_detail6                              -4.358178e-02  0.9573543
## junction_detail7                               2.872702e-01  1.3327843
## junction_detail8                               8.503491e-02  1.0887551
## junction_detail9                               1.785680e-01  1.1955041
## junction_control1                              6.040942e-01  1.8295942
## junction_control2                              2.583486e-01  1.2947901
## junction_control3                              4.060331e-02  1.0414389
## second_road_class                             -6.021036e-02  0.9415664
## second_road_number                            -4.883946e-05  0.9999512
## pedestrian_crossing_human_control1             5.855457e-01  1.7959708
## pedestrian_crossing_human_control2             2.941869e-01  1.3420347
## light_conditions4                             -2.276838e-01  0.7963761
## light_conditions5                             -7.794430e-01  0.4586614
## light_conditions6                              3.331103e-02  1.0338721
## light_conditions7                              3.449934e-01  1.4119806
## road_surface_conditions2                       2.179576e-01  1.2435344
## road_surface_conditions3                       7.776016e-01  2.1762466
## road_surface_conditions4                       4.717263e-01  1.6027586
## road_surface_conditions5                       9.462452e-02  1.0992460
## did_police_officer_attend_scene_of_collision1 -8.942235e-01  0.4089250
## 1|2                                           -5.221991e+00  1.0028078
## 2|3                                           -1.767972e+00  1.5256048
##                                                 Std. Error      p value
## police_force                                  1.348752e-03 3.762723e-02
## number_of_vehicles                            4.138042e-02 1.835193e-24
## number_of_casualties                          3.409343e-02 1.141256e-02
## first_road_number                             1.933466e-05 2.637887e-01
## speed_limit                                   2.159821e-03 8.217103e-07
## junction_detail1                              8.564934e-02 8.364238e-06
## junction_detail2                              1.593033e-02 1.088159e-29
## junction_detail5                              1.478322e-02 1.250165e-08
## junction_detail6                              6.785642e-02 5.207014e-01
## junction_detail7                              1.895339e-02 6.846003e-52
## junction_detail8                              1.231661e-01 4.899376e-01
## junction_detail9                              7.895421e-02 2.371811e-02
## junction_control1                             1.250450e-03 0.000000e+00
## junction_control2                             6.967706e-02 2.090675e-04
## junction_control3                             3.045438e-03 1.497836e-40
## second_road_class                             1.900684e-02 1.535831e-03
## second_road_number                            2.779943e-05 7.894314e-02
## pedestrian_crossing_human_control1            5.607103e-04 0.000000e+00
## pedestrian_crossing_human_control2            4.074396e-03 0.000000e+00
## light_conditions4                             5.773384e-02 8.024086e-05
## light_conditions5                             1.610522e-03 0.000000e+00
## light_conditions6                             7.572059e-03 1.086487e-05
## light_conditions7                             1.130846e-03 0.000000e+00
## road_surface_conditions2                      6.067263e-02 3.277032e-04
## road_surface_conditions3                      2.714258e-04 0.000000e+00
## road_surface_conditions4                      1.898218e-03 0.000000e+00
## road_surface_conditions5                      1.275162e-04 0.000000e+00
## did_police_officer_attend_scene_of_collision1 7.982335e-02 3.962518e-29
## 1|2                                           1.330876e-02 0.000000e+00
## 2|3                                           8.623728e-02 2.098531e-93
Table4_3[, 1:ncol(Table4_3)] <- round(Table4_3[, 1:ncol(Table4_3)], 3)
Table4_3
##                                                Value odds ratio Std. Error
## police_force                                   0.003      1.003      0.001
## number_of_vehicles                             0.422      1.526      0.041
## number_of_casualties                          -0.086      0.917      0.034
## first_road_number                              0.000      1.000      0.000
## speed_limit                                   -0.011      0.989      0.002
## junction_detail1                               0.382      1.465      0.086
## junction_detail2                               0.180      1.198      0.016
## junction_detail5                              -0.084      0.919      0.015
## junction_detail6                              -0.044      0.957      0.068
## junction_detail7                               0.287      1.333      0.019
## junction_detail8                               0.085      1.089      0.123
## junction_detail9                               0.179      1.196      0.079
## junction_control1                              0.604      1.830      0.001
## junction_control2                              0.258      1.295      0.070
## junction_control3                              0.041      1.041      0.003
## second_road_class                             -0.060      0.942      0.019
## second_road_number                             0.000      1.000      0.000
## pedestrian_crossing_human_control1             0.586      1.796      0.001
## pedestrian_crossing_human_control2             0.294      1.342      0.004
## light_conditions4                             -0.228      0.796      0.058
## light_conditions5                             -0.779      0.459      0.002
## light_conditions6                              0.033      1.034      0.008
## light_conditions7                              0.345      1.412      0.001
## road_surface_conditions2                       0.218      1.244      0.061
## road_surface_conditions3                       0.778      2.176      0.000
## road_surface_conditions4                       0.472      1.603      0.002
## road_surface_conditions5                       0.095      1.099      0.000
## did_police_officer_attend_scene_of_collision1 -0.894      0.409      0.080
## 1|2                                           -5.222      1.003      0.013
## 2|3                                           -1.768      1.526      0.086
##                                               p value
## police_force                                    0.038
## number_of_vehicles                              0.000
## number_of_casualties                            0.011
## first_road_number                               0.264
## speed_limit                                     0.000
## junction_detail1                                0.000
## junction_detail2                                0.000
## junction_detail5                                0.000
## junction_detail6                                0.521
## junction_detail7                                0.000
## junction_detail8                                0.490
## junction_detail9                                0.024
## junction_control1                               0.000
## junction_control2                               0.000
## junction_control3                               0.000
## second_road_class                               0.002
## second_road_number                              0.079
## pedestrian_crossing_human_control1              0.000
## pedestrian_crossing_human_control2              0.000
## light_conditions4                               0.000
## light_conditions5                               0.000
## light_conditions6                               0.000
## light_conditions7                               0.000
## road_surface_conditions2                        0.000
## road_surface_conditions3                        0.000
## road_surface_conditions4                        0.000
## road_surface_conditions5                        0.000
## did_police_officer_attend_scene_of_collision1   0.000
## 1|2                                             0.000
## 2|3                                             0.000
library(fpp3)
view(Table4_3)
#💚3 Output tables of Ordered logit models 
 
#💛3_1...for the raw estimations of logit coefficients  

library(stargazer)
table1 <- stargazer(step_test2, type="text", out="logit.htm")   
## 
## =========================================================================
##                                                   Dependent variable:    
##                                               ---------------------------
##                                                legacy_collision_severity 
## -------------------------------------------------------------------------
## police_force                                            0.003**          
##                                                         (0.001)          
##                                                                          
## number_of_vehicles                                     0.422***          
##                                                         (0.041)          
##                                                                          
## number_of_casualties                                   -0.086**          
##                                                         (0.034)          
##                                                                          
## first_road_number                                      -0.00002          
##                                                        (0.00002)         
##                                                                          
## speed_limit                                            -0.011***         
##                                                         (0.002)          
##                                                                          
## junction_detail1                                       0.382***          
##                                                         (0.086)          
##                                                                          
## junction_detail2                                       0.180***          
##                                                         (0.016)          
##                                                                          
## junction_detail5                                       -0.084***         
##                                                         (0.015)          
##                                                                          
## junction_detail6                                        -0.044           
##                                                         (0.068)          
##                                                                          
## junction_detail7                                       0.287***          
##                                                         (0.019)          
##                                                                          
## junction_detail8                                         0.085           
##                                                         (0.123)          
##                                                                          
## junction_detail9                                        0.179**          
##                                                         (0.079)          
##                                                                          
## junction_control1                                      0.604***          
##                                                         (0.001)          
##                                                                          
## junction_control2                                      0.258***          
##                                                         (0.070)          
##                                                                          
## junction_control3                                      0.041***          
##                                                         (0.003)          
##                                                                          
## second_road_class                                      -0.060***         
##                                                         (0.019)          
##                                                                          
## second_road_number                                     -0.00005*         
##                                                        (0.00003)         
##                                                                          
## pedestrian_crossing_human_control1                     0.586***          
##                                                         (0.001)          
##                                                                          
## pedestrian_crossing_human_control2                     0.294***          
##                                                         (0.004)          
##                                                                          
## light_conditions4                                      -0.228***         
##                                                         (0.058)          
##                                                                          
## light_conditions5                                      -0.779***         
##                                                         (0.002)          
##                                                                          
## light_conditions6                                      0.033***          
##                                                         (0.008)          
##                                                                          
## light_conditions7                                      0.345***          
##                                                         (0.001)          
##                                                                          
## road_surface_conditions2                               0.218***          
##                                                         (0.061)          
##                                                                          
## road_surface_conditions3                               0.778***          
##                                                        (0.0003)          
##                                                                          
## road_surface_conditions4                               0.472***          
##                                                         (0.002)          
##                                                                          
## road_surface_conditions5                               0.095***          
##                                                        (0.0001)          
##                                                                          
## did_police_officer_attend_scene_of_collision1          -0.894***         
##                                                         (0.080)          
##                                                                          
## -------------------------------------------------------------------------
## Observations                                             9,550           
## =========================================================================
## Note:                                         *p<0.1; **p<0.05; ***p<0.01
table1 
##  [1] ""                                                                         
##  [2] "========================================================================="
##  [3] "                                                  Dependent variable:    "
##  [4] "                                              ---------------------------"
##  [5] "                                               legacy_collision_severity "
##  [6] "-------------------------------------------------------------------------"
##  [7] "police_force                                            0.003**          "
##  [8] "                                                        (0.001)          "
##  [9] "                                                                         "
## [10] "number_of_vehicles                                     0.422***          "
## [11] "                                                        (0.041)          "
## [12] "                                                                         "
## [13] "number_of_casualties                                   -0.086**          "
## [14] "                                                        (0.034)          "
## [15] "                                                                         "
## [16] "first_road_number                                      -0.00002          "
## [17] "                                                       (0.00002)         "
## [18] "                                                                         "
## [19] "speed_limit                                            -0.011***         "
## [20] "                                                        (0.002)          "
## [21] "                                                                         "
## [22] "junction_detail1                                       0.382***          "
## [23] "                                                        (0.086)          "
## [24] "                                                                         "
## [25] "junction_detail2                                       0.180***          "
## [26] "                                                        (0.016)          "
## [27] "                                                                         "
## [28] "junction_detail5                                       -0.084***         "
## [29] "                                                        (0.015)          "
## [30] "                                                                         "
## [31] "junction_detail6                                        -0.044           "
## [32] "                                                        (0.068)          "
## [33] "                                                                         "
## [34] "junction_detail7                                       0.287***          "
## [35] "                                                        (0.019)          "
## [36] "                                                                         "
## [37] "junction_detail8                                         0.085           "
## [38] "                                                        (0.123)          "
## [39] "                                                                         "
## [40] "junction_detail9                                        0.179**          "
## [41] "                                                        (0.079)          "
## [42] "                                                                         "
## [43] "junction_control1                                      0.604***          "
## [44] "                                                        (0.001)          "
## [45] "                                                                         "
## [46] "junction_control2                                      0.258***          "
## [47] "                                                        (0.070)          "
## [48] "                                                                         "
## [49] "junction_control3                                      0.041***          "
## [50] "                                                        (0.003)          "
## [51] "                                                                         "
## [52] "second_road_class                                      -0.060***         "
## [53] "                                                        (0.019)          "
## [54] "                                                                         "
## [55] "second_road_number                                     -0.00005*         "
## [56] "                                                       (0.00003)         "
## [57] "                                                                         "
## [58] "pedestrian_crossing_human_control1                     0.586***          "
## [59] "                                                        (0.001)          "
## [60] "                                                                         "
## [61] "pedestrian_crossing_human_control2                     0.294***          "
## [62] "                                                        (0.004)          "
## [63] "                                                                         "
## [64] "light_conditions4                                      -0.228***         "
## [65] "                                                        (0.058)          "
## [66] "                                                                         "
## [67] "light_conditions5                                      -0.779***         "
## [68] "                                                        (0.002)          "
## [69] "                                                                         "
## [70] "light_conditions6                                      0.033***          "
## [71] "                                                        (0.008)          "
## [72] "                                                                         "
## [73] "light_conditions7                                      0.345***          "
## [74] "                                                        (0.001)          "
## [75] "                                                                         "
## [76] "road_surface_conditions2                               0.218***          "
## [77] "                                                        (0.061)          "
## [78] "                                                                         "
## [79] "road_surface_conditions3                               0.778***          "
## [80] "                                                       (0.0003)          "
## [81] "                                                                         "
## [82] "road_surface_conditions4                               0.472***          "
## [83] "                                                        (0.002)          "
## [84] "                                                                         "
## [85] "road_surface_conditions5                               0.095***          "
## [86] "                                                       (0.0001)          "
## [87] "                                                                         "
## [88] "did_police_officer_attend_scene_of_collision1          -0.894***         "
## [89] "                                                        (0.080)          "
## [90] "                                                                         "
## [91] "-------------------------------------------------------------------------"
## [92] "Observations                                             9,550           "
## [93] "========================================================================="
## [94] "Note:                                         *p<0.1; **p<0.05; ***p<0.01"
#We might prefer to print an output table of odds rather than an output table of raw estimates.
#💛3_2. Output tables of Odds Ratios
#step_test2.or <-  exp(coef(step_test2))   is value of odds ratio
step_test2.or
##                                  police_force 
##                                     1.0028078 
##                            number_of_vehicles 
##                                     1.5256048 
##                          number_of_casualties 
##                                     0.9173651 
##                             first_road_number 
##                                     0.9999784 
##                                   speed_limit 
##                                     0.9894083 
##                              junction_detail1 
##                                     1.4646595 
##                              junction_detail2 
##                                     1.1975460 
##                              junction_detail5 
##                                     0.9192869 
##                              junction_detail6 
##                                     0.9573543 
##                              junction_detail7 
##                                     1.3327843 
##                              junction_detail8 
##                                     1.0887551 
##                              junction_detail9 
##                                     1.1955041 
##                             junction_control1 
##                                     1.8295942 
##                             junction_control2 
##                                     1.2947901 
##                             junction_control3 
##                                     1.0414389 
##                             second_road_class 
##                                     0.9415664 
##                            second_road_number 
##                                     0.9999512 
##            pedestrian_crossing_human_control1 
##                                     1.7959708 
##            pedestrian_crossing_human_control2 
##                                     1.3420347 
##                             light_conditions4 
##                                     0.7963761 
##                             light_conditions5 
##                                     0.4586614 
##                             light_conditions6 
##                                     1.0338721 
##                             light_conditions7 
##                                     1.4119806 
##                      road_surface_conditions2 
##                                     1.2435344 
##                      road_surface_conditions3 
##                                     2.1762466 
##                      road_surface_conditions4 
##                                     1.6027586 
##                      road_surface_conditions5 
##                                     1.0992460 
## did_police_officer_attend_scene_of_collision1 
##                                     0.4089250
#Create using the stargazer() function
table2 <- stargazer(step_test2, type="text", coef=list(step_test2.or), p.auto=FALSE, out="m1or.htm")
## 
## =========================================================================
##                                                   Dependent variable:    
##                                               ---------------------------
##                                                legacy_collision_severity 
## -------------------------------------------------------------------------
## police_force                                            1.003**          
##                                                         (0.001)          
##                                                                          
## number_of_vehicles                                     1.526***          
##                                                         (0.041)          
##                                                                          
## number_of_casualties                                    0.917**          
##                                                         (0.034)          
##                                                                          
## first_road_number                                        1.000           
##                                                        (0.00002)         
##                                                                          
## speed_limit                                            0.989***          
##                                                         (0.002)          
##                                                                          
## junction_detail1                                       1.465***          
##                                                         (0.086)          
##                                                                          
## junction_detail2                                       1.198***          
##                                                         (0.016)          
##                                                                          
## junction_detail5                                       0.919***          
##                                                         (0.015)          
##                                                                          
## junction_detail6                                         0.957           
##                                                         (0.068)          
##                                                                          
## junction_detail7                                       1.333***          
##                                                         (0.019)          
##                                                                          
## junction_detail8                                         1.089           
##                                                         (0.123)          
##                                                                          
## junction_detail9                                        1.196**          
##                                                         (0.079)          
##                                                                          
## junction_control1                                      1.830***          
##                                                         (0.001)          
##                                                                          
## junction_control2                                      1.295***          
##                                                         (0.070)          
##                                                                          
## junction_control3                                      1.041***          
##                                                         (0.003)          
##                                                                          
## second_road_class                                      0.942***          
##                                                         (0.019)          
##                                                                          
## second_road_number                                      1.000*           
##                                                        (0.00003)         
##                                                                          
## pedestrian_crossing_human_control1                     1.796***          
##                                                         (0.001)          
##                                                                          
## pedestrian_crossing_human_control2                     1.342***          
##                                                         (0.004)          
##                                                                          
## light_conditions4                                      0.796***          
##                                                         (0.058)          
##                                                                          
## light_conditions5                                      0.459***          
##                                                         (0.002)          
##                                                                          
## light_conditions6                                      1.034***          
##                                                         (0.008)          
##                                                                          
## light_conditions7                                      1.412***          
##                                                         (0.001)          
##                                                                          
## road_surface_conditions2                               1.244***          
##                                                         (0.061)          
##                                                                          
## road_surface_conditions3                               2.176***          
##                                                        (0.0003)          
##                                                                          
## road_surface_conditions4                               1.603***          
##                                                         (0.002)          
##                                                                          
## road_surface_conditions5                               1.099***          
##                                                        (0.0001)          
##                                                                          
## did_police_officer_attend_scene_of_collision1          0.409***          
##                                                         (0.080)          
##                                                                          
## -------------------------------------------------------------------------
## Observations                                             9,550           
## =========================================================================
## Note:                                         *p<0.1; **p<0.05; ***p<0.01
table2
##  [1] ""                                                                         
##  [2] "========================================================================="
##  [3] "                                                  Dependent variable:    "
##  [4] "                                              ---------------------------"
##  [5] "                                               legacy_collision_severity "
##  [6] "-------------------------------------------------------------------------"
##  [7] "police_force                                            1.003**          "
##  [8] "                                                        (0.001)          "
##  [9] "                                                                         "
## [10] "number_of_vehicles                                     1.526***          "
## [11] "                                                        (0.041)          "
## [12] "                                                                         "
## [13] "number_of_casualties                                    0.917**          "
## [14] "                                                        (0.034)          "
## [15] "                                                                         "
## [16] "first_road_number                                        1.000           "
## [17] "                                                       (0.00002)         "
## [18] "                                                                         "
## [19] "speed_limit                                            0.989***          "
## [20] "                                                        (0.002)          "
## [21] "                                                                         "
## [22] "junction_detail1                                       1.465***          "
## [23] "                                                        (0.086)          "
## [24] "                                                                         "
## [25] "junction_detail2                                       1.198***          "
## [26] "                                                        (0.016)          "
## [27] "                                                                         "
## [28] "junction_detail5                                       0.919***          "
## [29] "                                                        (0.015)          "
## [30] "                                                                         "
## [31] "junction_detail6                                         0.957           "
## [32] "                                                        (0.068)          "
## [33] "                                                                         "
## [34] "junction_detail7                                       1.333***          "
## [35] "                                                        (0.019)          "
## [36] "                                                                         "
## [37] "junction_detail8                                         1.089           "
## [38] "                                                        (0.123)          "
## [39] "                                                                         "
## [40] "junction_detail9                                        1.196**          "
## [41] "                                                        (0.079)          "
## [42] "                                                                         "
## [43] "junction_control1                                      1.830***          "
## [44] "                                                        (0.001)          "
## [45] "                                                                         "
## [46] "junction_control2                                      1.295***          "
## [47] "                                                        (0.070)          "
## [48] "                                                                         "
## [49] "junction_control3                                      1.041***          "
## [50] "                                                        (0.003)          "
## [51] "                                                                         "
## [52] "second_road_class                                      0.942***          "
## [53] "                                                        (0.019)          "
## [54] "                                                                         "
## [55] "second_road_number                                      1.000*           "
## [56] "                                                       (0.00003)         "
## [57] "                                                                         "
## [58] "pedestrian_crossing_human_control1                     1.796***          "
## [59] "                                                        (0.001)          "
## [60] "                                                                         "
## [61] "pedestrian_crossing_human_control2                     1.342***          "
## [62] "                                                        (0.004)          "
## [63] "                                                                         "
## [64] "light_conditions4                                      0.796***          "
## [65] "                                                        (0.058)          "
## [66] "                                                                         "
## [67] "light_conditions5                                      0.459***          "
## [68] "                                                        (0.002)          "
## [69] "                                                                         "
## [70] "light_conditions6                                      1.034***          "
## [71] "                                                        (0.008)          "
## [72] "                                                                         "
## [73] "light_conditions7                                      1.412***          "
## [74] "                                                        (0.001)          "
## [75] "                                                                         "
## [76] "road_surface_conditions2                               1.244***          "
## [77] "                                                        (0.061)          "
## [78] "                                                                         "
## [79] "road_surface_conditions3                               2.176***          "
## [80] "                                                       (0.0003)          "
## [81] "                                                                         "
## [82] "road_surface_conditions4                               1.603***          "
## [83] "                                                        (0.002)          "
## [84] "                                                                         "
## [85] "road_surface_conditions5                               1.099***          "
## [86] "                                                       (0.0001)          "
## [87] "                                                                         "
## [88] "did_police_officer_attend_scene_of_collision1          0.409***          "
## [89] "                                                        (0.080)          "
## [90] "                                                                         "
## [91] "-------------------------------------------------------------------------"
## [92] "Observations                                             9,550           "
## [93] "========================================================================="
## [94] "Note:                                         *p<0.1; **p<0.05; ***p<0.01"
#💛3_3. Explain the odds ratio 

cat("In table2, holding all other variables constant, when 'number_of_vehicles' increases by one unit, 'severity' is 1.526 times more likely to belong to a higher-level category(e.g. from 2: Serious to 1: Fatal, from 3: Slight to 2: Serious). The coefficient of it is significant.")
## In table2, holding all other variables constant, when 'number_of_vehicles' increases by one unit, 'severity' is 1.526 times more likely to belong to a higher-level category(e.g. from 2: Serious to 1: Fatal, from 3: Slight to 2: Serious). The coefficient of it is significant.
#💚4  Predicted probabilities of Ordered logit models 

#💛4_1. Use the predict() function to predict the probability of the categorical response variable 'legacy_of_severity' (3 severity levels)

step_test2.pred <- predict(step_test2, type="prob")  
view(step_test2.pred)
head(step_test2.pred)
##             1         2         3
## 1 0.009798059 0.2285594 0.7616425
## 2 0.010426830 0.2395244 0.7500488
## 3 0.014829830 0.3077033 0.6774669
## 4 0.008627809 0.2072114 0.7841608
## 5 0.008886696 0.2120434 0.7790699
## 6 0.012671104 0.2760384 0.7112905
summary(step_test2.pred)#with 1000 observations, (Mean: 0.0108944   Mean: 0.23898   Mean: 0.7501) is the predicted probability of the Mean of each 'severity' after 1000 trials.
##        1                   2                 3         
##  Min.   :0.0007909   Min.   :0.02363   Min.   :0.4206  
##  1st Qu.:0.0075850   1st Qu.:0.18708   1st Qu.:0.6961  
##  Median :0.0107223   Median :0.24456   Median :0.7447  
##  Mean   :0.0108944   Mean   :0.23898   Mean   :0.7501  
##  3rd Qu.:0.0136188   3rd Qu.:0.29033   3rd Qu.:0.8053  
##  Max.   :0.0417351   Max.   :0.53765   Max.   :0.9756
data22 <- cbind(data4, step_test2.pred)
view(data22)
head(data22)
##   police_force legacy_collision_severity number_of_vehicles
## 1            1                         3                  1
## 2            1                         3                  2
## 3            1                         3                  2
## 4            1                         3                  2
## 5            1                         3                  2
## 6            1                         3                  1
##   number_of_casualties day_of_week first_road_class first_road_number road_type
## 1                    1           1                5                 0         2
## 2                    1           1                3               437         1
## 3                    1           1                3              3220         6
## 4                    1           1                3                 3         6
## 5                    3           1                6                 0         1
## 6                    1           1                3               503         3
##   speed_limit junction_detail junction_control second_road_class
## 1          20               9                4                 5
## 2          30               1                4                 6
## 3          30               8                4                 6
## 4          20               6                2                 3
## 5          20               1                4                 6
## 6          30               6                2                 3
##   second_road_number pedestrian_crossing_human_control
## 1                  0                                 2
## 2                  0                                 0
## 3                  0                                 0
## 4               3202                                 0
## 5                  0                                 0
## 6                105                                 0
##   pedestrian_crossing_physical_facilities light_conditions weather_conditions
## 1                                       5                4                  8
## 2                                       0                4                  1
## 3                                       0                4                  1
## 4                                       0                4                  1
## 5                                       0                4                  2
## 6                                       5                4                  2
##   road_surface_conditions special_conditions_at_site carriageway_hazards
## 1                       2                          0                   0
## 2                       1                          0                   0
## 3                       1                          0                   0
## 4                       2                          0                   0
## 5                       2                          0                   0
## 6                       2                          0                   0
##   did_police_officer_attend_scene_of_collision           1         2         3
## 1                                            1 0.009798059 0.2285594 0.7616425
## 2                                            1 0.010426830 0.2395244 0.7500488
## 3                                            1 0.014829830 0.3077033 0.6774669
## 4                                            1 0.008627809 0.2072114 0.7841608
## 5                                            1 0.008886696 0.2120434 0.7790699
## 6                                            1 0.012671104 0.2760384 0.7112905
# Calculate the average predicted probability for each 'severity'
mean_probs <- colMeans(data22[,22:24])
mean_probs
##          1          2          3 
## 0.01089437 0.23898116 0.75012447
cat("Conclusion: the probability when legacy_of_severity = ‘1:Fatal’ is 1.09%, ‘2:Serious’ is 23.90%, ‘3:Slight’ is 75.01%; Total is 100%")
## Conclusion: the probability when legacy_of_severity = ‘1:Fatal’ is 1.09%, ‘2:Serious’ is 23.90%, ‘3:Slight’ is 75.01%; Total is 100%
#💛4_2. Calculate predicted probability for "specific value"
#set up the values in a dataframe

#For step_test2, we regard there are 6 factors and 7 numbers. 

setup1 <- data.frame(police_force=rep(round(mean(data4$police_force),1),120),
          number_of_vehicles=rep(round(mean(data4$number_of_vehicles),1),120),
           number_of_casualties=rep(round(mean(data4$number_of_casualties),1),120),
           first_road_number=rep(round(mean(data4$first_road_number),1),120),
          speed_limit=rep(round(mean(data4$speed_limit),1),120),
                    junction_detail=rep(c(1:3,5:9),15),
                     junction_control=rep(c(1:4),30),
          second_road_class=rep(round(mean(data4$second_road_class),1),120),
          second_road_number=rep(round(mean(data4$second_road_number),1),120),
                     light_conditions=rep(c(1,4,5,6,7),24),
             road_surface_conditions=rep(c(1:5),24),
                     pedestrian_crossing_human_control=rep(c(0,1,2),40),
                    did_police_officer_attend_scene_of_collision=rep(c(1,2),60)
                   )   #120 is least common multiple of 2,3,4,5,8
setup1
##     police_force number_of_vehicles number_of_casualties first_road_number
## 1           22.7                1.8                  1.3             851.9
## 2           22.7                1.8                  1.3             851.9
## 3           22.7                1.8                  1.3             851.9
## 4           22.7                1.8                  1.3             851.9
## 5           22.7                1.8                  1.3             851.9
## 6           22.7                1.8                  1.3             851.9
## 7           22.7                1.8                  1.3             851.9
## 8           22.7                1.8                  1.3             851.9
## 9           22.7                1.8                  1.3             851.9
## 10          22.7                1.8                  1.3             851.9
## 11          22.7                1.8                  1.3             851.9
## 12          22.7                1.8                  1.3             851.9
## 13          22.7                1.8                  1.3             851.9
## 14          22.7                1.8                  1.3             851.9
## 15          22.7                1.8                  1.3             851.9
## 16          22.7                1.8                  1.3             851.9
## 17          22.7                1.8                  1.3             851.9
## 18          22.7                1.8                  1.3             851.9
## 19          22.7                1.8                  1.3             851.9
## 20          22.7                1.8                  1.3             851.9
## 21          22.7                1.8                  1.3             851.9
## 22          22.7                1.8                  1.3             851.9
## 23          22.7                1.8                  1.3             851.9
## 24          22.7                1.8                  1.3             851.9
## 25          22.7                1.8                  1.3             851.9
## 26          22.7                1.8                  1.3             851.9
## 27          22.7                1.8                  1.3             851.9
## 28          22.7                1.8                  1.3             851.9
## 29          22.7                1.8                  1.3             851.9
## 30          22.7                1.8                  1.3             851.9
## 31          22.7                1.8                  1.3             851.9
## 32          22.7                1.8                  1.3             851.9
## 33          22.7                1.8                  1.3             851.9
## 34          22.7                1.8                  1.3             851.9
## 35          22.7                1.8                  1.3             851.9
## 36          22.7                1.8                  1.3             851.9
## 37          22.7                1.8                  1.3             851.9
## 38          22.7                1.8                  1.3             851.9
## 39          22.7                1.8                  1.3             851.9
## 40          22.7                1.8                  1.3             851.9
## 41          22.7                1.8                  1.3             851.9
## 42          22.7                1.8                  1.3             851.9
## 43          22.7                1.8                  1.3             851.9
## 44          22.7                1.8                  1.3             851.9
## 45          22.7                1.8                  1.3             851.9
## 46          22.7                1.8                  1.3             851.9
## 47          22.7                1.8                  1.3             851.9
## 48          22.7                1.8                  1.3             851.9
## 49          22.7                1.8                  1.3             851.9
## 50          22.7                1.8                  1.3             851.9
## 51          22.7                1.8                  1.3             851.9
## 52          22.7                1.8                  1.3             851.9
## 53          22.7                1.8                  1.3             851.9
## 54          22.7                1.8                  1.3             851.9
## 55          22.7                1.8                  1.3             851.9
## 56          22.7                1.8                  1.3             851.9
## 57          22.7                1.8                  1.3             851.9
## 58          22.7                1.8                  1.3             851.9
## 59          22.7                1.8                  1.3             851.9
## 60          22.7                1.8                  1.3             851.9
## 61          22.7                1.8                  1.3             851.9
## 62          22.7                1.8                  1.3             851.9
## 63          22.7                1.8                  1.3             851.9
## 64          22.7                1.8                  1.3             851.9
## 65          22.7                1.8                  1.3             851.9
## 66          22.7                1.8                  1.3             851.9
## 67          22.7                1.8                  1.3             851.9
## 68          22.7                1.8                  1.3             851.9
## 69          22.7                1.8                  1.3             851.9
## 70          22.7                1.8                  1.3             851.9
## 71          22.7                1.8                  1.3             851.9
## 72          22.7                1.8                  1.3             851.9
## 73          22.7                1.8                  1.3             851.9
## 74          22.7                1.8                  1.3             851.9
## 75          22.7                1.8                  1.3             851.9
## 76          22.7                1.8                  1.3             851.9
## 77          22.7                1.8                  1.3             851.9
## 78          22.7                1.8                  1.3             851.9
## 79          22.7                1.8                  1.3             851.9
## 80          22.7                1.8                  1.3             851.9
## 81          22.7                1.8                  1.3             851.9
## 82          22.7                1.8                  1.3             851.9
## 83          22.7                1.8                  1.3             851.9
## 84          22.7                1.8                  1.3             851.9
## 85          22.7                1.8                  1.3             851.9
## 86          22.7                1.8                  1.3             851.9
## 87          22.7                1.8                  1.3             851.9
## 88          22.7                1.8                  1.3             851.9
## 89          22.7                1.8                  1.3             851.9
## 90          22.7                1.8                  1.3             851.9
## 91          22.7                1.8                  1.3             851.9
## 92          22.7                1.8                  1.3             851.9
## 93          22.7                1.8                  1.3             851.9
## 94          22.7                1.8                  1.3             851.9
## 95          22.7                1.8                  1.3             851.9
## 96          22.7                1.8                  1.3             851.9
## 97          22.7                1.8                  1.3             851.9
## 98          22.7                1.8                  1.3             851.9
## 99          22.7                1.8                  1.3             851.9
## 100         22.7                1.8                  1.3             851.9
## 101         22.7                1.8                  1.3             851.9
## 102         22.7                1.8                  1.3             851.9
## 103         22.7                1.8                  1.3             851.9
## 104         22.7                1.8                  1.3             851.9
## 105         22.7                1.8                  1.3             851.9
## 106         22.7                1.8                  1.3             851.9
## 107         22.7                1.8                  1.3             851.9
## 108         22.7                1.8                  1.3             851.9
## 109         22.7                1.8                  1.3             851.9
## 110         22.7                1.8                  1.3             851.9
## 111         22.7                1.8                  1.3             851.9
## 112         22.7                1.8                  1.3             851.9
## 113         22.7                1.8                  1.3             851.9
## 114         22.7                1.8                  1.3             851.9
## 115         22.7                1.8                  1.3             851.9
## 116         22.7                1.8                  1.3             851.9
## 117         22.7                1.8                  1.3             851.9
## 118         22.7                1.8                  1.3             851.9
## 119         22.7                1.8                  1.3             851.9
## 120         22.7                1.8                  1.3             851.9
##     speed_limit junction_detail junction_control second_road_class
## 1            33               1                1               5.3
## 2            33               2                2               5.3
## 3            33               3                3               5.3
## 4            33               5                4               5.3
## 5            33               6                1               5.3
## 6            33               7                2               5.3
## 7            33               8                3               5.3
## 8            33               9                4               5.3
## 9            33               1                1               5.3
## 10           33               2                2               5.3
## 11           33               3                3               5.3
## 12           33               5                4               5.3
## 13           33               6                1               5.3
## 14           33               7                2               5.3
## 15           33               8                3               5.3
## 16           33               9                4               5.3
## 17           33               1                1               5.3
## 18           33               2                2               5.3
## 19           33               3                3               5.3
## 20           33               5                4               5.3
## 21           33               6                1               5.3
## 22           33               7                2               5.3
## 23           33               8                3               5.3
## 24           33               9                4               5.3
## 25           33               1                1               5.3
## 26           33               2                2               5.3
## 27           33               3                3               5.3
## 28           33               5                4               5.3
## 29           33               6                1               5.3
## 30           33               7                2               5.3
## 31           33               8                3               5.3
## 32           33               9                4               5.3
## 33           33               1                1               5.3
## 34           33               2                2               5.3
## 35           33               3                3               5.3
## 36           33               5                4               5.3
## 37           33               6                1               5.3
## 38           33               7                2               5.3
## 39           33               8                3               5.3
## 40           33               9                4               5.3
## 41           33               1                1               5.3
## 42           33               2                2               5.3
## 43           33               3                3               5.3
## 44           33               5                4               5.3
## 45           33               6                1               5.3
## 46           33               7                2               5.3
## 47           33               8                3               5.3
## 48           33               9                4               5.3
## 49           33               1                1               5.3
## 50           33               2                2               5.3
## 51           33               3                3               5.3
## 52           33               5                4               5.3
## 53           33               6                1               5.3
## 54           33               7                2               5.3
## 55           33               8                3               5.3
## 56           33               9                4               5.3
## 57           33               1                1               5.3
## 58           33               2                2               5.3
## 59           33               3                3               5.3
## 60           33               5                4               5.3
## 61           33               6                1               5.3
## 62           33               7                2               5.3
## 63           33               8                3               5.3
## 64           33               9                4               5.3
## 65           33               1                1               5.3
## 66           33               2                2               5.3
## 67           33               3                3               5.3
## 68           33               5                4               5.3
## 69           33               6                1               5.3
## 70           33               7                2               5.3
## 71           33               8                3               5.3
## 72           33               9                4               5.3
## 73           33               1                1               5.3
## 74           33               2                2               5.3
## 75           33               3                3               5.3
## 76           33               5                4               5.3
## 77           33               6                1               5.3
## 78           33               7                2               5.3
## 79           33               8                3               5.3
## 80           33               9                4               5.3
## 81           33               1                1               5.3
## 82           33               2                2               5.3
## 83           33               3                3               5.3
## 84           33               5                4               5.3
## 85           33               6                1               5.3
## 86           33               7                2               5.3
## 87           33               8                3               5.3
## 88           33               9                4               5.3
## 89           33               1                1               5.3
## 90           33               2                2               5.3
## 91           33               3                3               5.3
## 92           33               5                4               5.3
## 93           33               6                1               5.3
## 94           33               7                2               5.3
## 95           33               8                3               5.3
## 96           33               9                4               5.3
## 97           33               1                1               5.3
## 98           33               2                2               5.3
## 99           33               3                3               5.3
## 100          33               5                4               5.3
## 101          33               6                1               5.3
## 102          33               7                2               5.3
## 103          33               8                3               5.3
## 104          33               9                4               5.3
## 105          33               1                1               5.3
## 106          33               2                2               5.3
## 107          33               3                3               5.3
## 108          33               5                4               5.3
## 109          33               6                1               5.3
## 110          33               7                2               5.3
## 111          33               8                3               5.3
## 112          33               9                4               5.3
## 113          33               1                1               5.3
## 114          33               2                2               5.3
## 115          33               3                3               5.3
## 116          33               5                4               5.3
## 117          33               6                1               5.3
## 118          33               7                2               5.3
## 119          33               8                3               5.3
## 120          33               9                4               5.3
##     second_road_number light_conditions road_surface_conditions
## 1                397.6                1                       1
## 2                397.6                4                       2
## 3                397.6                5                       3
## 4                397.6                6                       4
## 5                397.6                7                       5
## 6                397.6                1                       1
## 7                397.6                4                       2
## 8                397.6                5                       3
## 9                397.6                6                       4
## 10               397.6                7                       5
## 11               397.6                1                       1
## 12               397.6                4                       2
## 13               397.6                5                       3
## 14               397.6                6                       4
## 15               397.6                7                       5
## 16               397.6                1                       1
## 17               397.6                4                       2
## 18               397.6                5                       3
## 19               397.6                6                       4
## 20               397.6                7                       5
## 21               397.6                1                       1
## 22               397.6                4                       2
## 23               397.6                5                       3
## 24               397.6                6                       4
## 25               397.6                7                       5
## 26               397.6                1                       1
## 27               397.6                4                       2
## 28               397.6                5                       3
## 29               397.6                6                       4
## 30               397.6                7                       5
## 31               397.6                1                       1
## 32               397.6                4                       2
## 33               397.6                5                       3
## 34               397.6                6                       4
## 35               397.6                7                       5
## 36               397.6                1                       1
## 37               397.6                4                       2
## 38               397.6                5                       3
## 39               397.6                6                       4
## 40               397.6                7                       5
## 41               397.6                1                       1
## 42               397.6                4                       2
## 43               397.6                5                       3
## 44               397.6                6                       4
## 45               397.6                7                       5
## 46               397.6                1                       1
## 47               397.6                4                       2
## 48               397.6                5                       3
## 49               397.6                6                       4
## 50               397.6                7                       5
## 51               397.6                1                       1
## 52               397.6                4                       2
## 53               397.6                5                       3
## 54               397.6                6                       4
## 55               397.6                7                       5
## 56               397.6                1                       1
## 57               397.6                4                       2
## 58               397.6                5                       3
## 59               397.6                6                       4
## 60               397.6                7                       5
## 61               397.6                1                       1
## 62               397.6                4                       2
## 63               397.6                5                       3
## 64               397.6                6                       4
## 65               397.6                7                       5
## 66               397.6                1                       1
## 67               397.6                4                       2
## 68               397.6                5                       3
## 69               397.6                6                       4
## 70               397.6                7                       5
## 71               397.6                1                       1
## 72               397.6                4                       2
## 73               397.6                5                       3
## 74               397.6                6                       4
## 75               397.6                7                       5
## 76               397.6                1                       1
## 77               397.6                4                       2
## 78               397.6                5                       3
## 79               397.6                6                       4
## 80               397.6                7                       5
## 81               397.6                1                       1
## 82               397.6                4                       2
## 83               397.6                5                       3
## 84               397.6                6                       4
## 85               397.6                7                       5
## 86               397.6                1                       1
## 87               397.6                4                       2
## 88               397.6                5                       3
## 89               397.6                6                       4
## 90               397.6                7                       5
## 91               397.6                1                       1
## 92               397.6                4                       2
## 93               397.6                5                       3
## 94               397.6                6                       4
## 95               397.6                7                       5
## 96               397.6                1                       1
## 97               397.6                4                       2
## 98               397.6                5                       3
## 99               397.6                6                       4
## 100              397.6                7                       5
## 101              397.6                1                       1
## 102              397.6                4                       2
## 103              397.6                5                       3
## 104              397.6                6                       4
## 105              397.6                7                       5
## 106              397.6                1                       1
## 107              397.6                4                       2
## 108              397.6                5                       3
## 109              397.6                6                       4
## 110              397.6                7                       5
## 111              397.6                1                       1
## 112              397.6                4                       2
## 113              397.6                5                       3
## 114              397.6                6                       4
## 115              397.6                7                       5
## 116              397.6                1                       1
## 117              397.6                4                       2
## 118              397.6                5                       3
## 119              397.6                6                       4
## 120              397.6                7                       5
##     pedestrian_crossing_human_control
## 1                                   0
## 2                                   1
## 3                                   2
## 4                                   0
## 5                                   1
## 6                                   2
## 7                                   0
## 8                                   1
## 9                                   2
## 10                                  0
## 11                                  1
## 12                                  2
## 13                                  0
## 14                                  1
## 15                                  2
## 16                                  0
## 17                                  1
## 18                                  2
## 19                                  0
## 20                                  1
## 21                                  2
## 22                                  0
## 23                                  1
## 24                                  2
## 25                                  0
## 26                                  1
## 27                                  2
## 28                                  0
## 29                                  1
## 30                                  2
## 31                                  0
## 32                                  1
## 33                                  2
## 34                                  0
## 35                                  1
## 36                                  2
## 37                                  0
## 38                                  1
## 39                                  2
## 40                                  0
## 41                                  1
## 42                                  2
## 43                                  0
## 44                                  1
## 45                                  2
## 46                                  0
## 47                                  1
## 48                                  2
## 49                                  0
## 50                                  1
## 51                                  2
## 52                                  0
## 53                                  1
## 54                                  2
## 55                                  0
## 56                                  1
## 57                                  2
## 58                                  0
## 59                                  1
## 60                                  2
## 61                                  0
## 62                                  1
## 63                                  2
## 64                                  0
## 65                                  1
## 66                                  2
## 67                                  0
## 68                                  1
## 69                                  2
## 70                                  0
## 71                                  1
## 72                                  2
## 73                                  0
## 74                                  1
## 75                                  2
## 76                                  0
## 77                                  1
## 78                                  2
## 79                                  0
## 80                                  1
## 81                                  2
## 82                                  0
## 83                                  1
## 84                                  2
## 85                                  0
## 86                                  1
## 87                                  2
## 88                                  0
## 89                                  1
## 90                                  2
## 91                                  0
## 92                                  1
## 93                                  2
## 94                                  0
## 95                                  1
## 96                                  2
## 97                                  0
## 98                                  1
## 99                                  2
## 100                                 0
## 101                                 1
## 102                                 2
## 103                                 0
## 104                                 1
## 105                                 2
## 106                                 0
## 107                                 1
## 108                                 2
## 109                                 0
## 110                                 1
## 111                                 2
## 112                                 0
## 113                                 1
## 114                                 2
## 115                                 0
## 116                                 1
## 117                                 2
## 118                                 0
## 119                                 1
## 120                                 2
##     did_police_officer_attend_scene_of_collision
## 1                                              1
## 2                                              2
## 3                                              1
## 4                                              2
## 5                                              1
## 6                                              2
## 7                                              1
## 8                                              2
## 9                                              1
## 10                                             2
## 11                                             1
## 12                                             2
## 13                                             1
## 14                                             2
## 15                                             1
## 16                                             2
## 17                                             1
## 18                                             2
## 19                                             1
## 20                                             2
## 21                                             1
## 22                                             2
## 23                                             1
## 24                                             2
## 25                                             1
## 26                                             2
## 27                                             1
## 28                                             2
## 29                                             1
## 30                                             2
## 31                                             1
## 32                                             2
## 33                                             1
## 34                                             2
## 35                                             1
## 36                                             2
## 37                                             1
## 38                                             2
## 39                                             1
## 40                                             2
## 41                                             1
## 42                                             2
## 43                                             1
## 44                                             2
## 45                                             1
## 46                                             2
## 47                                             1
## 48                                             2
## 49                                             1
## 50                                             2
## 51                                             1
## 52                                             2
## 53                                             1
## 54                                             2
## 55                                             1
## 56                                             2
## 57                                             1
## 58                                             2
## 59                                             1
## 60                                             2
## 61                                             1
## 62                                             2
## 63                                             1
## 64                                             2
## 65                                             1
## 66                                             2
## 67                                             1
## 68                                             2
## 69                                             1
## 70                                             2
## 71                                             1
## 72                                             2
## 73                                             1
## 74                                             2
## 75                                             1
## 76                                             2
## 77                                             1
## 78                                             2
## 79                                             1
## 80                                             2
## 81                                             1
## 82                                             2
## 83                                             1
## 84                                             2
## 85                                             1
## 86                                             2
## 87                                             1
## 88                                             2
## 89                                             1
## 90                                             2
## 91                                             1
## 92                                             2
## 93                                             1
## 94                                             2
## 95                                             1
## 96                                             2
## 97                                             1
## 98                                             2
## 99                                             1
## 100                                            2
## 101                                            1
## 102                                            2
## 103                                            1
## 104                                            2
## 105                                            1
## 106                                            2
## 107                                            1
## 108                                            2
## 109                                            1
## 110                                            2
## 111                                            1
## 112                                            2
## 113                                            1
## 114                                            2
## 115                                            1
## 116                                            2
## 117                                            1
## 118                                            2
## 119                                            1
## 120                                            2
view(setup1)
head(setup1)
##   police_force number_of_vehicles number_of_casualties first_road_number
## 1         22.7                1.8                  1.3             851.9
## 2         22.7                1.8                  1.3             851.9
## 3         22.7                1.8                  1.3             851.9
## 4         22.7                1.8                  1.3             851.9
## 5         22.7                1.8                  1.3             851.9
## 6         22.7                1.8                  1.3             851.9
##   speed_limit junction_detail junction_control second_road_class
## 1          33               1                1               5.3
## 2          33               2                2               5.3
## 3          33               3                3               5.3
## 4          33               5                4               5.3
## 5          33               6                1               5.3
## 6          33               7                2               5.3
##   second_road_number light_conditions road_surface_conditions
## 1              397.6                1                       1
## 2              397.6                4                       2
## 3              397.6                5                       3
## 4              397.6                6                       4
## 5              397.6                7                       5
## 6              397.6                1                       1
##   pedestrian_crossing_human_control
## 1                                 0
## 2                                 1
## 3                                 2
## 4                                 0
## 5                                 1
## 6                                 2
##   did_police_officer_attend_scene_of_collision
## 1                                            1
## 2                                            2
## 3                                            1
## 4                                            2
## 5                                            1
## 6                                            2
str(setup1)
## 'data.frame':    120 obs. of  13 variables:
##  $ police_force                                : num  22.7 22.7 22.7 22.7 22.7 22.7 22.7 22.7 22.7 22.7 ...
##  $ number_of_vehicles                          : num  1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 ...
##  $ number_of_casualties                        : num  1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 ...
##  $ first_road_number                           : num  852 852 852 852 852 ...
##  $ speed_limit                                 : num  33 33 33 33 33 33 33 33 33 33 ...
##  $ junction_detail                             : int  1 2 3 5 6 7 8 9 1 2 ...
##  $ junction_control                            : int  1 2 3 4 1 2 3 4 1 2 ...
##  $ second_road_class                           : num  5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3 ...
##  $ second_road_number                          : num  398 398 398 398 398 ...
##  $ light_conditions                            : num  1 4 5 6 7 1 4 5 6 7 ...
##  $ road_surface_conditions                     : int  1 2 3 4 5 1 2 3 4 5 ...
##  $ pedestrian_crossing_human_control           : num  0 1 2 0 1 2 0 1 2 0 ...
##  $ did_police_officer_attend_scene_of_collision: num  1 2 1 2 1 2 1 2 1 2 ...
#💛4_3. Among 13 significant predictors in step_test2, it has 6 factors and 7 numeric, so this new dataset 'setup1' should has 6 factors as well
setup1$junction_detail <- as.factor(setup1$junction_detail)
setup1$junction_control <- as.factor(setup1$junction_control)
setup1$light_conditions <- as.factor(setup1$light_conditions)
setup1$road_surface_conditions <- as.factor(setup1$road_surface_conditions)
setup1$pedestrian_crossing_human_control <- as.factor(setup1$pedestrian_crossing_human_control)
 setup1$did_police_officer_attend_scene_of_collision <- as.factor(setup1$did_police_officer_attend_scene_of_collision )

str(setup1)
## 'data.frame':    120 obs. of  13 variables:
##  $ police_force                                : num  22.7 22.7 22.7 22.7 22.7 22.7 22.7 22.7 22.7 22.7 ...
##  $ number_of_vehicles                          : num  1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 ...
##  $ number_of_casualties                        : num  1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 ...
##  $ first_road_number                           : num  852 852 852 852 852 ...
##  $ speed_limit                                 : num  33 33 33 33 33 33 33 33 33 33 ...
##  $ junction_detail                             : Factor w/ 8 levels "1","2","3","5",..: 1 2 3 4 5 6 7 8 1 2 ...
##  $ junction_control                            : Factor w/ 4 levels "1","2","3","4": 1 2 3 4 1 2 3 4 1 2 ...
##  $ second_road_class                           : num  5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3 ...
##  $ second_road_number                          : num  398 398 398 398 398 ...
##  $ light_conditions                            : Factor w/ 5 levels "1","4","5","6",..: 1 2 3 4 5 1 2 3 4 5 ...
##  $ road_surface_conditions                     : Factor w/ 5 levels "1","2","3","4",..: 1 2 3 4 5 1 2 3 4 5 ...
##  $ pedestrian_crossing_human_control           : Factor w/ 3 levels "0","1","2": 1 2 3 1 2 3 1 2 3 1 ...
##  $ did_police_officer_attend_scene_of_collision: Factor w/ 2 levels "1","2": 1 2 1 2 1 2 1 2 1 2 ...
setup1[, c("pred.prob")] <- predict(step_test2, newdata=setup1, type="probs")
setup1
##     police_force number_of_vehicles number_of_casualties first_road_number
## 1           22.7                1.8                  1.3             851.9
## 2           22.7                1.8                  1.3             851.9
## 3           22.7                1.8                  1.3             851.9
## 4           22.7                1.8                  1.3             851.9
## 5           22.7                1.8                  1.3             851.9
## 6           22.7                1.8                  1.3             851.9
## 7           22.7                1.8                  1.3             851.9
## 8           22.7                1.8                  1.3             851.9
## 9           22.7                1.8                  1.3             851.9
## 10          22.7                1.8                  1.3             851.9
## 11          22.7                1.8                  1.3             851.9
## 12          22.7                1.8                  1.3             851.9
## 13          22.7                1.8                  1.3             851.9
## 14          22.7                1.8                  1.3             851.9
## 15          22.7                1.8                  1.3             851.9
## 16          22.7                1.8                  1.3             851.9
## 17          22.7                1.8                  1.3             851.9
## 18          22.7                1.8                  1.3             851.9
## 19          22.7                1.8                  1.3             851.9
## 20          22.7                1.8                  1.3             851.9
## 21          22.7                1.8                  1.3             851.9
## 22          22.7                1.8                  1.3             851.9
## 23          22.7                1.8                  1.3             851.9
## 24          22.7                1.8                  1.3             851.9
## 25          22.7                1.8                  1.3             851.9
## 26          22.7                1.8                  1.3             851.9
## 27          22.7                1.8                  1.3             851.9
## 28          22.7                1.8                  1.3             851.9
## 29          22.7                1.8                  1.3             851.9
## 30          22.7                1.8                  1.3             851.9
## 31          22.7                1.8                  1.3             851.9
## 32          22.7                1.8                  1.3             851.9
## 33          22.7                1.8                  1.3             851.9
## 34          22.7                1.8                  1.3             851.9
## 35          22.7                1.8                  1.3             851.9
## 36          22.7                1.8                  1.3             851.9
## 37          22.7                1.8                  1.3             851.9
## 38          22.7                1.8                  1.3             851.9
## 39          22.7                1.8                  1.3             851.9
## 40          22.7                1.8                  1.3             851.9
## 41          22.7                1.8                  1.3             851.9
## 42          22.7                1.8                  1.3             851.9
## 43          22.7                1.8                  1.3             851.9
## 44          22.7                1.8                  1.3             851.9
## 45          22.7                1.8                  1.3             851.9
## 46          22.7                1.8                  1.3             851.9
## 47          22.7                1.8                  1.3             851.9
## 48          22.7                1.8                  1.3             851.9
## 49          22.7                1.8                  1.3             851.9
## 50          22.7                1.8                  1.3             851.9
## 51          22.7                1.8                  1.3             851.9
## 52          22.7                1.8                  1.3             851.9
## 53          22.7                1.8                  1.3             851.9
## 54          22.7                1.8                  1.3             851.9
## 55          22.7                1.8                  1.3             851.9
## 56          22.7                1.8                  1.3             851.9
## 57          22.7                1.8                  1.3             851.9
## 58          22.7                1.8                  1.3             851.9
## 59          22.7                1.8                  1.3             851.9
## 60          22.7                1.8                  1.3             851.9
## 61          22.7                1.8                  1.3             851.9
## 62          22.7                1.8                  1.3             851.9
## 63          22.7                1.8                  1.3             851.9
## 64          22.7                1.8                  1.3             851.9
## 65          22.7                1.8                  1.3             851.9
## 66          22.7                1.8                  1.3             851.9
## 67          22.7                1.8                  1.3             851.9
## 68          22.7                1.8                  1.3             851.9
## 69          22.7                1.8                  1.3             851.9
## 70          22.7                1.8                  1.3             851.9
## 71          22.7                1.8                  1.3             851.9
## 72          22.7                1.8                  1.3             851.9
## 73          22.7                1.8                  1.3             851.9
## 74          22.7                1.8                  1.3             851.9
## 75          22.7                1.8                  1.3             851.9
## 76          22.7                1.8                  1.3             851.9
## 77          22.7                1.8                  1.3             851.9
## 78          22.7                1.8                  1.3             851.9
## 79          22.7                1.8                  1.3             851.9
## 80          22.7                1.8                  1.3             851.9
## 81          22.7                1.8                  1.3             851.9
## 82          22.7                1.8                  1.3             851.9
## 83          22.7                1.8                  1.3             851.9
## 84          22.7                1.8                  1.3             851.9
## 85          22.7                1.8                  1.3             851.9
## 86          22.7                1.8                  1.3             851.9
## 87          22.7                1.8                  1.3             851.9
## 88          22.7                1.8                  1.3             851.9
## 89          22.7                1.8                  1.3             851.9
## 90          22.7                1.8                  1.3             851.9
## 91          22.7                1.8                  1.3             851.9
## 92          22.7                1.8                  1.3             851.9
## 93          22.7                1.8                  1.3             851.9
## 94          22.7                1.8                  1.3             851.9
## 95          22.7                1.8                  1.3             851.9
## 96          22.7                1.8                  1.3             851.9
## 97          22.7                1.8                  1.3             851.9
## 98          22.7                1.8                  1.3             851.9
## 99          22.7                1.8                  1.3             851.9
## 100         22.7                1.8                  1.3             851.9
## 101         22.7                1.8                  1.3             851.9
## 102         22.7                1.8                  1.3             851.9
## 103         22.7                1.8                  1.3             851.9
## 104         22.7                1.8                  1.3             851.9
## 105         22.7                1.8                  1.3             851.9
## 106         22.7                1.8                  1.3             851.9
## 107         22.7                1.8                  1.3             851.9
## 108         22.7                1.8                  1.3             851.9
## 109         22.7                1.8                  1.3             851.9
## 110         22.7                1.8                  1.3             851.9
## 111         22.7                1.8                  1.3             851.9
## 112         22.7                1.8                  1.3             851.9
## 113         22.7                1.8                  1.3             851.9
## 114         22.7                1.8                  1.3             851.9
## 115         22.7                1.8                  1.3             851.9
## 116         22.7                1.8                  1.3             851.9
## 117         22.7                1.8                  1.3             851.9
## 118         22.7                1.8                  1.3             851.9
## 119         22.7                1.8                  1.3             851.9
## 120         22.7                1.8                  1.3             851.9
##     speed_limit junction_detail junction_control second_road_class
## 1            33               1                1               5.3
## 2            33               2                2               5.3
## 3            33               3                3               5.3
## 4            33               5                4               5.3
## 5            33               6                1               5.3
## 6            33               7                2               5.3
## 7            33               8                3               5.3
## 8            33               9                4               5.3
## 9            33               1                1               5.3
## 10           33               2                2               5.3
## 11           33               3                3               5.3
## 12           33               5                4               5.3
## 13           33               6                1               5.3
## 14           33               7                2               5.3
## 15           33               8                3               5.3
## 16           33               9                4               5.3
## 17           33               1                1               5.3
## 18           33               2                2               5.3
## 19           33               3                3               5.3
## 20           33               5                4               5.3
## 21           33               6                1               5.3
## 22           33               7                2               5.3
## 23           33               8                3               5.3
## 24           33               9                4               5.3
## 25           33               1                1               5.3
## 26           33               2                2               5.3
## 27           33               3                3               5.3
## 28           33               5                4               5.3
## 29           33               6                1               5.3
## 30           33               7                2               5.3
## 31           33               8                3               5.3
## 32           33               9                4               5.3
## 33           33               1                1               5.3
## 34           33               2                2               5.3
## 35           33               3                3               5.3
## 36           33               5                4               5.3
## 37           33               6                1               5.3
## 38           33               7                2               5.3
## 39           33               8                3               5.3
## 40           33               9                4               5.3
## 41           33               1                1               5.3
## 42           33               2                2               5.3
## 43           33               3                3               5.3
## 44           33               5                4               5.3
## 45           33               6                1               5.3
## 46           33               7                2               5.3
## 47           33               8                3               5.3
## 48           33               9                4               5.3
## 49           33               1                1               5.3
## 50           33               2                2               5.3
## 51           33               3                3               5.3
## 52           33               5                4               5.3
## 53           33               6                1               5.3
## 54           33               7                2               5.3
## 55           33               8                3               5.3
## 56           33               9                4               5.3
## 57           33               1                1               5.3
## 58           33               2                2               5.3
## 59           33               3                3               5.3
## 60           33               5                4               5.3
## 61           33               6                1               5.3
## 62           33               7                2               5.3
## 63           33               8                3               5.3
## 64           33               9                4               5.3
## 65           33               1                1               5.3
## 66           33               2                2               5.3
## 67           33               3                3               5.3
## 68           33               5                4               5.3
## 69           33               6                1               5.3
## 70           33               7                2               5.3
## 71           33               8                3               5.3
## 72           33               9                4               5.3
## 73           33               1                1               5.3
## 74           33               2                2               5.3
## 75           33               3                3               5.3
## 76           33               5                4               5.3
## 77           33               6                1               5.3
## 78           33               7                2               5.3
## 79           33               8                3               5.3
## 80           33               9                4               5.3
## 81           33               1                1               5.3
## 82           33               2                2               5.3
## 83           33               3                3               5.3
## 84           33               5                4               5.3
## 85           33               6                1               5.3
## 86           33               7                2               5.3
## 87           33               8                3               5.3
## 88           33               9                4               5.3
## 89           33               1                1               5.3
## 90           33               2                2               5.3
## 91           33               3                3               5.3
## 92           33               5                4               5.3
## 93           33               6                1               5.3
## 94           33               7                2               5.3
## 95           33               8                3               5.3
## 96           33               9                4               5.3
## 97           33               1                1               5.3
## 98           33               2                2               5.3
## 99           33               3                3               5.3
## 100          33               5                4               5.3
## 101          33               6                1               5.3
## 102          33               7                2               5.3
## 103          33               8                3               5.3
## 104          33               9                4               5.3
## 105          33               1                1               5.3
## 106          33               2                2               5.3
## 107          33               3                3               5.3
## 108          33               5                4               5.3
## 109          33               6                1               5.3
## 110          33               7                2               5.3
## 111          33               8                3               5.3
## 112          33               9                4               5.3
## 113          33               1                1               5.3
## 114          33               2                2               5.3
## 115          33               3                3               5.3
## 116          33               5                4               5.3
## 117          33               6                1               5.3
## 118          33               7                2               5.3
## 119          33               8                3               5.3
## 120          33               9                4               5.3
##     second_road_number light_conditions road_surface_conditions
## 1                397.6                1                       1
## 2                397.6                4                       2
## 3                397.6                5                       3
## 4                397.6                6                       4
## 5                397.6                7                       5
## 6                397.6                1                       1
## 7                397.6                4                       2
## 8                397.6                5                       3
## 9                397.6                6                       4
## 10               397.6                7                       5
## 11               397.6                1                       1
## 12               397.6                4                       2
## 13               397.6                5                       3
## 14               397.6                6                       4
## 15               397.6                7                       5
## 16               397.6                1                       1
## 17               397.6                4                       2
## 18               397.6                5                       3
## 19               397.6                6                       4
## 20               397.6                7                       5
## 21               397.6                1                       1
## 22               397.6                4                       2
## 23               397.6                5                       3
## 24               397.6                6                       4
## 25               397.6                7                       5
## 26               397.6                1                       1
## 27               397.6                4                       2
## 28               397.6                5                       3
## 29               397.6                6                       4
## 30               397.6                7                       5
## 31               397.6                1                       1
## 32               397.6                4                       2
## 33               397.6                5                       3
## 34               397.6                6                       4
## 35               397.6                7                       5
## 36               397.6                1                       1
## 37               397.6                4                       2
## 38               397.6                5                       3
## 39               397.6                6                       4
## 40               397.6                7                       5
## 41               397.6                1                       1
## 42               397.6                4                       2
## 43               397.6                5                       3
## 44               397.6                6                       4
## 45               397.6                7                       5
## 46               397.6                1                       1
## 47               397.6                4                       2
## 48               397.6                5                       3
## 49               397.6                6                       4
## 50               397.6                7                       5
## 51               397.6                1                       1
## 52               397.6                4                       2
## 53               397.6                5                       3
## 54               397.6                6                       4
## 55               397.6                7                       5
## 56               397.6                1                       1
## 57               397.6                4                       2
## 58               397.6                5                       3
## 59               397.6                6                       4
## 60               397.6                7                       5
## 61               397.6                1                       1
## 62               397.6                4                       2
## 63               397.6                5                       3
## 64               397.6                6                       4
## 65               397.6                7                       5
## 66               397.6                1                       1
## 67               397.6                4                       2
## 68               397.6                5                       3
## 69               397.6                6                       4
## 70               397.6                7                       5
## 71               397.6                1                       1
## 72               397.6                4                       2
## 73               397.6                5                       3
## 74               397.6                6                       4
## 75               397.6                7                       5
## 76               397.6                1                       1
## 77               397.6                4                       2
## 78               397.6                5                       3
## 79               397.6                6                       4
## 80               397.6                7                       5
## 81               397.6                1                       1
## 82               397.6                4                       2
## 83               397.6                5                       3
## 84               397.6                6                       4
## 85               397.6                7                       5
## 86               397.6                1                       1
## 87               397.6                4                       2
## 88               397.6                5                       3
## 89               397.6                6                       4
## 90               397.6                7                       5
## 91               397.6                1                       1
## 92               397.6                4                       2
## 93               397.6                5                       3
## 94               397.6                6                       4
## 95               397.6                7                       5
## 96               397.6                1                       1
## 97               397.6                4                       2
## 98               397.6                5                       3
## 99               397.6                6                       4
## 100              397.6                7                       5
## 101              397.6                1                       1
## 102              397.6                4                       2
## 103              397.6                5                       3
## 104              397.6                6                       4
## 105              397.6                7                       5
## 106              397.6                1                       1
## 107              397.6                4                       2
## 108              397.6                5                       3
## 109              397.6                6                       4
## 110              397.6                7                       5
## 111              397.6                1                       1
## 112              397.6                4                       2
## 113              397.6                5                       3
## 114              397.6                6                       4
## 115              397.6                7                       5
## 116              397.6                1                       1
## 117              397.6                4                       2
## 118              397.6                5                       3
## 119              397.6                6                       4
## 120              397.6                7                       5
##     pedestrian_crossing_human_control
## 1                                   0
## 2                                   1
## 3                                   2
## 4                                   0
## 5                                   1
## 6                                   2
## 7                                   0
## 8                                   1
## 9                                   2
## 10                                  0
## 11                                  1
## 12                                  2
## 13                                  0
## 14                                  1
## 15                                  2
## 16                                  0
## 17                                  1
## 18                                  2
## 19                                  0
## 20                                  1
## 21                                  2
## 22                                  0
## 23                                  1
## 24                                  2
## 25                                  0
## 26                                  1
## 27                                  2
## 28                                  0
## 29                                  1
## 30                                  2
## 31                                  0
## 32                                  1
## 33                                  2
## 34                                  0
## 35                                  1
## 36                                  2
## 37                                  0
## 38                                  1
## 39                                  2
## 40                                  0
## 41                                  1
## 42                                  2
## 43                                  0
## 44                                  1
## 45                                  2
## 46                                  0
## 47                                  1
## 48                                  2
## 49                                  0
## 50                                  1
## 51                                  2
## 52                                  0
## 53                                  1
## 54                                  2
## 55                                  0
## 56                                  1
## 57                                  2
## 58                                  0
## 59                                  1
## 60                                  2
## 61                                  0
## 62                                  1
## 63                                  2
## 64                                  0
## 65                                  1
## 66                                  2
## 67                                  0
## 68                                  1
## 69                                  2
## 70                                  0
## 71                                  1
## 72                                  2
## 73                                  0
## 74                                  1
## 75                                  2
## 76                                  0
## 77                                  1
## 78                                  2
## 79                                  0
## 80                                  1
## 81                                  2
## 82                                  0
## 83                                  1
## 84                                  2
## 85                                  0
## 86                                  1
## 87                                  2
## 88                                  0
## 89                                  1
## 90                                  2
## 91                                  0
## 92                                  1
## 93                                  2
## 94                                  0
## 95                                  1
## 96                                  2
## 97                                  0
## 98                                  1
## 99                                  2
## 100                                 0
## 101                                 1
## 102                                 2
## 103                                 0
## 104                                 1
## 105                                 2
## 106                                 0
## 107                                 1
## 108                                 2
## 109                                 0
## 110                                 1
## 111                                 2
## 112                                 0
## 113                                 1
## 114                                 2
## 115                                 0
## 116                                 1
## 117                                 2
## 118                                 0
## 119                                 1
## 120                                 2
##     did_police_officer_attend_scene_of_collision pred.prob.1 pred.prob.2
## 1                                              1 0.004883582 0.129474622
## 2                                              2 0.001946197 0.056144087
## 3                                              1 0.009338635 0.220328146
## 4                                              2 0.003517898 0.096921792
## 5                                              1 0.002686195 0.075812598
## 6                                              2 0.002316698 0.066099660
## 7                                              1 0.011576022 0.258712965
## 8                                              2 0.002502999 0.071023422
## 9                                              1 0.002201956 0.063039935
## 10                                             2 0.002229539 0.063777388
## 11                                             1 0.006982004 0.174937887
## 12                                             2 0.004382294 0.117816381
## 13                                             1 0.007465756 0.184712836
## 14                                             2 0.001046048 0.031010562
## 15                                             1 0.005537238 0.144196894
## 16                                             2 0.004478158 0.120071242
## 17                                             1 0.002751647 0.077511178
## 18                                             2 0.002582386 0.073105128
## 19                                             1 0.007562934 0.186646703
## 20                                             2 0.002094186 0.060147052
## 21                                             1 0.005563421 0.144775655
## 22                                             2 0.003136895 0.087378264
## 23                                             1 0.006428234 0.163436329
## 24                                             2 0.002018703 0.058109724
## 25                                             1 0.003151882 0.087757654
## 26                                             2 0.001927396 0.055632996
## 27                                             1 0.009411864 0.221652872
## 28                                             2 0.005826536 0.150545971
## 29                                             1 0.002516518 0.071378631
## 30                                             2 0.001493839 0.043685143
## 31                                             1 0.011465262 0.256909702
## 32                                             2 0.002522762 0.071542585
## 33                                             1 0.003650164 0.100186145
## 34                                             2 0.002088648 0.059997876
## 35                                             1 0.004509583 0.120807775
## 36                                             2 0.004340062 0.116819155
## 37                                             1 0.007524410 0.185881241
## 38                                             2 0.001735348 0.050379100
## 39                                             1 0.005188409 0.136406336
## 40                                             2 0.002889802 0.081075223
## 41                                             1 0.002725086 0.076822673
## 42                                             2 0.002602774 0.073638202
## 43                                             1 0.012492869 0.273279367
## 44                                             2 0.001961831 0.056568646
## 45                                             1 0.003591523 0.098741933
## 46                                             2 0.003106627 0.086611037
## 47                                             1 0.006478790 0.164500513
## 48                                             2 0.003346791 0.092661825
## 49                                             1 0.002952877 0.082692822
## 50                                             2 0.001242640 0.036617716
## 51                                             1 0.009321616 0.220019563
## 52                                             2 0.005872388 0.151543107
## 53                                             1 0.004170747 0.112797193
## 54                                             2 0.001399373 0.041040046
## 55                                             1 0.007417118 0.183741248
## 56                                             2 0.002498406 0.070902683
## 57                                             1 0.003678952 0.100893368
## 58                                             2 0.003462593 0.095549477
## 59                                             1 0.004225219 0.114095323
## 60                                             2 0.002800550 0.078776045
## 61                                             1 0.007452124 0.184440774
## 62                                             2 0.001749061 0.050756264
## 63                                             1 0.008583886 0.206385245
## 64                                             2 0.002707300 0.076361016
## 65                                             1 0.001757429 0.050986268
## 66                                             2 0.002577647 0.072981151
## 67                                             1 0.012590517 0.274793777
## 68                                             2 0.003252626 0.090299416
## 69                                             1 0.003364853 0.093113497
## 70                                             2 0.002003760 0.057705330
## 71                                             1 0.006416485 0.163188592
## 72                                             2 0.003373195 0.093321936
## 73                                             1 0.004892538 0.129679965
## 74                                             2 0.001164040 0.034384018
## 75                                             1 0.006025735 0.154859944
## 76                                             2 0.005815880 0.150313875
## 77                                             1 0.004203624 0.113581174
## 78                                             2 0.002320958 0.066212851
## 79                                             1 0.006950691 0.174296512
## 80                                             2 0.001611111 0.046947805
## 81                                             1 0.003643474 0.100021618
## 82                                             2 0.003489907 0.096227785
## 83                                             1 0.006994782 0.175199303
## 84                                             2 0.002623669 0.074183826
## 85                                             1 0.004814035 0.127876630
## 86                                             2 0.001732161 0.050291404
## 87                                             1 0.008651249 0.207651495
## 88                                             2 0.004486374 0.120263936
## 89                                             1 0.001646322 0.047922917
## 90                                             2 0.001662257 0.048363530
## 91                                             1 0.012470173 0.272926388
## 92                                             2 0.003278289 0.090944532
## 93                                             1 0.005573618 0.145000814
## 94                                             2 0.001877109 0.054263146
## 95                                             1 0.004143486 0.112146024
## 96                                             2 0.003340655 0.092508271
## 97                                             1 0.004931077 0.130562364
## 98                                             2 0.001930941 0.055729418
## 99                                             1 0.005646307 0.146602343
## 100                                            2 0.003754838 0.102752025
## 101                                            1 0.004163107 0.112614785
## 102                                            2 0.002339288 0.066699580
## 103                                            1 0.011486150 0.257250510
## 104                                            2 0.001509241 0.044114954
## 105                                            1 0.002350473 0.066996334
## 106                                            2 0.003456245 0.095391685
## 107                                            1 0.007049762 0.176322102
## 108                                            2 0.004348026 0.117007390
## 109                                            1 0.004510559 0.120830610
## 110                                            2 0.001116689 0.033033152
## 111                                            1 0.008568231 0.206090328
## 112                                            2 0.004521728 0.121092058
## 113                                            1 0.002730095 0.076952590
## 114                                            2 0.001557158 0.045449635
## 115                                            1 0.008070113 0.196582338
## 116                                            2 0.003246662 0.090149354
## 117                                            1 0.005617490 0.145968205
## 118                                            2 0.003112335 0.086755820
## 119                                            1 0.003882117 0.105851391
## 120                                            2 0.002154886 0.061778730
##     pred.prob.3
## 1   0.865641796
## 2   0.941909716
## 3   0.770333219
## 4   0.899560310
## 5   0.921501207
## 6   0.931583642
## 7   0.729711013
## 8   0.926473579
## 9   0.934758109
## 10  0.933993072
## 11  0.818080109
## 12  0.877801325
## 13  0.807821408
## 14  0.967943390
## 15  0.850265868
## 16  0.875450600
## 17  0.919737175
## 18  0.924312487
## 19  0.805790363
## 20  0.937758762
## 21  0.849660924
## 22  0.909484841
## 23  0.830135437
## 24  0.939871574
## 25  0.909090464
## 26  0.942439608
## 27  0.768935264
## 28  0.843627493
## 29  0.926104851
## 30  0.954821018
## 31  0.731625035
## 32  0.925934653
## 33  0.896163692
## 34  0.937913476
## 35  0.874682642
## 36  0.878840783
## 37  0.806594349
## 38  0.947885552
## 39  0.858405255
## 40  0.916034975
## 41  0.920452241
## 42  0.923759024
## 43  0.714227764
## 44  0.941469523
## 45  0.897666544
## 46  0.910282335
## 47  0.829020697
## 48  0.903991383
## 49  0.914354301
## 50  0.962139644
## 51  0.770658822
## 52  0.842584505
## 53  0.883032060
## 54  0.957560581
## 55  0.808841634
## 56  0.926598911
## 57  0.895427679
## 58  0.900987930
## 59  0.881679458
## 60  0.918423406
## 61  0.808107102
## 62  0.947494675
## 63  0.785030869
## 64  0.920931685
## 65  0.947256303
## 66  0.924441202
## 67  0.712615706
## 68  0.906447958
## 69  0.903521650
## 70  0.940290910
## 71  0.830394923
## 72  0.903304869
## 73  0.865427496
## 74  0.964451942
## 75  0.839114321
## 76  0.843870245
## 77  0.882215202
## 78  0.931466191
## 79  0.818752797
## 80  0.951441084
## 81  0.896334909
## 82  0.900282308
## 83  0.817805916
## 84  0.923192505
## 85  0.867309336
## 86  0.947976435
## 87  0.783697256
## 88  0.875249690
## 89  0.950430761
## 90  0.949974213
## 91  0.714603439
## 92  0.905777178
## 93  0.849425569
## 94  0.943859744
## 95  0.883710490
## 96  0.904151074
## 97  0.864506559
## 98  0.942339641
## 99  0.847751350
## 100 0.893493137
## 101 0.883222108
## 102 0.930961133
## 103 0.731263340
## 104 0.954375805
## 105 0.930653194
## 106 0.901152070
## 107 0.816628136
## 108 0.878644584
## 109 0.874658832
## 110 0.965850159
## 111 0.785341441
## 112 0.874386214
## 113 0.920317316
## 114 0.952993207
## 115 0.795347549
## 116 0.906603985
## 117 0.848414305
## 118 0.910131844
## 119 0.890266492
## 120 0.936066384
view(setup1)
setup1[, c("pred.prob")] <- round(predict(step_test2, newdata=setup1, type="probs"),4)
#Table 4_9
setup1
##     police_force number_of_vehicles number_of_casualties first_road_number
## 1           22.7                1.8                  1.3             851.9
## 2           22.7                1.8                  1.3             851.9
## 3           22.7                1.8                  1.3             851.9
## 4           22.7                1.8                  1.3             851.9
## 5           22.7                1.8                  1.3             851.9
## 6           22.7                1.8                  1.3             851.9
## 7           22.7                1.8                  1.3             851.9
## 8           22.7                1.8                  1.3             851.9
## 9           22.7                1.8                  1.3             851.9
## 10          22.7                1.8                  1.3             851.9
## 11          22.7                1.8                  1.3             851.9
## 12          22.7                1.8                  1.3             851.9
## 13          22.7                1.8                  1.3             851.9
## 14          22.7                1.8                  1.3             851.9
## 15          22.7                1.8                  1.3             851.9
## 16          22.7                1.8                  1.3             851.9
## 17          22.7                1.8                  1.3             851.9
## 18          22.7                1.8                  1.3             851.9
## 19          22.7                1.8                  1.3             851.9
## 20          22.7                1.8                  1.3             851.9
## 21          22.7                1.8                  1.3             851.9
## 22          22.7                1.8                  1.3             851.9
## 23          22.7                1.8                  1.3             851.9
## 24          22.7                1.8                  1.3             851.9
## 25          22.7                1.8                  1.3             851.9
## 26          22.7                1.8                  1.3             851.9
## 27          22.7                1.8                  1.3             851.9
## 28          22.7                1.8                  1.3             851.9
## 29          22.7                1.8                  1.3             851.9
## 30          22.7                1.8                  1.3             851.9
## 31          22.7                1.8                  1.3             851.9
## 32          22.7                1.8                  1.3             851.9
## 33          22.7                1.8                  1.3             851.9
## 34          22.7                1.8                  1.3             851.9
## 35          22.7                1.8                  1.3             851.9
## 36          22.7                1.8                  1.3             851.9
## 37          22.7                1.8                  1.3             851.9
## 38          22.7                1.8                  1.3             851.9
## 39          22.7                1.8                  1.3             851.9
## 40          22.7                1.8                  1.3             851.9
## 41          22.7                1.8                  1.3             851.9
## 42          22.7                1.8                  1.3             851.9
## 43          22.7                1.8                  1.3             851.9
## 44          22.7                1.8                  1.3             851.9
## 45          22.7                1.8                  1.3             851.9
## 46          22.7                1.8                  1.3             851.9
## 47          22.7                1.8                  1.3             851.9
## 48          22.7                1.8                  1.3             851.9
## 49          22.7                1.8                  1.3             851.9
## 50          22.7                1.8                  1.3             851.9
## 51          22.7                1.8                  1.3             851.9
## 52          22.7                1.8                  1.3             851.9
## 53          22.7                1.8                  1.3             851.9
## 54          22.7                1.8                  1.3             851.9
## 55          22.7                1.8                  1.3             851.9
## 56          22.7                1.8                  1.3             851.9
## 57          22.7                1.8                  1.3             851.9
## 58          22.7                1.8                  1.3             851.9
## 59          22.7                1.8                  1.3             851.9
## 60          22.7                1.8                  1.3             851.9
## 61          22.7                1.8                  1.3             851.9
## 62          22.7                1.8                  1.3             851.9
## 63          22.7                1.8                  1.3             851.9
## 64          22.7                1.8                  1.3             851.9
## 65          22.7                1.8                  1.3             851.9
## 66          22.7                1.8                  1.3             851.9
## 67          22.7                1.8                  1.3             851.9
## 68          22.7                1.8                  1.3             851.9
## 69          22.7                1.8                  1.3             851.9
## 70          22.7                1.8                  1.3             851.9
## 71          22.7                1.8                  1.3             851.9
## 72          22.7                1.8                  1.3             851.9
## 73          22.7                1.8                  1.3             851.9
## 74          22.7                1.8                  1.3             851.9
## 75          22.7                1.8                  1.3             851.9
## 76          22.7                1.8                  1.3             851.9
## 77          22.7                1.8                  1.3             851.9
## 78          22.7                1.8                  1.3             851.9
## 79          22.7                1.8                  1.3             851.9
## 80          22.7                1.8                  1.3             851.9
## 81          22.7                1.8                  1.3             851.9
## 82          22.7                1.8                  1.3             851.9
## 83          22.7                1.8                  1.3             851.9
## 84          22.7                1.8                  1.3             851.9
## 85          22.7                1.8                  1.3             851.9
## 86          22.7                1.8                  1.3             851.9
## 87          22.7                1.8                  1.3             851.9
## 88          22.7                1.8                  1.3             851.9
## 89          22.7                1.8                  1.3             851.9
## 90          22.7                1.8                  1.3             851.9
## 91          22.7                1.8                  1.3             851.9
## 92          22.7                1.8                  1.3             851.9
## 93          22.7                1.8                  1.3             851.9
## 94          22.7                1.8                  1.3             851.9
## 95          22.7                1.8                  1.3             851.9
## 96          22.7                1.8                  1.3             851.9
## 97          22.7                1.8                  1.3             851.9
## 98          22.7                1.8                  1.3             851.9
## 99          22.7                1.8                  1.3             851.9
## 100         22.7                1.8                  1.3             851.9
## 101         22.7                1.8                  1.3             851.9
## 102         22.7                1.8                  1.3             851.9
## 103         22.7                1.8                  1.3             851.9
## 104         22.7                1.8                  1.3             851.9
## 105         22.7                1.8                  1.3             851.9
## 106         22.7                1.8                  1.3             851.9
## 107         22.7                1.8                  1.3             851.9
## 108         22.7                1.8                  1.3             851.9
## 109         22.7                1.8                  1.3             851.9
## 110         22.7                1.8                  1.3             851.9
## 111         22.7                1.8                  1.3             851.9
## 112         22.7                1.8                  1.3             851.9
## 113         22.7                1.8                  1.3             851.9
## 114         22.7                1.8                  1.3             851.9
## 115         22.7                1.8                  1.3             851.9
## 116         22.7                1.8                  1.3             851.9
## 117         22.7                1.8                  1.3             851.9
## 118         22.7                1.8                  1.3             851.9
## 119         22.7                1.8                  1.3             851.9
## 120         22.7                1.8                  1.3             851.9
##     speed_limit junction_detail junction_control second_road_class
## 1            33               1                1               5.3
## 2            33               2                2               5.3
## 3            33               3                3               5.3
## 4            33               5                4               5.3
## 5            33               6                1               5.3
## 6            33               7                2               5.3
## 7            33               8                3               5.3
## 8            33               9                4               5.3
## 9            33               1                1               5.3
## 10           33               2                2               5.3
## 11           33               3                3               5.3
## 12           33               5                4               5.3
## 13           33               6                1               5.3
## 14           33               7                2               5.3
## 15           33               8                3               5.3
## 16           33               9                4               5.3
## 17           33               1                1               5.3
## 18           33               2                2               5.3
## 19           33               3                3               5.3
## 20           33               5                4               5.3
## 21           33               6                1               5.3
## 22           33               7                2               5.3
## 23           33               8                3               5.3
## 24           33               9                4               5.3
## 25           33               1                1               5.3
## 26           33               2                2               5.3
## 27           33               3                3               5.3
## 28           33               5                4               5.3
## 29           33               6                1               5.3
## 30           33               7                2               5.3
## 31           33               8                3               5.3
## 32           33               9                4               5.3
## 33           33               1                1               5.3
## 34           33               2                2               5.3
## 35           33               3                3               5.3
## 36           33               5                4               5.3
## 37           33               6                1               5.3
## 38           33               7                2               5.3
## 39           33               8                3               5.3
## 40           33               9                4               5.3
## 41           33               1                1               5.3
## 42           33               2                2               5.3
## 43           33               3                3               5.3
## 44           33               5                4               5.3
## 45           33               6                1               5.3
## 46           33               7                2               5.3
## 47           33               8                3               5.3
## 48           33               9                4               5.3
## 49           33               1                1               5.3
## 50           33               2                2               5.3
## 51           33               3                3               5.3
## 52           33               5                4               5.3
## 53           33               6                1               5.3
## 54           33               7                2               5.3
## 55           33               8                3               5.3
## 56           33               9                4               5.3
## 57           33               1                1               5.3
## 58           33               2                2               5.3
## 59           33               3                3               5.3
## 60           33               5                4               5.3
## 61           33               6                1               5.3
## 62           33               7                2               5.3
## 63           33               8                3               5.3
## 64           33               9                4               5.3
## 65           33               1                1               5.3
## 66           33               2                2               5.3
## 67           33               3                3               5.3
## 68           33               5                4               5.3
## 69           33               6                1               5.3
## 70           33               7                2               5.3
## 71           33               8                3               5.3
## 72           33               9                4               5.3
## 73           33               1                1               5.3
## 74           33               2                2               5.3
## 75           33               3                3               5.3
## 76           33               5                4               5.3
## 77           33               6                1               5.3
## 78           33               7                2               5.3
## 79           33               8                3               5.3
## 80           33               9                4               5.3
## 81           33               1                1               5.3
## 82           33               2                2               5.3
## 83           33               3                3               5.3
## 84           33               5                4               5.3
## 85           33               6                1               5.3
## 86           33               7                2               5.3
## 87           33               8                3               5.3
## 88           33               9                4               5.3
## 89           33               1                1               5.3
## 90           33               2                2               5.3
## 91           33               3                3               5.3
## 92           33               5                4               5.3
## 93           33               6                1               5.3
## 94           33               7                2               5.3
## 95           33               8                3               5.3
## 96           33               9                4               5.3
## 97           33               1                1               5.3
## 98           33               2                2               5.3
## 99           33               3                3               5.3
## 100          33               5                4               5.3
## 101          33               6                1               5.3
## 102          33               7                2               5.3
## 103          33               8                3               5.3
## 104          33               9                4               5.3
## 105          33               1                1               5.3
## 106          33               2                2               5.3
## 107          33               3                3               5.3
## 108          33               5                4               5.3
## 109          33               6                1               5.3
## 110          33               7                2               5.3
## 111          33               8                3               5.3
## 112          33               9                4               5.3
## 113          33               1                1               5.3
## 114          33               2                2               5.3
## 115          33               3                3               5.3
## 116          33               5                4               5.3
## 117          33               6                1               5.3
## 118          33               7                2               5.3
## 119          33               8                3               5.3
## 120          33               9                4               5.3
##     second_road_number light_conditions road_surface_conditions
## 1                397.6                1                       1
## 2                397.6                4                       2
## 3                397.6                5                       3
## 4                397.6                6                       4
## 5                397.6                7                       5
## 6                397.6                1                       1
## 7                397.6                4                       2
## 8                397.6                5                       3
## 9                397.6                6                       4
## 10               397.6                7                       5
## 11               397.6                1                       1
## 12               397.6                4                       2
## 13               397.6                5                       3
## 14               397.6                6                       4
## 15               397.6                7                       5
## 16               397.6                1                       1
## 17               397.6                4                       2
## 18               397.6                5                       3
## 19               397.6                6                       4
## 20               397.6                7                       5
## 21               397.6                1                       1
## 22               397.6                4                       2
## 23               397.6                5                       3
## 24               397.6                6                       4
## 25               397.6                7                       5
## 26               397.6                1                       1
## 27               397.6                4                       2
## 28               397.6                5                       3
## 29               397.6                6                       4
## 30               397.6                7                       5
## 31               397.6                1                       1
## 32               397.6                4                       2
## 33               397.6                5                       3
## 34               397.6                6                       4
## 35               397.6                7                       5
## 36               397.6                1                       1
## 37               397.6                4                       2
## 38               397.6                5                       3
## 39               397.6                6                       4
## 40               397.6                7                       5
## 41               397.6                1                       1
## 42               397.6                4                       2
## 43               397.6                5                       3
## 44               397.6                6                       4
## 45               397.6                7                       5
## 46               397.6                1                       1
## 47               397.6                4                       2
## 48               397.6                5                       3
## 49               397.6                6                       4
## 50               397.6                7                       5
## 51               397.6                1                       1
## 52               397.6                4                       2
## 53               397.6                5                       3
## 54               397.6                6                       4
## 55               397.6                7                       5
## 56               397.6                1                       1
## 57               397.6                4                       2
## 58               397.6                5                       3
## 59               397.6                6                       4
## 60               397.6                7                       5
## 61               397.6                1                       1
## 62               397.6                4                       2
## 63               397.6                5                       3
## 64               397.6                6                       4
## 65               397.6                7                       5
## 66               397.6                1                       1
## 67               397.6                4                       2
## 68               397.6                5                       3
## 69               397.6                6                       4
## 70               397.6                7                       5
## 71               397.6                1                       1
## 72               397.6                4                       2
## 73               397.6                5                       3
## 74               397.6                6                       4
## 75               397.6                7                       5
## 76               397.6                1                       1
## 77               397.6                4                       2
## 78               397.6                5                       3
## 79               397.6                6                       4
## 80               397.6                7                       5
## 81               397.6                1                       1
## 82               397.6                4                       2
## 83               397.6                5                       3
## 84               397.6                6                       4
## 85               397.6                7                       5
## 86               397.6                1                       1
## 87               397.6                4                       2
## 88               397.6                5                       3
## 89               397.6                6                       4
## 90               397.6                7                       5
## 91               397.6                1                       1
## 92               397.6                4                       2
## 93               397.6                5                       3
## 94               397.6                6                       4
## 95               397.6                7                       5
## 96               397.6                1                       1
## 97               397.6                4                       2
## 98               397.6                5                       3
## 99               397.6                6                       4
## 100              397.6                7                       5
## 101              397.6                1                       1
## 102              397.6                4                       2
## 103              397.6                5                       3
## 104              397.6                6                       4
## 105              397.6                7                       5
## 106              397.6                1                       1
## 107              397.6                4                       2
## 108              397.6                5                       3
## 109              397.6                6                       4
## 110              397.6                7                       5
## 111              397.6                1                       1
## 112              397.6                4                       2
## 113              397.6                5                       3
## 114              397.6                6                       4
## 115              397.6                7                       5
## 116              397.6                1                       1
## 117              397.6                4                       2
## 118              397.6                5                       3
## 119              397.6                6                       4
## 120              397.6                7                       5
##     pedestrian_crossing_human_control
## 1                                   0
## 2                                   1
## 3                                   2
## 4                                   0
## 5                                   1
## 6                                   2
## 7                                   0
## 8                                   1
## 9                                   2
## 10                                  0
## 11                                  1
## 12                                  2
## 13                                  0
## 14                                  1
## 15                                  2
## 16                                  0
## 17                                  1
## 18                                  2
## 19                                  0
## 20                                  1
## 21                                  2
## 22                                  0
## 23                                  1
## 24                                  2
## 25                                  0
## 26                                  1
## 27                                  2
## 28                                  0
## 29                                  1
## 30                                  2
## 31                                  0
## 32                                  1
## 33                                  2
## 34                                  0
## 35                                  1
## 36                                  2
## 37                                  0
## 38                                  1
## 39                                  2
## 40                                  0
## 41                                  1
## 42                                  2
## 43                                  0
## 44                                  1
## 45                                  2
## 46                                  0
## 47                                  1
## 48                                  2
## 49                                  0
## 50                                  1
## 51                                  2
## 52                                  0
## 53                                  1
## 54                                  2
## 55                                  0
## 56                                  1
## 57                                  2
## 58                                  0
## 59                                  1
## 60                                  2
## 61                                  0
## 62                                  1
## 63                                  2
## 64                                  0
## 65                                  1
## 66                                  2
## 67                                  0
## 68                                  1
## 69                                  2
## 70                                  0
## 71                                  1
## 72                                  2
## 73                                  0
## 74                                  1
## 75                                  2
## 76                                  0
## 77                                  1
## 78                                  2
## 79                                  0
## 80                                  1
## 81                                  2
## 82                                  0
## 83                                  1
## 84                                  2
## 85                                  0
## 86                                  1
## 87                                  2
## 88                                  0
## 89                                  1
## 90                                  2
## 91                                  0
## 92                                  1
## 93                                  2
## 94                                  0
## 95                                  1
## 96                                  2
## 97                                  0
## 98                                  1
## 99                                  2
## 100                                 0
## 101                                 1
## 102                                 2
## 103                                 0
## 104                                 1
## 105                                 2
## 106                                 0
## 107                                 1
## 108                                 2
## 109                                 0
## 110                                 1
## 111                                 2
## 112                                 0
## 113                                 1
## 114                                 2
## 115                                 0
## 116                                 1
## 117                                 2
## 118                                 0
## 119                                 1
## 120                                 2
##     did_police_officer_attend_scene_of_collision pred.prob.1 pred.prob.2
## 1                                              1      0.0049      0.1295
## 2                                              2      0.0019      0.0561
## 3                                              1      0.0093      0.2203
## 4                                              2      0.0035      0.0969
## 5                                              1      0.0027      0.0758
## 6                                              2      0.0023      0.0661
## 7                                              1      0.0116      0.2587
## 8                                              2      0.0025      0.0710
## 9                                              1      0.0022      0.0630
## 10                                             2      0.0022      0.0638
## 11                                             1      0.0070      0.1749
## 12                                             2      0.0044      0.1178
## 13                                             1      0.0075      0.1847
## 14                                             2      0.0010      0.0310
## 15                                             1      0.0055      0.1442
## 16                                             2      0.0045      0.1201
## 17                                             1      0.0028      0.0775
## 18                                             2      0.0026      0.0731
## 19                                             1      0.0076      0.1866
## 20                                             2      0.0021      0.0601
## 21                                             1      0.0056      0.1448
## 22                                             2      0.0031      0.0874
## 23                                             1      0.0064      0.1634
## 24                                             2      0.0020      0.0581
## 25                                             1      0.0032      0.0878
## 26                                             2      0.0019      0.0556
## 27                                             1      0.0094      0.2217
## 28                                             2      0.0058      0.1505
## 29                                             1      0.0025      0.0714
## 30                                             2      0.0015      0.0437
## 31                                             1      0.0115      0.2569
## 32                                             2      0.0025      0.0715
## 33                                             1      0.0037      0.1002
## 34                                             2      0.0021      0.0600
## 35                                             1      0.0045      0.1208
## 36                                             2      0.0043      0.1168
## 37                                             1      0.0075      0.1859
## 38                                             2      0.0017      0.0504
## 39                                             1      0.0052      0.1364
## 40                                             2      0.0029      0.0811
## 41                                             1      0.0027      0.0768
## 42                                             2      0.0026      0.0736
## 43                                             1      0.0125      0.2733
## 44                                             2      0.0020      0.0566
## 45                                             1      0.0036      0.0987
## 46                                             2      0.0031      0.0866
## 47                                             1      0.0065      0.1645
## 48                                             2      0.0033      0.0927
## 49                                             1      0.0030      0.0827
## 50                                             2      0.0012      0.0366
## 51                                             1      0.0093      0.2200
## 52                                             2      0.0059      0.1515
## 53                                             1      0.0042      0.1128
## 54                                             2      0.0014      0.0410
## 55                                             1      0.0074      0.1837
## 56                                             2      0.0025      0.0709
## 57                                             1      0.0037      0.1009
## 58                                             2      0.0035      0.0955
## 59                                             1      0.0042      0.1141
## 60                                             2      0.0028      0.0788
## 61                                             1      0.0075      0.1844
## 62                                             2      0.0017      0.0508
## 63                                             1      0.0086      0.2064
## 64                                             2      0.0027      0.0764
## 65                                             1      0.0018      0.0510
## 66                                             2      0.0026      0.0730
## 67                                             1      0.0126      0.2748
## 68                                             2      0.0033      0.0903
## 69                                             1      0.0034      0.0931
## 70                                             2      0.0020      0.0577
## 71                                             1      0.0064      0.1632
## 72                                             2      0.0034      0.0933
## 73                                             1      0.0049      0.1297
## 74                                             2      0.0012      0.0344
## 75                                             1      0.0060      0.1549
## 76                                             2      0.0058      0.1503
## 77                                             1      0.0042      0.1136
## 78                                             2      0.0023      0.0662
## 79                                             1      0.0070      0.1743
## 80                                             2      0.0016      0.0469
## 81                                             1      0.0036      0.1000
## 82                                             2      0.0035      0.0962
## 83                                             1      0.0070      0.1752
## 84                                             2      0.0026      0.0742
## 85                                             1      0.0048      0.1279
## 86                                             2      0.0017      0.0503
## 87                                             1      0.0087      0.2077
## 88                                             2      0.0045      0.1203
## 89                                             1      0.0016      0.0479
## 90                                             2      0.0017      0.0484
## 91                                             1      0.0125      0.2729
## 92                                             2      0.0033      0.0909
## 93                                             1      0.0056      0.1450
## 94                                             2      0.0019      0.0543
## 95                                             1      0.0041      0.1121
## 96                                             2      0.0033      0.0925
## 97                                             1      0.0049      0.1306
## 98                                             2      0.0019      0.0557
## 99                                             1      0.0056      0.1466
## 100                                            2      0.0038      0.1028
## 101                                            1      0.0042      0.1126
## 102                                            2      0.0023      0.0667
## 103                                            1      0.0115      0.2573
## 104                                            2      0.0015      0.0441
## 105                                            1      0.0024      0.0670
## 106                                            2      0.0035      0.0954
## 107                                            1      0.0070      0.1763
## 108                                            2      0.0043      0.1170
## 109                                            1      0.0045      0.1208
## 110                                            2      0.0011      0.0330
## 111                                            1      0.0086      0.2061
## 112                                            2      0.0045      0.1211
## 113                                            1      0.0027      0.0770
## 114                                            2      0.0016      0.0454
## 115                                            1      0.0081      0.1966
## 116                                            2      0.0032      0.0901
## 117                                            1      0.0056      0.1460
## 118                                            2      0.0031      0.0868
## 119                                            1      0.0039      0.1059
## 120                                            2      0.0022      0.0618
##     pred.prob.3
## 1        0.8656
## 2        0.9419
## 3        0.7703
## 4        0.8996
## 5        0.9215
## 6        0.9316
## 7        0.7297
## 8        0.9265
## 9        0.9348
## 10       0.9340
## 11       0.8181
## 12       0.8778
## 13       0.8078
## 14       0.9679
## 15       0.8503
## 16       0.8755
## 17       0.9197
## 18       0.9243
## 19       0.8058
## 20       0.9378
## 21       0.8497
## 22       0.9095
## 23       0.8301
## 24       0.9399
## 25       0.9091
## 26       0.9424
## 27       0.7689
## 28       0.8436
## 29       0.9261
## 30       0.9548
## 31       0.7316
## 32       0.9259
## 33       0.8962
## 34       0.9379
## 35       0.8747
## 36       0.8788
## 37       0.8066
## 38       0.9479
## 39       0.8584
## 40       0.9160
## 41       0.9205
## 42       0.9238
## 43       0.7142
## 44       0.9415
## 45       0.8977
## 46       0.9103
## 47       0.8290
## 48       0.9040
## 49       0.9144
## 50       0.9621
## 51       0.7707
## 52       0.8426
## 53       0.8830
## 54       0.9576
## 55       0.8088
## 56       0.9266
## 57       0.8954
## 58       0.9010
## 59       0.8817
## 60       0.9184
## 61       0.8081
## 62       0.9475
## 63       0.7850
## 64       0.9209
## 65       0.9473
## 66       0.9244
## 67       0.7126
## 68       0.9064
## 69       0.9035
## 70       0.9403
## 71       0.8304
## 72       0.9033
## 73       0.8654
## 74       0.9645
## 75       0.8391
## 76       0.8439
## 77       0.8822
## 78       0.9315
## 79       0.8188
## 80       0.9514
## 81       0.8963
## 82       0.9003
## 83       0.8178
## 84       0.9232
## 85       0.8673
## 86       0.9480
## 87       0.7837
## 88       0.8752
## 89       0.9504
## 90       0.9500
## 91       0.7146
## 92       0.9058
## 93       0.8494
## 94       0.9439
## 95       0.8837
## 96       0.9042
## 97       0.8645
## 98       0.9423
## 99       0.8478
## 100      0.8935
## 101      0.8832
## 102      0.9310
## 103      0.7313
## 104      0.9544
## 105      0.9307
## 106      0.9012
## 107      0.8166
## 108      0.8786
## 109      0.8747
## 110      0.9659
## 111      0.7853
## 112      0.8744
## 113      0.9203
## 114      0.9530
## 115      0.7953
## 116      0.9066
## 117      0.8484
## 118      0.9101
## 119      0.8903
## 120      0.9361
view(setup1)
predict(step_test2, newdata=setup1, type="probs")
##               1          2         3
## 1   0.004883582 0.12947462 0.8656418
## 2   0.001946197 0.05614409 0.9419097
## 3   0.009338635 0.22032815 0.7703332
## 4   0.003517898 0.09692179 0.8995603
## 5   0.002686195 0.07581260 0.9215012
## 6   0.002316698 0.06609966 0.9315836
## 7   0.011576022 0.25871296 0.7297110
## 8   0.002502999 0.07102342 0.9264736
## 9   0.002201956 0.06303994 0.9347581
## 10  0.002229539 0.06377739 0.9339931
## 11  0.006982004 0.17493789 0.8180801
## 12  0.004382294 0.11781638 0.8778013
## 13  0.007465756 0.18471284 0.8078214
## 14  0.001046048 0.03101056 0.9679434
## 15  0.005537238 0.14419689 0.8502659
## 16  0.004478158 0.12007124 0.8754506
## 17  0.002751647 0.07751118 0.9197372
## 18  0.002582386 0.07310513 0.9243125
## 19  0.007562934 0.18664670 0.8057904
## 20  0.002094186 0.06014705 0.9377588
## 21  0.005563421 0.14477565 0.8496609
## 22  0.003136895 0.08737826 0.9094848
## 23  0.006428234 0.16343633 0.8301354
## 24  0.002018703 0.05810972 0.9398716
## 25  0.003151882 0.08775765 0.9090905
## 26  0.001927396 0.05563300 0.9424396
## 27  0.009411864 0.22165287 0.7689353
## 28  0.005826536 0.15054597 0.8436275
## 29  0.002516518 0.07137863 0.9261049
## 30  0.001493839 0.04368514 0.9548210
## 31  0.011465262 0.25690970 0.7316250
## 32  0.002522762 0.07154258 0.9259347
## 33  0.003650164 0.10018614 0.8961637
## 34  0.002088648 0.05999788 0.9379135
## 35  0.004509583 0.12080777 0.8746826
## 36  0.004340062 0.11681916 0.8788408
## 37  0.007524410 0.18588124 0.8065943
## 38  0.001735348 0.05037910 0.9478856
## 39  0.005188409 0.13640634 0.8584053
## 40  0.002889802 0.08107522 0.9160350
## 41  0.002725086 0.07682267 0.9204522
## 42  0.002602774 0.07363820 0.9237590
## 43  0.012492869 0.27327937 0.7142278
## 44  0.001961831 0.05656865 0.9414695
## 45  0.003591523 0.09874193 0.8976665
## 46  0.003106627 0.08661104 0.9102823
## 47  0.006478790 0.16450051 0.8290207
## 48  0.003346791 0.09266183 0.9039914
## 49  0.002952877 0.08269282 0.9143543
## 50  0.001242640 0.03661772 0.9621396
## 51  0.009321616 0.22001956 0.7706588
## 52  0.005872388 0.15154311 0.8425845
## 53  0.004170747 0.11279719 0.8830321
## 54  0.001399373 0.04104005 0.9575606
## 55  0.007417118 0.18374125 0.8088416
## 56  0.002498406 0.07090268 0.9265989
## 57  0.003678952 0.10089337 0.8954277
## 58  0.003462593 0.09554948 0.9009879
## 59  0.004225219 0.11409532 0.8816795
## 60  0.002800550 0.07877604 0.9184234
## 61  0.007452124 0.18444077 0.8081071
## 62  0.001749061 0.05075626 0.9474947
## 63  0.008583886 0.20638524 0.7850309
## 64  0.002707300 0.07636102 0.9209317
## 65  0.001757429 0.05098627 0.9472563
## 66  0.002577647 0.07298115 0.9244412
## 67  0.012590517 0.27479378 0.7126157
## 68  0.003252626 0.09029942 0.9064480
## 69  0.003364853 0.09311350 0.9035216
## 70  0.002003760 0.05770533 0.9402909
## 71  0.006416485 0.16318859 0.8303949
## 72  0.003373195 0.09332194 0.9033049
## 73  0.004892538 0.12967997 0.8654275
## 74  0.001164040 0.03438402 0.9644519
## 75  0.006025735 0.15485994 0.8391143
## 76  0.005815880 0.15031387 0.8438702
## 77  0.004203624 0.11358117 0.8822152
## 78  0.002320958 0.06621285 0.9314662
## 79  0.006950691 0.17429651 0.8187528
## 80  0.001611111 0.04694781 0.9514411
## 81  0.003643474 0.10002162 0.8963349
## 82  0.003489907 0.09622778 0.9002823
## 83  0.006994782 0.17519930 0.8178059
## 84  0.002623669 0.07418383 0.9231925
## 85  0.004814035 0.12787663 0.8673093
## 86  0.001732161 0.05029140 0.9479764
## 87  0.008651249 0.20765150 0.7836973
## 88  0.004486374 0.12026394 0.8752497
## 89  0.001646322 0.04792292 0.9504308
## 90  0.001662257 0.04836353 0.9499742
## 91  0.012470173 0.27292639 0.7146034
## 92  0.003278289 0.09094453 0.9057772
## 93  0.005573618 0.14500081 0.8494256
## 94  0.001877109 0.05426315 0.9438597
## 95  0.004143486 0.11214602 0.8837105
## 96  0.003340655 0.09250827 0.9041511
## 97  0.004931077 0.13056236 0.8645066
## 98  0.001930941 0.05572942 0.9423396
## 99  0.005646307 0.14660234 0.8477514
## 100 0.003754838 0.10275203 0.8934931
## 101 0.004163107 0.11261478 0.8832221
## 102 0.002339288 0.06669958 0.9309611
## 103 0.011486150 0.25725051 0.7312633
## 104 0.001509241 0.04411495 0.9543758
## 105 0.002350473 0.06699633 0.9306532
## 106 0.003456245 0.09539169 0.9011521
## 107 0.007049762 0.17632210 0.8166281
## 108 0.004348026 0.11700739 0.8786446
## 109 0.004510559 0.12083061 0.8746588
## 110 0.001116689 0.03303315 0.9658502
## 111 0.008568231 0.20609033 0.7853414
## 112 0.004521728 0.12109206 0.8743862
## 113 0.002730095 0.07695259 0.9203173
## 114 0.001557158 0.04544964 0.9529932
## 115 0.008070113 0.19658234 0.7953475
## 116 0.003246662 0.09014935 0.9066040
## 117 0.005617490 0.14596820 0.8484143
## 118 0.003112335 0.08675582 0.9101318
## 119 0.003882117 0.10585139 0.8902665
## 120 0.002154886 0.06177873 0.9360664
#Table 4_10
Table4_10 <- round(predict(step_test2, newdata=setup1, type="probs"),4)
Table4_10
##          1      2      3
## 1   0.0049 0.1295 0.8656
## 2   0.0019 0.0561 0.9419
## 3   0.0093 0.2203 0.7703
## 4   0.0035 0.0969 0.8996
## 5   0.0027 0.0758 0.9215
## 6   0.0023 0.0661 0.9316
## 7   0.0116 0.2587 0.7297
## 8   0.0025 0.0710 0.9265
## 9   0.0022 0.0630 0.9348
## 10  0.0022 0.0638 0.9340
## 11  0.0070 0.1749 0.8181
## 12  0.0044 0.1178 0.8778
## 13  0.0075 0.1847 0.8078
## 14  0.0010 0.0310 0.9679
## 15  0.0055 0.1442 0.8503
## 16  0.0045 0.1201 0.8755
## 17  0.0028 0.0775 0.9197
## 18  0.0026 0.0731 0.9243
## 19  0.0076 0.1866 0.8058
## 20  0.0021 0.0601 0.9378
## 21  0.0056 0.1448 0.8497
## 22  0.0031 0.0874 0.9095
## 23  0.0064 0.1634 0.8301
## 24  0.0020 0.0581 0.9399
## 25  0.0032 0.0878 0.9091
## 26  0.0019 0.0556 0.9424
## 27  0.0094 0.2217 0.7689
## 28  0.0058 0.1505 0.8436
## 29  0.0025 0.0714 0.9261
## 30  0.0015 0.0437 0.9548
## 31  0.0115 0.2569 0.7316
## 32  0.0025 0.0715 0.9259
## 33  0.0037 0.1002 0.8962
## 34  0.0021 0.0600 0.9379
## 35  0.0045 0.1208 0.8747
## 36  0.0043 0.1168 0.8788
## 37  0.0075 0.1859 0.8066
## 38  0.0017 0.0504 0.9479
## 39  0.0052 0.1364 0.8584
## 40  0.0029 0.0811 0.9160
## 41  0.0027 0.0768 0.9205
## 42  0.0026 0.0736 0.9238
## 43  0.0125 0.2733 0.7142
## 44  0.0020 0.0566 0.9415
## 45  0.0036 0.0987 0.8977
## 46  0.0031 0.0866 0.9103
## 47  0.0065 0.1645 0.8290
## 48  0.0033 0.0927 0.9040
## 49  0.0030 0.0827 0.9144
## 50  0.0012 0.0366 0.9621
## 51  0.0093 0.2200 0.7707
## 52  0.0059 0.1515 0.8426
## 53  0.0042 0.1128 0.8830
## 54  0.0014 0.0410 0.9576
## 55  0.0074 0.1837 0.8088
## 56  0.0025 0.0709 0.9266
## 57  0.0037 0.1009 0.8954
## 58  0.0035 0.0955 0.9010
## 59  0.0042 0.1141 0.8817
## 60  0.0028 0.0788 0.9184
## 61  0.0075 0.1844 0.8081
## 62  0.0017 0.0508 0.9475
## 63  0.0086 0.2064 0.7850
## 64  0.0027 0.0764 0.9209
## 65  0.0018 0.0510 0.9473
## 66  0.0026 0.0730 0.9244
## 67  0.0126 0.2748 0.7126
## 68  0.0033 0.0903 0.9064
## 69  0.0034 0.0931 0.9035
## 70  0.0020 0.0577 0.9403
## 71  0.0064 0.1632 0.8304
## 72  0.0034 0.0933 0.9033
## 73  0.0049 0.1297 0.8654
## 74  0.0012 0.0344 0.9645
## 75  0.0060 0.1549 0.8391
## 76  0.0058 0.1503 0.8439
## 77  0.0042 0.1136 0.8822
## 78  0.0023 0.0662 0.9315
## 79  0.0070 0.1743 0.8188
## 80  0.0016 0.0469 0.9514
## 81  0.0036 0.1000 0.8963
## 82  0.0035 0.0962 0.9003
## 83  0.0070 0.1752 0.8178
## 84  0.0026 0.0742 0.9232
## 85  0.0048 0.1279 0.8673
## 86  0.0017 0.0503 0.9480
## 87  0.0087 0.2077 0.7837
## 88  0.0045 0.1203 0.8752
## 89  0.0016 0.0479 0.9504
## 90  0.0017 0.0484 0.9500
## 91  0.0125 0.2729 0.7146
## 92  0.0033 0.0909 0.9058
## 93  0.0056 0.1450 0.8494
## 94  0.0019 0.0543 0.9439
## 95  0.0041 0.1121 0.8837
## 96  0.0033 0.0925 0.9042
## 97  0.0049 0.1306 0.8645
## 98  0.0019 0.0557 0.9423
## 99  0.0056 0.1466 0.8478
## 100 0.0038 0.1028 0.8935
## 101 0.0042 0.1126 0.8832
## 102 0.0023 0.0667 0.9310
## 103 0.0115 0.2573 0.7313
## 104 0.0015 0.0441 0.9544
## 105 0.0024 0.0670 0.9307
## 106 0.0035 0.0954 0.9012
## 107 0.0070 0.1763 0.8166
## 108 0.0043 0.1170 0.8786
## 109 0.0045 0.1208 0.8747
## 110 0.0011 0.0330 0.9659
## 111 0.0086 0.2061 0.7853
## 112 0.0045 0.1211 0.8744
## 113 0.0027 0.0770 0.9203
## 114 0.0016 0.0454 0.9530
## 115 0.0081 0.1966 0.7953
## 116 0.0032 0.0901 0.9066
## 117 0.0056 0.1460 0.8484
## 118 0.0031 0.0868 0.9101
## 119 0.0039 0.1059 0.8903
## 120 0.0022 0.0618 0.9361
view(Table4_10)
#The i-th row and j-th column represent the probability that the i-th observation (accident victim) under given 6-factor conditons belongs to the j-th severity among all 3 conditons:"1: Fatal, 2: Serious, 3: Slight".

#For example, Row 9 & Column 13+1 is 0.0022, meaning a victim (sample size is 2),  who is under 6-factor conditons: "junction_detail(1),junction_control(1), light_conditions(6), road_surface_conditions(4), pedestrian_crossing_human_control(2) and did_police_officer_attend_scene_of_collision(1)", has a probability of 2.2% to be fatal in crash.

view(setup1)
head(setup1)
##   police_force number_of_vehicles number_of_casualties first_road_number
## 1         22.7                1.8                  1.3             851.9
## 2         22.7                1.8                  1.3             851.9
## 3         22.7                1.8                  1.3             851.9
## 4         22.7                1.8                  1.3             851.9
## 5         22.7                1.8                  1.3             851.9
## 6         22.7                1.8                  1.3             851.9
##   speed_limit junction_detail junction_control second_road_class
## 1          33               1                1               5.3
## 2          33               2                2               5.3
## 3          33               3                3               5.3
## 4          33               5                4               5.3
## 5          33               6                1               5.3
## 6          33               7                2               5.3
##   second_road_number light_conditions road_surface_conditions
## 1              397.6                1                       1
## 2              397.6                4                       2
## 3              397.6                5                       3
## 4              397.6                6                       4
## 5              397.6                7                       5
## 6              397.6                1                       1
##   pedestrian_crossing_human_control
## 1                                 0
## 2                                 1
## 3                                 2
## 4                                 0
## 5                                 1
## 6                                 2
##   did_police_officer_attend_scene_of_collision pred.prob.1 pred.prob.2
## 1                                            1      0.0049      0.1295
## 2                                            2      0.0019      0.0561
## 3                                            1      0.0093      0.2203
## 4                                            2      0.0035      0.0969
## 5                                            1      0.0027      0.0758
## 6                                            2      0.0023      0.0661
##   pred.prob.3
## 1      0.8656
## 2      0.9419
## 3      0.7703
## 4      0.8996
## 5      0.9215
## 6      0.9316
dim(setup1)
## [1] 120  14
##Plot the results of Table4_10

library(reshape2)
library(ggplot2)
is.data.frame(Table4_10)
## [1] FALSE
# Create a data frame for Table 4_10
Table4_10_ <-  data.frame(
  Case = 1:120, # Case numbers
  Severity_1 = c(0.0049, 0.0019, 0.0093, 0.0035, 0.0027, 0.0023, 0.0116, 0.0025, 0.0022, 0.0022, 
                 0.0070, 0.0044, 0.0075, 0.0010, 0.0055, 0.0045, 0.0028, 0.0026, 0.0076, 0.0021,
                 0.0056, 0.0031, 0.0064, 0.0020, 0.0032, 0.0019, 0.0094, 0.0058, 0.0025, 0.0015,
                 0.0115, 0.0025, 0.0037, 0.0021, 0.0045, 0.0043, 0.0075, 0.0017, 0.0052, 0.0029,
                 0.0027, 0.0026, 0.0125, 0.0020, 0.0036, 0.0031, 0.0065, 0.0033, 0.0030, 0.0012,
                 0.0093, 0.0059, 0.0042, 0.0014, 0.0074, 0.0025, 0.0037, 0.0035, 0.0042, 0.0028,
                 0.0075, 0.0017, 0.0086, 0.0027, 0.0018, 0.0026, 0.0126, 0.0033, 0.0034, 0.0020,
                 0.0064, 0.0034, 0.0049, 0.0012, 0.0060, 0.0058, 0.0042, 0.0023, 0.0070, 0.0016,
                 0.0036, 0.0035, 0.0070, 0.0026, 0.0048, 0.0017, 0.0087, 0.0045, 0.0016, 0.0017,
                 0.0125, 0.0033, 0.0056, 0.0019, 0.0041, 0.0033, 0.0049, 0.0019, 0.0056, 0.0038,
                 0.0042, 0.0023, 0.0115, 0.0015, 0.0024, 0.0035, 0.0070, 0.0043, 0.0045, 0.0011,
                 0.0086, 0.0045, 0.0027, 0.0016, 0.0081, 0.0032, 0.0056, 0.0031, 0.0039, 0.0022),
  Severity_2 = c(0.1295, 0.0561, 0.2203, 0.0969, 0.0758, 0.0661, 0.2587, 0.0710, 0.0630, 0.0638, 
                 0.1749, 0.1178, 0.1847, 0.0310, 0.1442, 0.1201, 0.0775, 0.0731, 0.1866, 0.0601,
                 0.1448, 0.0874, 0.1634, 0.0581, 0.0878, 0.0556, 0.2217, 0.1505, 0.0714, 0.0437,
                 0.2569, 0.0715, 0.1002, 0.0600, 0.1208, 0.1168, 0.1859, 0.0504, 0.1364, 0.0811,
                 0.0768, 0.0736, 0.2733, 0.0566, 0.0987, 0.0866, 0.1645, 0.0927, 0.0827, 0.0366,
                 0.2200, 0.1515, 0.1128, 0.0410, 0.1837, 0.0709, 0.1009, 0.0955, 0.1141, 0.0788,
                 0.1844, 0.0508, 0.2064, 0.0764, 0.0510, 0.0730, 0.2748, 0.0903, 0.0931, 0.0577,
                 0.1632, 0.0933, 0.1297, 0.0344, 0.1549, 0.1503, 0.1136, 0.0662, 0.1743, 0.0469,
                 0.1000, 0.0962, 0.1752, 0.0742, 0.1279, 0.0503, 0.2077, 0.1203, 0.0479, 0.0484,
                 0.2729, 0.0909, 0.1450, 0.0543, 0.1121, 0.0925, 0.1306, 0.0557, 0.1466, 0.1028,
                 0.1126, 0.0667, 0.2573, 0.0441, 0.0670, 0.0954, 0.1763, 0.1170, 0.1208, 0.0330,
                 0.2061, 0.1211, 0.0770, 0.0454, 0.1966, 0.0901, 0.1460, 0.0868, 0.1059, 0.0618),
  Severity_3 = c(0.8656, 0.9419, 0.7703, 0.8996, 0.9215, 0.9316, 0.7297, 0.9265, 0.9348, 0.9340, 
                 0.8181, 0.8778, 0.8078, 0.9679, 0.8503, 0.8755, 0.9197, 0.9243, 0.8058, 0.9378,
                 0.8497, 0.9095, 0.8301, 0.9399, 0.9091, 0.9424, 0.7689, 0.8436, 0.9261, 0.9548,
                 0.7316, 0.9259, 0.8962, 0.9379, 0.8747, 0.8788, 0.8066, 0.9479, 0.8584, 0.9160,
                 0.9205, 0.9238, 0.7142, 0.9415, 0.8977, 0.9103, 0.8290, 0.9040, 0.9144, 0.9621,
                 0.7707, 0.8426, 0.8830, 0.9576, 0.8088, 0.9266, 0.8954, 0.9010, 0.8817, 0.9184,
                 0.8081, 0.9475, 0.7850, 0.9209, 0.9473, 0.9244, 0.7126, 0.9064, 0.9035, 0.9403,
                 0.8304, 0.9033, 0.8654, 0.9645, 0.8391, 0.8439, 0.8822, 0.9315, 0.8188, 0.9514,0.8963, 0.9003, 0.8178, 0.9232, 0.8673, 0.9480, 0.7837, 0.8752, 0.9504, 0.9500, 0.7146, 0.9058, 0.8494, 0.9439, 0.8837, 0.9042, 0.8645, 0.9423, 0.8478, 0.8935, 0.8832, 0.9310, 0.7313, 0.9544, 0.9307, 0.9012, 0.8166, 0.8786, 0.8747, 0.9659, 0.7853, 0.8744, 0.9203, 0.9503, 0.7953, 0.9066, 0.8484, 0.9101, 0.8903, 0.9361)
)

Table4_10_ 
##     Case Severity_1 Severity_2 Severity_3
## 1      1     0.0049     0.1295     0.8656
## 2      2     0.0019     0.0561     0.9419
## 3      3     0.0093     0.2203     0.7703
## 4      4     0.0035     0.0969     0.8996
## 5      5     0.0027     0.0758     0.9215
## 6      6     0.0023     0.0661     0.9316
## 7      7     0.0116     0.2587     0.7297
## 8      8     0.0025     0.0710     0.9265
## 9      9     0.0022     0.0630     0.9348
## 10    10     0.0022     0.0638     0.9340
## 11    11     0.0070     0.1749     0.8181
## 12    12     0.0044     0.1178     0.8778
## 13    13     0.0075     0.1847     0.8078
## 14    14     0.0010     0.0310     0.9679
## 15    15     0.0055     0.1442     0.8503
## 16    16     0.0045     0.1201     0.8755
## 17    17     0.0028     0.0775     0.9197
## 18    18     0.0026     0.0731     0.9243
## 19    19     0.0076     0.1866     0.8058
## 20    20     0.0021     0.0601     0.9378
## 21    21     0.0056     0.1448     0.8497
## 22    22     0.0031     0.0874     0.9095
## 23    23     0.0064     0.1634     0.8301
## 24    24     0.0020     0.0581     0.9399
## 25    25     0.0032     0.0878     0.9091
## 26    26     0.0019     0.0556     0.9424
## 27    27     0.0094     0.2217     0.7689
## 28    28     0.0058     0.1505     0.8436
## 29    29     0.0025     0.0714     0.9261
## 30    30     0.0015     0.0437     0.9548
## 31    31     0.0115     0.2569     0.7316
## 32    32     0.0025     0.0715     0.9259
## 33    33     0.0037     0.1002     0.8962
## 34    34     0.0021     0.0600     0.9379
## 35    35     0.0045     0.1208     0.8747
## 36    36     0.0043     0.1168     0.8788
## 37    37     0.0075     0.1859     0.8066
## 38    38     0.0017     0.0504     0.9479
## 39    39     0.0052     0.1364     0.8584
## 40    40     0.0029     0.0811     0.9160
## 41    41     0.0027     0.0768     0.9205
## 42    42     0.0026     0.0736     0.9238
## 43    43     0.0125     0.2733     0.7142
## 44    44     0.0020     0.0566     0.9415
## 45    45     0.0036     0.0987     0.8977
## 46    46     0.0031     0.0866     0.9103
## 47    47     0.0065     0.1645     0.8290
## 48    48     0.0033     0.0927     0.9040
## 49    49     0.0030     0.0827     0.9144
## 50    50     0.0012     0.0366     0.9621
## 51    51     0.0093     0.2200     0.7707
## 52    52     0.0059     0.1515     0.8426
## 53    53     0.0042     0.1128     0.8830
## 54    54     0.0014     0.0410     0.9576
## 55    55     0.0074     0.1837     0.8088
## 56    56     0.0025     0.0709     0.9266
## 57    57     0.0037     0.1009     0.8954
## 58    58     0.0035     0.0955     0.9010
## 59    59     0.0042     0.1141     0.8817
## 60    60     0.0028     0.0788     0.9184
## 61    61     0.0075     0.1844     0.8081
## 62    62     0.0017     0.0508     0.9475
## 63    63     0.0086     0.2064     0.7850
## 64    64     0.0027     0.0764     0.9209
## 65    65     0.0018     0.0510     0.9473
## 66    66     0.0026     0.0730     0.9244
## 67    67     0.0126     0.2748     0.7126
## 68    68     0.0033     0.0903     0.9064
## 69    69     0.0034     0.0931     0.9035
## 70    70     0.0020     0.0577     0.9403
## 71    71     0.0064     0.1632     0.8304
## 72    72     0.0034     0.0933     0.9033
## 73    73     0.0049     0.1297     0.8654
## 74    74     0.0012     0.0344     0.9645
## 75    75     0.0060     0.1549     0.8391
## 76    76     0.0058     0.1503     0.8439
## 77    77     0.0042     0.1136     0.8822
## 78    78     0.0023     0.0662     0.9315
## 79    79     0.0070     0.1743     0.8188
## 80    80     0.0016     0.0469     0.9514
## 81    81     0.0036     0.1000     0.8963
## 82    82     0.0035     0.0962     0.9003
## 83    83     0.0070     0.1752     0.8178
## 84    84     0.0026     0.0742     0.9232
## 85    85     0.0048     0.1279     0.8673
## 86    86     0.0017     0.0503     0.9480
## 87    87     0.0087     0.2077     0.7837
## 88    88     0.0045     0.1203     0.8752
## 89    89     0.0016     0.0479     0.9504
## 90    90     0.0017     0.0484     0.9500
## 91    91     0.0125     0.2729     0.7146
## 92    92     0.0033     0.0909     0.9058
## 93    93     0.0056     0.1450     0.8494
## 94    94     0.0019     0.0543     0.9439
## 95    95     0.0041     0.1121     0.8837
## 96    96     0.0033     0.0925     0.9042
## 97    97     0.0049     0.1306     0.8645
## 98    98     0.0019     0.0557     0.9423
## 99    99     0.0056     0.1466     0.8478
## 100  100     0.0038     0.1028     0.8935
## 101  101     0.0042     0.1126     0.8832
## 102  102     0.0023     0.0667     0.9310
## 103  103     0.0115     0.2573     0.7313
## 104  104     0.0015     0.0441     0.9544
## 105  105     0.0024     0.0670     0.9307
## 106  106     0.0035     0.0954     0.9012
## 107  107     0.0070     0.1763     0.8166
## 108  108     0.0043     0.1170     0.8786
## 109  109     0.0045     0.1208     0.8747
## 110  110     0.0011     0.0330     0.9659
## 111  111     0.0086     0.2061     0.7853
## 112  112     0.0045     0.1211     0.8744
## 113  113     0.0027     0.0770     0.9203
## 114  114     0.0016     0.0454     0.9503
## 115  115     0.0081     0.1966     0.7953
## 116  116     0.0032     0.0901     0.9066
## 117  117     0.0056     0.1460     0.8484
## 118  118     0.0031     0.0868     0.9101
## 119  119     0.0039     0.1059     0.8903
## 120  120     0.0022     0.0618     0.9361
view(Table4_10_ )

#
mean(Table4_10_$Severity_1)
## [1] 0.004351667
var(Table4_10_$Severity_1)
## [1] 7.38151e-06
mean(Table4_10_$Severity_2)
## [1] 0.1125842
var(Table4_10_$Severity_2)
## [1] 0.003517145
mean(Table4_10_$Severity_3)
## [1] 0.8830417
var(Table4_10_$Severity_3)
## [1] 0.003842368
# Melt data for ggplot2
Table4_10_long <- melt(Table4_10_, id.vars = "Case", 
                       variable.name = "Severity", 
                       value.name = "Probability")
Table4_10_long
##     Case   Severity Probability
## 1      1 Severity_1      0.0049
## 2      2 Severity_1      0.0019
## 3      3 Severity_1      0.0093
## 4      4 Severity_1      0.0035
## 5      5 Severity_1      0.0027
## 6      6 Severity_1      0.0023
## 7      7 Severity_1      0.0116
## 8      8 Severity_1      0.0025
## 9      9 Severity_1      0.0022
## 10    10 Severity_1      0.0022
## 11    11 Severity_1      0.0070
## 12    12 Severity_1      0.0044
## 13    13 Severity_1      0.0075
## 14    14 Severity_1      0.0010
## 15    15 Severity_1      0.0055
## 16    16 Severity_1      0.0045
## 17    17 Severity_1      0.0028
## 18    18 Severity_1      0.0026
## 19    19 Severity_1      0.0076
## 20    20 Severity_1      0.0021
## 21    21 Severity_1      0.0056
## 22    22 Severity_1      0.0031
## 23    23 Severity_1      0.0064
## 24    24 Severity_1      0.0020
## 25    25 Severity_1      0.0032
## 26    26 Severity_1      0.0019
## 27    27 Severity_1      0.0094
## 28    28 Severity_1      0.0058
## 29    29 Severity_1      0.0025
## 30    30 Severity_1      0.0015
## 31    31 Severity_1      0.0115
## 32    32 Severity_1      0.0025
## 33    33 Severity_1      0.0037
## 34    34 Severity_1      0.0021
## 35    35 Severity_1      0.0045
## 36    36 Severity_1      0.0043
## 37    37 Severity_1      0.0075
## 38    38 Severity_1      0.0017
## 39    39 Severity_1      0.0052
## 40    40 Severity_1      0.0029
## 41    41 Severity_1      0.0027
## 42    42 Severity_1      0.0026
## 43    43 Severity_1      0.0125
## 44    44 Severity_1      0.0020
## 45    45 Severity_1      0.0036
## 46    46 Severity_1      0.0031
## 47    47 Severity_1      0.0065
## 48    48 Severity_1      0.0033
## 49    49 Severity_1      0.0030
## 50    50 Severity_1      0.0012
## 51    51 Severity_1      0.0093
## 52    52 Severity_1      0.0059
## 53    53 Severity_1      0.0042
## 54    54 Severity_1      0.0014
## 55    55 Severity_1      0.0074
## 56    56 Severity_1      0.0025
## 57    57 Severity_1      0.0037
## 58    58 Severity_1      0.0035
## 59    59 Severity_1      0.0042
## 60    60 Severity_1      0.0028
## 61    61 Severity_1      0.0075
## 62    62 Severity_1      0.0017
## 63    63 Severity_1      0.0086
## 64    64 Severity_1      0.0027
## 65    65 Severity_1      0.0018
## 66    66 Severity_1      0.0026
## 67    67 Severity_1      0.0126
## 68    68 Severity_1      0.0033
## 69    69 Severity_1      0.0034
## 70    70 Severity_1      0.0020
## 71    71 Severity_1      0.0064
## 72    72 Severity_1      0.0034
## 73    73 Severity_1      0.0049
## 74    74 Severity_1      0.0012
## 75    75 Severity_1      0.0060
## 76    76 Severity_1      0.0058
## 77    77 Severity_1      0.0042
## 78    78 Severity_1      0.0023
## 79    79 Severity_1      0.0070
## 80    80 Severity_1      0.0016
## 81    81 Severity_1      0.0036
## 82    82 Severity_1      0.0035
## 83    83 Severity_1      0.0070
## 84    84 Severity_1      0.0026
## 85    85 Severity_1      0.0048
## 86    86 Severity_1      0.0017
## 87    87 Severity_1      0.0087
## 88    88 Severity_1      0.0045
## 89    89 Severity_1      0.0016
## 90    90 Severity_1      0.0017
## 91    91 Severity_1      0.0125
## 92    92 Severity_1      0.0033
## 93    93 Severity_1      0.0056
## 94    94 Severity_1      0.0019
## 95    95 Severity_1      0.0041
## 96    96 Severity_1      0.0033
## 97    97 Severity_1      0.0049
## 98    98 Severity_1      0.0019
## 99    99 Severity_1      0.0056
## 100  100 Severity_1      0.0038
## 101  101 Severity_1      0.0042
## 102  102 Severity_1      0.0023
## 103  103 Severity_1      0.0115
## 104  104 Severity_1      0.0015
## 105  105 Severity_1      0.0024
## 106  106 Severity_1      0.0035
## 107  107 Severity_1      0.0070
## 108  108 Severity_1      0.0043
## 109  109 Severity_1      0.0045
## 110  110 Severity_1      0.0011
## 111  111 Severity_1      0.0086
## 112  112 Severity_1      0.0045
## 113  113 Severity_1      0.0027
## 114  114 Severity_1      0.0016
## 115  115 Severity_1      0.0081
## 116  116 Severity_1      0.0032
## 117  117 Severity_1      0.0056
## 118  118 Severity_1      0.0031
## 119  119 Severity_1      0.0039
## 120  120 Severity_1      0.0022
## 121    1 Severity_2      0.1295
## 122    2 Severity_2      0.0561
## 123    3 Severity_2      0.2203
## 124    4 Severity_2      0.0969
## 125    5 Severity_2      0.0758
## 126    6 Severity_2      0.0661
## 127    7 Severity_2      0.2587
## 128    8 Severity_2      0.0710
## 129    9 Severity_2      0.0630
## 130   10 Severity_2      0.0638
## 131   11 Severity_2      0.1749
## 132   12 Severity_2      0.1178
## 133   13 Severity_2      0.1847
## 134   14 Severity_2      0.0310
## 135   15 Severity_2      0.1442
## 136   16 Severity_2      0.1201
## 137   17 Severity_2      0.0775
## 138   18 Severity_2      0.0731
## 139   19 Severity_2      0.1866
## 140   20 Severity_2      0.0601
## 141   21 Severity_2      0.1448
## 142   22 Severity_2      0.0874
## 143   23 Severity_2      0.1634
## 144   24 Severity_2      0.0581
## 145   25 Severity_2      0.0878
## 146   26 Severity_2      0.0556
## 147   27 Severity_2      0.2217
## 148   28 Severity_2      0.1505
## 149   29 Severity_2      0.0714
## 150   30 Severity_2      0.0437
## 151   31 Severity_2      0.2569
## 152   32 Severity_2      0.0715
## 153   33 Severity_2      0.1002
## 154   34 Severity_2      0.0600
## 155   35 Severity_2      0.1208
## 156   36 Severity_2      0.1168
## 157   37 Severity_2      0.1859
## 158   38 Severity_2      0.0504
## 159   39 Severity_2      0.1364
## 160   40 Severity_2      0.0811
## 161   41 Severity_2      0.0768
## 162   42 Severity_2      0.0736
## 163   43 Severity_2      0.2733
## 164   44 Severity_2      0.0566
## 165   45 Severity_2      0.0987
## 166   46 Severity_2      0.0866
## 167   47 Severity_2      0.1645
## 168   48 Severity_2      0.0927
## 169   49 Severity_2      0.0827
## 170   50 Severity_2      0.0366
## 171   51 Severity_2      0.2200
## 172   52 Severity_2      0.1515
## 173   53 Severity_2      0.1128
## 174   54 Severity_2      0.0410
## 175   55 Severity_2      0.1837
## 176   56 Severity_2      0.0709
## 177   57 Severity_2      0.1009
## 178   58 Severity_2      0.0955
## 179   59 Severity_2      0.1141
## 180   60 Severity_2      0.0788
## 181   61 Severity_2      0.1844
## 182   62 Severity_2      0.0508
## 183   63 Severity_2      0.2064
## 184   64 Severity_2      0.0764
## 185   65 Severity_2      0.0510
## 186   66 Severity_2      0.0730
## 187   67 Severity_2      0.2748
## 188   68 Severity_2      0.0903
## 189   69 Severity_2      0.0931
## 190   70 Severity_2      0.0577
## 191   71 Severity_2      0.1632
## 192   72 Severity_2      0.0933
## 193   73 Severity_2      0.1297
## 194   74 Severity_2      0.0344
## 195   75 Severity_2      0.1549
## 196   76 Severity_2      0.1503
## 197   77 Severity_2      0.1136
## 198   78 Severity_2      0.0662
## 199   79 Severity_2      0.1743
## 200   80 Severity_2      0.0469
## 201   81 Severity_2      0.1000
## 202   82 Severity_2      0.0962
## 203   83 Severity_2      0.1752
## 204   84 Severity_2      0.0742
## 205   85 Severity_2      0.1279
## 206   86 Severity_2      0.0503
## 207   87 Severity_2      0.2077
## 208   88 Severity_2      0.1203
## 209   89 Severity_2      0.0479
## 210   90 Severity_2      0.0484
## 211   91 Severity_2      0.2729
## 212   92 Severity_2      0.0909
## 213   93 Severity_2      0.1450
## 214   94 Severity_2      0.0543
## 215   95 Severity_2      0.1121
## 216   96 Severity_2      0.0925
## 217   97 Severity_2      0.1306
## 218   98 Severity_2      0.0557
## 219   99 Severity_2      0.1466
## 220  100 Severity_2      0.1028
## 221  101 Severity_2      0.1126
## 222  102 Severity_2      0.0667
## 223  103 Severity_2      0.2573
## 224  104 Severity_2      0.0441
## 225  105 Severity_2      0.0670
## 226  106 Severity_2      0.0954
## 227  107 Severity_2      0.1763
## 228  108 Severity_2      0.1170
## 229  109 Severity_2      0.1208
## 230  110 Severity_2      0.0330
## 231  111 Severity_2      0.2061
## 232  112 Severity_2      0.1211
## 233  113 Severity_2      0.0770
## 234  114 Severity_2      0.0454
## 235  115 Severity_2      0.1966
## 236  116 Severity_2      0.0901
## 237  117 Severity_2      0.1460
## 238  118 Severity_2      0.0868
## 239  119 Severity_2      0.1059
## 240  120 Severity_2      0.0618
## 241    1 Severity_3      0.8656
## 242    2 Severity_3      0.9419
## 243    3 Severity_3      0.7703
## 244    4 Severity_3      0.8996
## 245    5 Severity_3      0.9215
## 246    6 Severity_3      0.9316
## 247    7 Severity_3      0.7297
## 248    8 Severity_3      0.9265
## 249    9 Severity_3      0.9348
## 250   10 Severity_3      0.9340
## 251   11 Severity_3      0.8181
## 252   12 Severity_3      0.8778
## 253   13 Severity_3      0.8078
## 254   14 Severity_3      0.9679
## 255   15 Severity_3      0.8503
## 256   16 Severity_3      0.8755
## 257   17 Severity_3      0.9197
## 258   18 Severity_3      0.9243
## 259   19 Severity_3      0.8058
## 260   20 Severity_3      0.9378
## 261   21 Severity_3      0.8497
## 262   22 Severity_3      0.9095
## 263   23 Severity_3      0.8301
## 264   24 Severity_3      0.9399
## 265   25 Severity_3      0.9091
## 266   26 Severity_3      0.9424
## 267   27 Severity_3      0.7689
## 268   28 Severity_3      0.8436
## 269   29 Severity_3      0.9261
## 270   30 Severity_3      0.9548
## 271   31 Severity_3      0.7316
## 272   32 Severity_3      0.9259
## 273   33 Severity_3      0.8962
## 274   34 Severity_3      0.9379
## 275   35 Severity_3      0.8747
## 276   36 Severity_3      0.8788
## 277   37 Severity_3      0.8066
## 278   38 Severity_3      0.9479
## 279   39 Severity_3      0.8584
## 280   40 Severity_3      0.9160
## 281   41 Severity_3      0.9205
## 282   42 Severity_3      0.9238
## 283   43 Severity_3      0.7142
## 284   44 Severity_3      0.9415
## 285   45 Severity_3      0.8977
## 286   46 Severity_3      0.9103
## 287   47 Severity_3      0.8290
## 288   48 Severity_3      0.9040
## 289   49 Severity_3      0.9144
## 290   50 Severity_3      0.9621
## 291   51 Severity_3      0.7707
## 292   52 Severity_3      0.8426
## 293   53 Severity_3      0.8830
## 294   54 Severity_3      0.9576
## 295   55 Severity_3      0.8088
## 296   56 Severity_3      0.9266
## 297   57 Severity_3      0.8954
## 298   58 Severity_3      0.9010
## 299   59 Severity_3      0.8817
## 300   60 Severity_3      0.9184
## 301   61 Severity_3      0.8081
## 302   62 Severity_3      0.9475
## 303   63 Severity_3      0.7850
## 304   64 Severity_3      0.9209
## 305   65 Severity_3      0.9473
## 306   66 Severity_3      0.9244
## 307   67 Severity_3      0.7126
## 308   68 Severity_3      0.9064
## 309   69 Severity_3      0.9035
## 310   70 Severity_3      0.9403
## 311   71 Severity_3      0.8304
## 312   72 Severity_3      0.9033
## 313   73 Severity_3      0.8654
## 314   74 Severity_3      0.9645
## 315   75 Severity_3      0.8391
## 316   76 Severity_3      0.8439
## 317   77 Severity_3      0.8822
## 318   78 Severity_3      0.9315
## 319   79 Severity_3      0.8188
## 320   80 Severity_3      0.9514
## 321   81 Severity_3      0.8963
## 322   82 Severity_3      0.9003
## 323   83 Severity_3      0.8178
## 324   84 Severity_3      0.9232
## 325   85 Severity_3      0.8673
## 326   86 Severity_3      0.9480
## 327   87 Severity_3      0.7837
## 328   88 Severity_3      0.8752
## 329   89 Severity_3      0.9504
## 330   90 Severity_3      0.9500
## 331   91 Severity_3      0.7146
## 332   92 Severity_3      0.9058
## 333   93 Severity_3      0.8494
## 334   94 Severity_3      0.9439
## 335   95 Severity_3      0.8837
## 336   96 Severity_3      0.9042
## 337   97 Severity_3      0.8645
## 338   98 Severity_3      0.9423
## 339   99 Severity_3      0.8478
## 340  100 Severity_3      0.8935
## 341  101 Severity_3      0.8832
## 342  102 Severity_3      0.9310
## 343  103 Severity_3      0.7313
## 344  104 Severity_3      0.9544
## 345  105 Severity_3      0.9307
## 346  106 Severity_3      0.9012
## 347  107 Severity_3      0.8166
## 348  108 Severity_3      0.8786
## 349  109 Severity_3      0.8747
## 350  110 Severity_3      0.9659
## 351  111 Severity_3      0.7853
## 352  112 Severity_3      0.8744
## 353  113 Severity_3      0.9203
## 354  114 Severity_3      0.9503
## 355  115 Severity_3      0.7953
## 356  116 Severity_3      0.9066
## 357  117 Severity_3      0.8484
## 358  118 Severity_3      0.9101
## 359  119 Severity_3      0.8903
## 360  120 Severity_3      0.9361
view(Table4_10_long)

# Create the plot Table4_9
Table4_9 <- ggplot(Table4_10_long, aes(x = Case, y = Probability, color = Severity)) +
  geom_line() + 
  theme_minimal() +
  theme(legend.position = "top") + # Legend on top
  labs(title = "Predicted Probabilities for Severity Levels",
       x = "Case Number", 
       y = "Predicted Probability", 
       color = "Severity Levels")



####Can delete
###💛4_4. Plot all predicted probabilities for different conditions

#dwrite11 <- data.frame(pedestrian_crossing_human_control =rep(c("0", "1", "2"), each = 6), did_police_officer_attend_scene_of_collision = rep(c("1", "2"), each = 9), number_of_vehicles = rep(c(1:9),2))    #3,9 has least common :9
view(dwrite11) 
## store the predicted probabilities into new dataset
test2 <- polr(legacy_collision_severity ~ pedestrian_crossing_human_control + did_police_officer_attend_scene_of_collision + number_of_vehicles, data = data4, Hess = TRUE)  
summary(test2)
## Call:
## polr(formula = legacy_collision_severity ~ pedestrian_crossing_human_control + 
##     did_police_officer_attend_scene_of_collision + number_of_vehicles, 
##     data = data4, Hess = TRUE)
## 
## Coefficients:
##                                                 Value Std. Error t value
## pedestrian_crossing_human_control1             0.6031    0.36860   1.636
## pedestrian_crossing_human_control2             0.4405    0.17692   2.490
## did_police_officer_attend_scene_of_collision1 -0.9161    0.08532 -10.737
## number_of_vehicles                             0.3750    0.04109   9.126
## 
## Intercepts:
##     Value    Std. Error t value 
## 1|2  -4.6608   0.1439   -32.3948
## 2|3  -1.2251   0.1077   -11.3743
## 
## Residual Deviance: 11365.08 
## AIC: 11377.08
view(predict(test2, newdata = dwrite11, type = "probs", se = TRUE))
pp.write2 <- cbind(dwrite11, predict(test2, newdata = dwrite11, type = "probs", se = TRUE))
view(pp.write2)
##View the average predicted probability for different values of severity within each level of chosen predictor.
by(pp.write2[, 4:6], pp.write2$pedestrian_crossing_human_control, colMeans)
## pp.write2$pedestrian_crossing_human_control: 0
##           1           2           3 
## 0.007666382 0.175530866 0.816802752 
## ------------------------------------------------------------ 
## pp.write2$pedestrian_crossing_human_control: 1
##           1           2           3 
## 0.001613859 0.045233061 0.953153080 
## ------------------------------------------------------------ 
## pp.write2$pedestrian_crossing_human_control: 2
##            1            2            3 
## 0.0006472783 0.0189332579 0.9804194638
#9. plot the Predicted Probabilities against the "number_of_vehicles" by the Level of "pedestrian_crossing_human_control" for 3 Severity levels: 1,2,3
## melt data set to long for ggplot2
library(reshape2)
lpp2 <- melt(pp.write2, id.vars = c("pedestrian_crossing_human_control","did_police_officer_attend_scene_of_collision", "number_of_vehicles"), value.name = "probability")
view(lpp2)
tail(lpp2)
##    pedestrian_crossing_human_control
## 49                                 2
## 50                                 2
## 51                                 2
## 52                                 2
## 53                                 2
## 54                                 2
##    did_police_officer_attend_scene_of_collision number_of_vehicles variable
## 49                                            2                  4        3
## 50                                            2                  5        3
## 51                                            2                  6        3
## 52                                            2                  7        3
## 53                                            2                  8        3
## 54                                            2                  9        3
##    probability
## 49   0.9595139
## 50   0.9718170
## 51   0.9804575
## 52   0.9864858
## 53   0.9906723
## 54   0.9935703
## plot Predicted Probabilities across "number_of_vehicles" values for each level of "ped...."
## facetted by program type: prog
ggplot(lpp2, aes(x = number_of_vehicles, y = probability, colour = pedestrian_crossing_human_control)) + geom_line()+ facet_grid(variable ~
    ., scales = "free")  +
  theme(legend.position = "top")

ggplot(lpp2, aes(x = number_of_vehicles, y = probability, colour = did_police_officer_attend_scene_of_collision)) + geom_line()+ facet_grid(variable ~
    ., scales = "free")  +
  theme(legend.position = "top")

####Can delete

#💚5  Marginal effects of logit models

#💛5_1. Original logit model, use the ocME() function in the erer package

library(erer)
x <- ocME(step_test2)  
x
##                                               effect.1 effect.2 effect.3
## police_force                                     0.000    0.000    0.001
## number_of_vehicles                              -0.004   -0.073    0.077
## number_of_casualties                             0.001    0.015   -0.016
## first_road_number                                0.000    0.000    0.000
## speed_limit                                      0.000    0.002   -0.002
## junction_detail1                                -0.003   -0.061    0.064
## junction_detail2                                -0.002   -0.030    0.031
## junction_detail5                                 0.001    0.015   -0.016
## junction_detail6                                 0.000    0.008   -0.008
## junction_detail7                                -0.002   -0.046    0.049
## junction_detail8                                -0.001   -0.014    0.015
## junction_detail9                                -0.002   -0.030    0.031
## junction_control1                               -0.004   -0.089    0.093
## junction_control2                               -0.002   -0.043    0.045
## junction_control3                                0.000   -0.007    0.007
## second_road_class                                0.001    0.010   -0.011
## second_road_number                               0.000    0.000    0.000
## pedestrian_crossing_human_control1              -0.004   -0.086    0.090
## pedestrian_crossing_human_control2              -0.003   -0.047    0.050
## light_conditions4                                0.002    0.040   -0.043
## light_conditions5                                0.011    0.156   -0.167
## light_conditions6                                0.000   -0.006    0.006
## light_conditions7                               -0.003   -0.054    0.057
## road_surface_conditions2                        -0.002   -0.036    0.038
## road_surface_conditions3                        -0.005   -0.108    0.113
## road_surface_conditions4                        -0.004   -0.072    0.076
## road_surface_conditions5                        -0.001   -0.016    0.017
## did_police_officer_attend_scene_of_collision1    0.007    0.129   -0.135
#Interpretation
cat("The marginal effects indicate that for one instant change in 'number_of_vehicles ', it is 0.4 percentage points less likely to become 'Fatal :severity = 1', 7.3 percentage points less likely to to become 'Serious :severity = 2', 7.7 percentage points more likely to to become 'Slight :severity = 3'.")
## The marginal effects indicate that for one instant change in 'number_of_vehicles ', it is 0.4 percentage points less likely to become 'Fatal :severity = 1', 7.3 percentage points less likely to to become 'Serious :severity = 2', 7.7 percentage points more likely to to become 'Slight :severity = 3'.
#💚6  get proportional odds ratio

##Odds Ratios
exp(coef(step_test2))   #exponentiate the estimates
##                                  police_force 
##                                     1.0028078 
##                            number_of_vehicles 
##                                     1.5256048 
##                          number_of_casualties 
##                                     0.9173651 
##                             first_road_number 
##                                     0.9999784 
##                                   speed_limit 
##                                     0.9894083 
##                              junction_detail1 
##                                     1.4646595 
##                              junction_detail2 
##                                     1.1975460 
##                              junction_detail5 
##                                     0.9192869 
##                              junction_detail6 
##                                     0.9573543 
##                              junction_detail7 
##                                     1.3327843 
##                              junction_detail8 
##                                     1.0887551 
##                              junction_detail9 
##                                     1.1955041 
##                             junction_control1 
##                                     1.8295942 
##                             junction_control2 
##                                     1.2947901 
##                             junction_control3 
##                                     1.0414389 
##                             second_road_class 
##                                     0.9415664 
##                            second_road_number 
##                                     0.9999512 
##            pedestrian_crossing_human_control1 
##                                     1.7959708 
##            pedestrian_crossing_human_control2 
##                                     1.3420347 
##                             light_conditions4 
##                                     0.7963761 
##                             light_conditions5 
##                                     0.4586614 
##                             light_conditions6 
##                                     1.0338721 
##                             light_conditions7 
##                                     1.4119806 
##                      road_surface_conditions2 
##                                     1.2435344 
##                      road_surface_conditions3 
##                                     2.1762466 
##                      road_surface_conditions4 
##                                     1.6027586 
##                      road_surface_conditions5 
##                                     1.0992460 
## did_police_officer_attend_scene_of_collision1 
##                                     0.4089250
#💛6_0. bind Log odds ratio and odds ratio
round(cbind(Estimate = coef(step_test2),  OR = exp(coef(step_test2))),4)
##                                               Estimate     OR
## police_force                                    0.0028 1.0028
## number_of_vehicles                              0.4224 1.5256
## number_of_casualties                           -0.0862 0.9174
## first_road_number                               0.0000 1.0000
## speed_limit                                    -0.0106 0.9894
## junction_detail1                                0.3816 1.4647
## junction_detail2                                0.1803 1.1975
## junction_detail5                               -0.0842 0.9193
## junction_detail6                               -0.0436 0.9574
## junction_detail7                                0.2873 1.3328
## junction_detail8                                0.0850 1.0888
## junction_detail9                                0.1786 1.1955
## junction_control1                               0.6041 1.8296
## junction_control2                               0.2583 1.2948
## junction_control3                               0.0406 1.0414
## second_road_class                              -0.0602 0.9416
## second_road_number                              0.0000 1.0000
## pedestrian_crossing_human_control1              0.5855 1.7960
## pedestrian_crossing_human_control2              0.2942 1.3420
## light_conditions4                              -0.2277 0.7964
## light_conditions5                              -0.7794 0.4587
## light_conditions6                               0.0333 1.0339
## light_conditions7                               0.3450 1.4120
## road_surface_conditions2                        0.2180 1.2435
## road_surface_conditions3                        0.7776 2.1762
## road_surface_conditions4                        0.4717 1.6028
## road_surface_conditions5                        0.0946 1.0992
## did_police_officer_attend_scene_of_collision1  -0.8942 0.4089
#log(odds ratio of police_force ) = 0.0028*police_force
#How to explain odds ratio of police_force is 1.0028,say, log(1.0028) =0.0028*police_force? When police_force increases one unit,it is 1.0028 times more likely to be in a higher category of severity.

#💛6_1. proportional Odds Ratios ( a table with OR and CI)

cbind(OR = coef(step_test2), ci)    #get table of Log odds containing Log OR and Log CI
##                                                          OR         2.5 %
## police_force                                   2.803911e-03  1.604051e-04
## number_of_vehicles                             4.223909e-01  3.412868e-01
## number_of_casualties                          -8.624976e-02 -1.530717e-01
## first_road_number                             -2.160612e-05 -5.950136e-05
## speed_limit                                   -1.064822e-02 -1.488139e-02
## junction_detail1                               3.816228e-01  2.137532e-01
## junction_detail2                               1.802745e-01  1.490516e-01
## junction_detail5                              -8.415701e-02 -1.131316e-01
## junction_detail6                              -4.358178e-02 -1.765779e-01
## junction_detail7                               2.872702e-01  2.501222e-01
## junction_detail8                               8.503491e-02 -1.563663e-01
## junction_detail9                               1.785680e-01  2.382056e-02
## junction_control1                              6.040942e-01  6.016434e-01
## junction_control2                              2.583486e-01  1.217841e-01
## junction_control3                              4.060331e-02  3.463436e-02
## second_road_class                             -6.021036e-02 -9.746308e-02
## second_road_number                            -4.883946e-05 -1.033253e-04
## pedestrian_crossing_human_control1             5.855457e-01  5.844468e-01
## pedestrian_crossing_human_control2             2.941869e-01  2.862012e-01
## light_conditions4                             -2.276838e-01 -3.408400e-01
## light_conditions5                             -7.794430e-01 -7.825995e-01
## light_conditions6                              3.331103e-02  1.847007e-02
## light_conditions7                              3.449934e-01  3.427770e-01
## road_surface_conditions2                       2.179576e-01  9.904145e-02
## road_surface_conditions3                       7.776016e-01  7.770697e-01
## road_surface_conditions4                       4.717263e-01  4.680059e-01
## road_surface_conditions5                       9.462452e-02  9.437459e-02
## did_police_officer_attend_scene_of_collision1 -8.942235e-01 -1.050674e+00
##                                                      97.5 %
## police_force                                   5.447416e-03
## number_of_vehicles                             5.034950e-01
## number_of_casualties                          -1.942787e-02
## first_road_number                              1.628912e-05
## speed_limit                                   -6.415048e-03
## junction_detail1                               5.494924e-01
## junction_detail2                               2.114974e-01
## junction_detail5                              -5.518244e-02
## junction_detail6                               8.941436e-02
## junction_detail7                               3.244182e-01
## junction_detail8                               3.264361e-01
## junction_detail9                               3.333154e-01
## junction_control1                              6.065450e-01
## junction_control2                              3.949131e-01
## junction_control3                              4.657226e-02
## second_road_class                             -2.295765e-02
## second_road_number                             5.646414e-06
## pedestrian_crossing_human_control1             5.866447e-01
## pedestrian_crossing_human_control2             3.021726e-01
## light_conditions4                             -1.145275e-01
## light_conditions5                             -7.762864e-01
## light_conditions6                              4.815199e-02
## light_conditions7                              3.472098e-01
## road_surface_conditions2                       3.368738e-01
## road_surface_conditions3                       7.781336e-01
## road_surface_conditions4                       4.754467e-01
## road_surface_conditions5                       9.487444e-02
## did_police_officer_attend_scene_of_collision1 -7.377726e-01
proportional_Odds_Ratio <- exp(cbind(OR = coef(step_test2), ci))   ##exponentiate the Log odds table
proportional_Odds_Ratio
##                                                      OR     2.5 %    97.5 %
## police_force                                  1.0028078 1.0001604 1.0054623
## number_of_vehicles                            1.5256048 1.4067566 1.6544937
## number_of_casualties                          0.9173651 0.8580682 0.9807596
## first_road_number                             0.9999784 0.9999405 1.0000163
## speed_limit                                   0.9894083 0.9852288 0.9936055
## junction_detail1                              1.4646595 1.2383170 1.7323735
## junction_detail2                              1.1975460 1.1607329 1.2355267
## junction_detail5                              0.9192869 0.8930331 0.9463125
## junction_detail6                              0.9573543 0.8381335 1.0935337
## junction_detail7                              1.3327843 1.2841824 1.3832256
## junction_detail8                              1.0887551 0.8552459 1.3860197
## junction_detail9                              1.1955041 1.0241065 1.3955874
## junction_control1                             1.8295942 1.8251157 1.8340837
## junction_control2                             1.2947901 1.1295102 1.4842552
## junction_control3                             1.0414389 1.0352411 1.0476738
## second_road_class                             0.9415664 0.9071358 0.9773039
## second_road_number                            0.9999512 0.9998967 1.0000056
## pedestrian_crossing_human_control1            1.7959708 1.7939982 1.7979456
## pedestrian_crossing_human_control2            1.3420347 1.3313603 1.3527947
## light_conditions4                             0.7963761 0.7111727 0.8917874
## light_conditions5                             0.4586614 0.4572159 0.4601115
## light_conditions6                             1.0338721 1.0186417 1.0493301
## light_conditions7                             1.4119806 1.4088545 1.4151136
## road_surface_conditions2                      1.2435344 1.1041121 1.4005623
## road_surface_conditions3                      2.1762466 2.1750892 2.1774046
## road_surface_conditions4                      1.6027586 1.5968068 1.6087327
## road_surface_conditions5                      1.0992460 1.0989713 1.0995208
## did_police_officer_attend_scene_of_collision1 0.4089250 0.3497018 0.4781778
#These coefficients are called proportional odds ratios.  

#💛6_2. Interpreting the proportional odds ratio:

cat("1. Attendence of Police officer: (*) For police officer who did attend scene of collision(1), the odds of being more serious  (i.e., from 2 to 1, from 3 to 1 or 2) for 'legacy_of_severity' is 0.4089 times that of police officer who did NOT attend scene of collision(2), holding onstant all other variables (positive odds ratio). "  )
## 1. Attendence of Police officer: (*) For police officer who did attend scene of collision(1), the odds of being more serious  (i.e., from 2 to 1, from 3 to 1 or 2) for 'legacy_of_severity' is 0.4089 times that of police officer who did NOT attend scene of collision(2), holding onstant all other variables (positive odds ratio).
cat("2. Human control of pedestrian crossing: (*) For pedestrian crossing(2) who had human control by other authorised personl(2), the odds of being more serious  (i.e., 2:Serious or 3: Slight versus 1: Fatal) for 'legacy_of_severity' is 1.3420 times than that of  pedestrian crossing(0) who had  NO human control within 50 metres(0); While For pedestrian crossing who had human control by school crossing patrol(1), the odds of being more serious  (i.e., from 2 to 1, from 3 to 1 or 2) for 'legacy_of_severity' is 1.796 times than that of  pedestrian crossing(0) who had  NO human control within 50 metres(0), holding onstant all other variables (positive odds ratio). "  )
## 2. Human control of pedestrian crossing: (*) For pedestrian crossing(2) who had human control by other authorised personl(2), the odds of being more serious  (i.e., 2:Serious or 3: Slight versus 1: Fatal) for 'legacy_of_severity' is 1.3420 times than that of  pedestrian crossing(0) who had  NO human control within 50 metres(0); While For pedestrian crossing who had human control by school crossing patrol(1), the odds of being more serious  (i.e., from 2 to 1, from 3 to 1 or 2) for 'legacy_of_severity' is 1.796 times than that of  pedestrian crossing(0) who had  NO human control within 50 metres(0), holding onstant all other variables (positive odds ratio).
cat("3. Vehicle numbers: (*) For each unit increase in 'number_of_vehicles', the odds of being more serious  (i.e., from 2 to 1, from 3 to 1 or 2) for 'legacy_of_severity' will increases by 52.6%(say multiplied 1.526 times) , holding constant all other variables." )
## 3. Vehicle numbers: (*) For each unit increase in 'number_of_vehicles', the odds of being more serious  (i.e., from 2 to 1, from 3 to 1 or 2) for 'legacy_of_severity' will increases by 52.6%(say multiplied 1.526 times) , holding constant all other variables.
#The (*) symbol below denotes the easiest interpretation among the choices.v

#pedestrian_crossing_human_control:
#0:   None within 50 metres     #1:   Control by school crossing patrol 
#2: Control by other authorised person

#💚7 Assess the Proportional Odds Assumption

#Method 1: Calculation
#💛7_1. s Table

#sf function calculates the log odds of being greater than or equal to each value of the target variable
library(Hmisc)
## 
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:dplyr':
## 
##     src, summarize
## The following objects are masked from 'package:base':
## 
##     format.pval, units
sf <- function(y) {#Calculates the log odds of being greater than or equal to each value of the target variable
  c('Y>=1' = qlogis(mean(y >= 1)),  #qlogis() converts the probability to logit to get log odds
    'Y>=2' = qlogis(mean(y >= 2)),
    'Y>=3' = qlogis(mean(y >= 3)))   #The response 'severity'  has 3 levels: 1, 2, 3 (if 0, 1, 2, it needs to be changed)
}

s <- with(data4, summary(as.numeric(legacy_collision_severity) ~ police_force + number_of_vehicles + number_of_casualties + first_road_number + speed_limit + junction_detail + junction_control + second_road_class + second_road_number + pedestrian_crossing_human_control + light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision, fun=sf))
s #The table s displays the (linear) predicted values to obtain if we regressed our dependent variable 'legacy_collision_severity' on our 13 predictors one at a time, 
## as.numeric(legacy_collision_severity)      N= 9550  
## 
## +--------------------------------------------+----------+----+----+--------+---------+
## |                                            |          |   N|Y>=1|    Y>=2|     Y>=3|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                                police_force|   [ 1, 5)|2665| Inf|4.990810|1.0811772|
## |                                            |   [ 5,21)|2671| Inf|4.444547|1.1303131|
## |                                            |   [21,44)|1980| Inf|4.244405|1.0718548|
## |                                            |   [44,63]|2234| Inf|4.403553|1.1141908|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                          number_of_vehicles|         1|2446| Inf|4.023273|0.7085179|
## |                                            |         2|6388| Inf|4.994222|1.2578018|
## |                                            |         3| 571| Inf|3.483951|1.1434840|
## |                                            |         4| 110| Inf|4.691348|1.6993861|
## |                                            |         5|  22| Inf|     Inf|0.9808293|
## |                                            |         6|   8| Inf|     Inf|1.0986123|
## |                                            |         7|   3| Inf|     Inf|      Inf|
## |                                            |         8|   2| Inf|     Inf|      Inf|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                        number_of_casualties|         1|7598| Inf|4.649453|1.1017735|
## |                                            |    [2,17]|1952| Inf|4.094345|1.0958819|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                           first_road_number|         0|3880| Inf|4.491246|1.1165624|
## |                                            |[  1,  44)| 920| Inf|5.026071|1.2181574|
## |                                            |[ 44, 603)|2363| Inf|4.714238|1.1161815|
## |                                            |[603,9204]|2387| Inf|4.237086|1.0170349|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                                 speed_limit|        20|1654| Inf|4.567407|1.1066899|
## |                                            |        30|5736| Inf|4.909499|1.1466102|
## |                                            |        40| 857| Inf|4.173203|1.1828559|
## |                                            |        50| 374| Inf|3.823192|0.8883819|
## |                                            |        60| 781| Inf|3.451309|0.7710075|
## |                                            |        70| 148| Inf|     Inf|1.2484246|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                             junction_detail|         3|4679| Inf|4.508054|1.0167802|
## |                                            |         1|1089| Inf|5.378975|1.4435195|
## |                                            |         2| 242| Inf|4.787492|1.2474579|
## |                                            |         5| 185| Inf|4.105394|0.8089790|
## |                                            |         6|1642| Inf|4.502276|1.0552320|
## |                                            |         7| 275| Inf|4.215824|1.4091787|
## |                                            |         8| 370| Inf|4.516339|1.0771061|
## |                                            |         9|1068| Inf|4.124284|1.1854014|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                            junction_control|         4|7546| Inf|4.428272|1.0521492|
## |                                            |         1| 125| Inf|     Inf|1.5998685|
## |                                            |         2|1767| Inf|4.760463|1.2913778|
## |                                            |         3| 112| Inf|     Inf|1.0515448|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                           second_road_class|         1|  41| Inf|     Inf|1.4170660|
## |                                            |         2|   9| Inf|     Inf|0.2231436|
## |                                            |         3|1500| Inf|4.664786|1.2734534|
## |                                            |         4| 685| Inf|5.426417|1.1478833|
## |                                            |         5| 402| Inf|5.993961|1.0657146|
## |                                            |         6|6913| Inf|4.374293|1.0621056|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                          second_road_number|         0|7315| Inf|4.419810|1.0623038|
## |                                            |  [1,6547]|2235| Inf|4.871148|1.2313183|
## +--------------------------------------------+----------+----+----+--------+---------+
## |           pedestrian_crossing_human_control|         0|9289| Inf|4.480936|1.0918773|
## |                                            |         1|  53| Inf|     Inf|1.5869651|
## |                                            |         2| 208| Inf|     Inf|1.4044217|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                            light_conditions|         1|6963| Inf|4.851596|1.1457003|
## |                                            |         4|2208| Inf|3.942968|0.9903987|
## |                                            |         5|  57| Inf|3.314186|0.4643056|
## |                                            |         6| 235| Inf|4.056123|0.8778813|
## |                                            |         7|  87| Inf|3.749504|1.5686159|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                     road_surface_conditions|         1|7330| Inf|4.571958|1.0700750|
## |                                            |         2|2035| Inf|4.309058|1.1809054|
## |                                            |         3|  30| Inf|     Inf|1.8718022|
## |                                            |         4| 151| Inf|5.010635|1.4367252|
## |                                            |         5|   4| Inf|1.098612|1.0986123|
## +--------------------------------------------+----------+----+----+--------+---------+
## |did_police_officer_attend_scene_of_collision|         2|1314| Inf|7.180070|1.8797282|
## |                                            |         1|8236| Inf|4.368956|1.0030909|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                                     Overall|          |9550| Inf|4.508956|1.1005679|
## +--------------------------------------------+----------+----+----+--------+---------+
#💛7_2. other Tables
#💙7_2_1 for 'did_police' predictor, it has 2 types:1,2, we compare 1 and 2 

Table1 <- glm(I(as.numeric(legacy_collision_severity) >= 2) ~ did_police_officer_attend_scene_of_collision, family="binomial", data = data4)
Table2 <- glm(I(as.numeric(legacy_collision_severity) >= 3) ~ did_police_officer_attend_scene_of_collision, family="binomial", data = data4)
Table1  #(Intercept)7.180 did_police...collision(1)    -2.811
## 
## Call:  glm(formula = I(as.numeric(legacy_collision_severity) >= 2) ~ 
##     did_police_officer_attend_scene_of_collision, family = "binomial", 
##     data = data4)
## 
## Coefficients:
##                                   (Intercept)  
##                                         7.180  
## did_police_officer_attend_scene_of_collision1  
##                                        -2.811  
## 
## Degrees of Freedom: 9549 Total (i.e. Null);  9548 Residual
## Null Deviance:       1147 
## Residual Deviance: 1124  AIC: 1128
Table2  #1.8797  -0.8766
## 
## Call:  glm(formula = I(as.numeric(legacy_collision_severity) >= 3) ~ 
##     did_police_officer_attend_scene_of_collision, family = "binomial", 
##     data = data4)
## 
## Coefficients:
##                                   (Intercept)  
##                                        1.8797  
## did_police_officer_attend_scene_of_collision1  
##                                       -0.8766  
## 
## Degrees of Freedom: 9549 Total (i.e. Null);  9548 Residual
## Null Deviance:       10730 
## Residual Deviance: 10610     AIC: 10610
data4$did_police_officer_attend_scene_of_collision[1]  #Baseline:2 
## [1] 1
## Levels: 2 1
#Change baseline of did.. from 2 to 1
data4$did_police_officer_attend_scene_of_collision <- relevel(data4$did_police_officer_attend_scene_of_collision, ref = "1") 
data4$did_police_officer_attend_scene_of_collision[1]   #Baseline:1 in Row165
## [1] 1
## Levels: 1 2
Table3 <- glm(I(as.numeric(legacy_collision_severity) >= 2) ~ did_police_officer_attend_scene_of_collision, family="binomial", data = data4)
Table4 <- glm(I(as.numeric(legacy_collision_severity) >= 3) ~ did_police_officer_attend_scene_of_collision, family="binomial", data = data4)
Table3   #  4.369     2.811
## 
## Call:  glm(formula = I(as.numeric(legacy_collision_severity) >= 2) ~ 
##     did_police_officer_attend_scene_of_collision, family = "binomial", 
##     data = data4)
## 
## Coefficients:
##                                   (Intercept)  
##                                         4.369  
## did_police_officer_attend_scene_of_collision2  
##                                         2.811  
## 
## Degrees of Freedom: 9549 Total (i.e. Null);  9548 Residual
## Null Deviance:       1147 
## Residual Deviance: 1124  AIC: 1128
Table4   #  1.0031    0.8766 
## 
## Call:  glm(formula = I(as.numeric(legacy_collision_severity) >= 3) ~ 
##     did_police_officer_attend_scene_of_collision, family = "binomial", 
##     data = data4)
## 
## Coefficients:
##                                   (Intercept)  
##                                        1.0031  
## did_police_officer_attend_scene_of_collision2  
##                                        0.8766  
## 
## Degrees of Freedom: 9549 Total (i.e. Null);  9548 Residual
## Null Deviance:       10730 
## Residual Deviance: 10610     AIC: 10610
#For example, in Table 1~4, when 'did_police_officer_attend_scene_of_collision' is equal to “2: No” the difference between the predicted value for 'legacy_collision_severity' greater than or equal to 2 and ...3 is roughly 5 (7.180-1.8797 = 5.3003 ) in Table1 - Table2, quite different from that when it is equal to “1:Yes” (4.369-1.0031 = 3.3659 ) in Table3 - Table4. That indicates that the effect of '1:police officer attending scene of collision' versus '2:police officer Not attending scene of collision' is different for the transition of response from "1:Fatal to ""2:Serious" and "2:Serious" to "3:Slight")
data4$pedestrian_crossing_human_control[1]   #Baseline:0 in Row155
## [1] 2
## Levels: 0 1 2
#💙7_2_2 for 'pedestrian' predictor, it has 3 types:0,1,2, we compare 0 and 2 as an example.
#Baseline: 0 for pedestrian
Table5 <- glm(I(as.numeric(legacy_collision_severity) >= 2) ~ pedestrian_crossing_human_control, family="binomial", data = data4)
Table6 <- glm(I(as.numeric(legacy_collision_severity) >= 3) ~ pedestrian_crossing_human_control, family="binomial", data = data4)
Table5  # (Intercept)4.481    14.085  14.085
## 
## Call:  glm(formula = I(as.numeric(legacy_collision_severity) >= 2) ~ 
##     pedestrian_crossing_human_control, family = "binomial", data = data4)
## 
## Coefficients:
##                        (Intercept)  pedestrian_crossing_human_control1  
##                              4.481                              14.085  
## pedestrian_crossing_human_control2  
##                             14.085  
## 
## Degrees of Freedom: 9549 Total (i.e. Null);  9547 Residual
## Null Deviance:       1147 
## Residual Deviance: 1141  AIC: 1147
Table6  # (Intercept)1.0919   0.4951  0.3125 
## 
## Call:  glm(formula = I(as.numeric(legacy_collision_severity) >= 3) ~ 
##     pedestrian_crossing_human_control, family = "binomial", data = data4)
## 
## Coefficients:
##                        (Intercept)  pedestrian_crossing_human_control1  
##                             1.0919                              0.4951  
## pedestrian_crossing_human_control2  
##                             0.3125  
## 
## Degrees of Freedom: 9549 Total (i.e. Null);  9547 Residual
## Null Deviance:       10730 
## Residual Deviance: 10730     AIC: 10730
#Baseline: 2 for pedestrian
data4$pedestrian_crossing_human_control <- relevel(data4$pedestrian_crossing_human_control, ref = "2")
data4$pedestrian_crossing_human_control[1]  #Baseline:2
## [1] 2
## Levels: 2 0 1
Table7 <- glm(I(as.numeric(legacy_collision_severity) >= 2) ~ pedestrian_crossing_human_control, family="binomial", data = data4)
Table8 <- glm(I(as.numeric(legacy_collision_severity) >= 3) ~ pedestrian_crossing_human_control, family="binomial", data = data4)
Table7  # (Intercept)1.857e+01   -1.409e+01 -3.874e-10
## 
## Call:  glm(formula = I(as.numeric(legacy_collision_severity) >= 2) ~ 
##     pedestrian_crossing_human_control, family = "binomial", data = data4)
## 
## Coefficients:
##                        (Intercept)  pedestrian_crossing_human_control0  
##                          1.857e+01                          -1.409e+01  
## pedestrian_crossing_human_control1  
##                         -3.874e-10  
## 
## Degrees of Freedom: 9549 Total (i.e. Null);  9547 Residual
## Null Deviance:       1147 
## Residual Deviance: 1141  AIC: 1147
Table8  # (Intercept) 1.4044     -0.3125    0.1825
## 
## Call:  glm(formula = I(as.numeric(legacy_collision_severity) >= 3) ~ 
##     pedestrian_crossing_human_control, family = "binomial", data = data4)
## 
## Coefficients:
##                        (Intercept)  pedestrian_crossing_human_control0  
##                             1.4044                             -0.3125  
## pedestrian_crossing_human_control1  
##                             0.1825  
## 
## Degrees of Freedom: 9549 Total (i.e. Null);  9547 Residual
## Null Deviance:       10730 
## Residual Deviance: 10730     AIC: 10730
#For example, in Table 5~8, when 'pedestrian_crossing_human_control' is equal to Baseline “0:None” the difference between the predicted value for 'legacy_collision_severity' greater than or equal to 2 and ...3 is roughly 3 (4.481 - 1.0919 = 3.3891 ) in Table5 - Table6, quite different from that when it is equal to “2:human control by a carrot” (1.857e+01 - 1.4044 =  17.1656 ) in Table7 - Table8. That indicates that the effect of '0:None within 50 meters' versus '2: human control by a carret' is different for the transition of response from "1:Fatal to ""2:Serious" and "2:Serious" to "3:Slight")

#💙7_2_3  Conclusion for parallel assumption

cat("the parallel slopes assumption does NOT hold for both categorical predictors: 'did_police_officer_attend_scene_of_collision' and 'pedestrian_crossing_human_control'.")
## the parallel slopes assumption does NOT hold for both categorical predictors: 'did_police_officer_attend_scene_of_collision' and 'pedestrian_crossing_human_control'.
#Method 1: Calculation

#Method 2: plot

#💛7_3. plots

?with
s
## as.numeric(legacy_collision_severity)      N= 9550  
## 
## +--------------------------------------------+----------+----+----+--------+---------+
## |                                            |          |   N|Y>=1|    Y>=2|     Y>=3|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                                police_force|   [ 1, 5)|2665| Inf|4.990810|1.0811772|
## |                                            |   [ 5,21)|2671| Inf|4.444547|1.1303131|
## |                                            |   [21,44)|1980| Inf|4.244405|1.0718548|
## |                                            |   [44,63]|2234| Inf|4.403553|1.1141908|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                          number_of_vehicles|         1|2446| Inf|4.023273|0.7085179|
## |                                            |         2|6388| Inf|4.994222|1.2578018|
## |                                            |         3| 571| Inf|3.483951|1.1434840|
## |                                            |         4| 110| Inf|4.691348|1.6993861|
## |                                            |         5|  22| Inf|     Inf|0.9808293|
## |                                            |         6|   8| Inf|     Inf|1.0986123|
## |                                            |         7|   3| Inf|     Inf|      Inf|
## |                                            |         8|   2| Inf|     Inf|      Inf|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                        number_of_casualties|         1|7598| Inf|4.649453|1.1017735|
## |                                            |    [2,17]|1952| Inf|4.094345|1.0958819|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                           first_road_number|         0|3880| Inf|4.491246|1.1165624|
## |                                            |[  1,  44)| 920| Inf|5.026071|1.2181574|
## |                                            |[ 44, 603)|2363| Inf|4.714238|1.1161815|
## |                                            |[603,9204]|2387| Inf|4.237086|1.0170349|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                                 speed_limit|        20|1654| Inf|4.567407|1.1066899|
## |                                            |        30|5736| Inf|4.909499|1.1466102|
## |                                            |        40| 857| Inf|4.173203|1.1828559|
## |                                            |        50| 374| Inf|3.823192|0.8883819|
## |                                            |        60| 781| Inf|3.451309|0.7710075|
## |                                            |        70| 148| Inf|     Inf|1.2484246|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                             junction_detail|         3|4679| Inf|4.508054|1.0167802|
## |                                            |         1|1089| Inf|5.378975|1.4435195|
## |                                            |         2| 242| Inf|4.787492|1.2474579|
## |                                            |         5| 185| Inf|4.105394|0.8089790|
## |                                            |         6|1642| Inf|4.502276|1.0552320|
## |                                            |         7| 275| Inf|4.215824|1.4091787|
## |                                            |         8| 370| Inf|4.516339|1.0771061|
## |                                            |         9|1068| Inf|4.124284|1.1854014|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                            junction_control|         4|7546| Inf|4.428272|1.0521492|
## |                                            |         1| 125| Inf|     Inf|1.5998685|
## |                                            |         2|1767| Inf|4.760463|1.2913778|
## |                                            |         3| 112| Inf|     Inf|1.0515448|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                           second_road_class|         1|  41| Inf|     Inf|1.4170660|
## |                                            |         2|   9| Inf|     Inf|0.2231436|
## |                                            |         3|1500| Inf|4.664786|1.2734534|
## |                                            |         4| 685| Inf|5.426417|1.1478833|
## |                                            |         5| 402| Inf|5.993961|1.0657146|
## |                                            |         6|6913| Inf|4.374293|1.0621056|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                          second_road_number|         0|7315| Inf|4.419810|1.0623038|
## |                                            |  [1,6547]|2235| Inf|4.871148|1.2313183|
## +--------------------------------------------+----------+----+----+--------+---------+
## |           pedestrian_crossing_human_control|         0|9289| Inf|4.480936|1.0918773|
## |                                            |         1|  53| Inf|     Inf|1.5869651|
## |                                            |         2| 208| Inf|     Inf|1.4044217|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                            light_conditions|         1|6963| Inf|4.851596|1.1457003|
## |                                            |         4|2208| Inf|3.942968|0.9903987|
## |                                            |         5|  57| Inf|3.314186|0.4643056|
## |                                            |         6| 235| Inf|4.056123|0.8778813|
## |                                            |         7|  87| Inf|3.749504|1.5686159|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                     road_surface_conditions|         1|7330| Inf|4.571958|1.0700750|
## |                                            |         2|2035| Inf|4.309058|1.1809054|
## |                                            |         3|  30| Inf|     Inf|1.8718022|
## |                                            |         4| 151| Inf|5.010635|1.4367252|
## |                                            |         5|   4| Inf|1.098612|1.0986123|
## +--------------------------------------------+----------+----+----+--------+---------+
## |did_police_officer_attend_scene_of_collision|         2|1314| Inf|7.180070|1.8797282|
## |                                            |         1|8236| Inf|4.368956|1.0030909|
## +--------------------------------------------+----------+----+----+--------+---------+
## |                                     Overall|          |9550| Inf|4.508956|1.1005679|
## +--------------------------------------------+----------+----+----+--------+---------+
s[, 4] <- s[, 4] - s[, 3]
s[, 4]
## as.numeric(legacy_collision_severity)      N= 9550  
## 
## +--------------------------------------------+----------+---------+
## |                                            |          |     Y>=3|
## +--------------------------------------------+----------+---------+
## |                                police_force|   [ 1, 5)|-3.909633|
## |                                            |   [ 5,21)|-3.314234|
## |                                            |   [21,44)|-3.172550|
## |                                            |   [44,63]|-3.289362|
## +--------------------------------------------+----------+---------+
## |                          number_of_vehicles|         1|-3.314755|
## |                                            |         2|-3.736420|
## |                                            |         3|-2.340467|
## |                                            |         4|-2.991962|
## |                                            |         5|     -Inf|
## |                                            |         6|     -Inf|
## |                                            |         7|         |
## |                                            |         8|         |
## +--------------------------------------------+----------+---------+
## |                        number_of_casualties|         1|-3.547679|
## |                                            |    [2,17]|-2.998463|
## +--------------------------------------------+----------+---------+
## |                           first_road_number|         0|-3.374684|
## |                                            |[  1,  44)|-3.807914|
## |                                            |[ 44, 603)|-3.598057|
## |                                            |[603,9204]|-3.220051|
## +--------------------------------------------+----------+---------+
## |                                 speed_limit|        20|-3.460717|
## |                                            |        30|-3.762888|
## |                                            |        40|-2.990347|
## |                                            |        50|-2.934810|
## |                                            |        60|-2.680302|
## |                                            |        70|     -Inf|
## +--------------------------------------------+----------+---------+
## |                             junction_detail|         3|-3.491274|
## |                                            |         1|-3.935456|
## |                                            |         2|-3.540034|
## |                                            |         5|-3.296415|
## |                                            |         6|-3.447044|
## |                                            |         7|-2.806646|
## |                                            |         8|-3.439233|
## |                                            |         9|-2.938883|
## +--------------------------------------------+----------+---------+
## |                            junction_control|         4|-3.376123|
## |                                            |         1|     -Inf|
## |                                            |         2|-3.469085|
## |                                            |         3|     -Inf|
## +--------------------------------------------+----------+---------+
## |                           second_road_class|         1|     -Inf|
## |                                            |         2|     -Inf|
## |                                            |         3|-3.391333|
## |                                            |         4|-4.278534|
## |                                            |         5|-4.928247|
## |                                            |         6|-3.312188|
## +--------------------------------------------+----------+---------+
## |                          second_road_number|         0|-3.357506|
## |                                            |  [1,6547]|-3.639830|
## +--------------------------------------------+----------+---------+
## |           pedestrian_crossing_human_control|         0|-3.389059|
## |                                            |         1|     -Inf|
## |                                            |         2|     -Inf|
## +--------------------------------------------+----------+---------+
## |                            light_conditions|         1|-3.705896|
## |                                            |         4|-2.952569|
## |                                            |         5|-2.849880|
## |                                            |         6|-3.178242|
## |                                            |         7|-2.180888|
## +--------------------------------------------+----------+---------+
## |                     road_surface_conditions|         1|-3.501883|
## |                                            |         2|-3.128152|
## |                                            |         3|     -Inf|
## |                                            |         4|-3.573910|
## |                                            |         5| 0.000000|
## +--------------------------------------------+----------+---------+
## |did_police_officer_attend_scene_of_collision|         2|-5.300342|
## |                                            |         1|-3.365865|
## +--------------------------------------------+----------+---------+
## |                                     Overall|          |-3.408388|
## +--------------------------------------------+----------+---------+
s[, 3] <- s[, 3] - s[, 3]
s[, 3]
## as.numeric(legacy_collision_severity)      N= 9550  
## 
## +--------------------------------------------+----------+----+
## |                                            |          |Y>=2|
## +--------------------------------------------+----------+----+
## |                                police_force|   [ 1, 5)|   0|
## |                                            |   [ 5,21)|   0|
## |                                            |   [21,44)|   0|
## |                                            |   [44,63]|   0|
## +--------------------------------------------+----------+----+
## |                          number_of_vehicles|         1|   0|
## |                                            |         2|   0|
## |                                            |         3|   0|
## |                                            |         4|   0|
## |                                            |         5|    |
## |                                            |         6|    |
## |                                            |         7|    |
## |                                            |         8|    |
## +--------------------------------------------+----------+----+
## |                        number_of_casualties|         1|   0|
## |                                            |    [2,17]|   0|
## +--------------------------------------------+----------+----+
## |                           first_road_number|         0|   0|
## |                                            |[  1,  44)|   0|
## |                                            |[ 44, 603)|   0|
## |                                            |[603,9204]|   0|
## +--------------------------------------------+----------+----+
## |                                 speed_limit|        20|   0|
## |                                            |        30|   0|
## |                                            |        40|   0|
## |                                            |        50|   0|
## |                                            |        60|   0|
## |                                            |        70|    |
## +--------------------------------------------+----------+----+
## |                             junction_detail|         3|   0|
## |                                            |         1|   0|
## |                                            |         2|   0|
## |                                            |         5|   0|
## |                                            |         6|   0|
## |                                            |         7|   0|
## |                                            |         8|   0|
## |                                            |         9|   0|
## +--------------------------------------------+----------+----+
## |                            junction_control|         4|   0|
## |                                            |         1|    |
## |                                            |         2|   0|
## |                                            |         3|    |
## +--------------------------------------------+----------+----+
## |                           second_road_class|         1|    |
## |                                            |         2|    |
## |                                            |         3|   0|
## |                                            |         4|   0|
## |                                            |         5|   0|
## |                                            |         6|   0|
## +--------------------------------------------+----------+----+
## |                          second_road_number|         0|   0|
## |                                            |  [1,6547]|   0|
## +--------------------------------------------+----------+----+
## |           pedestrian_crossing_human_control|         0|   0|
## |                                            |         1|    |
## |                                            |         2|    |
## +--------------------------------------------+----------+----+
## |                            light_conditions|         1|   0|
## |                                            |         4|   0|
## |                                            |         5|   0|
## |                                            |         6|   0|
## |                                            |         7|   0|
## +--------------------------------------------+----------+----+
## |                     road_surface_conditions|         1|   0|
## |                                            |         2|   0|
## |                                            |         3|    |
## |                                            |         4|   0|
## |                                            |         5|   0|
## +--------------------------------------------+----------+----+
## |did_police_officer_attend_scene_of_collision|         2|   0|
## |                                            |         1|   0|
## +--------------------------------------------+----------+----+
## |                                     Overall|          |   0|
## +--------------------------------------------+----------+----+
s 
## as.numeric(legacy_collision_severity)      N= 9550  
## 
## +--------------------------------------------+----------+----+----+----+---------+
## |                                            |          |   N|Y>=1|Y>=2|     Y>=3|
## +--------------------------------------------+----------+----+----+----+---------+
## |                                police_force|   [ 1, 5)|2665| Inf|   0|-3.909633|
## |                                            |   [ 5,21)|2671| Inf|   0|-3.314234|
## |                                            |   [21,44)|1980| Inf|   0|-3.172550|
## |                                            |   [44,63]|2234| Inf|   0|-3.289362|
## +--------------------------------------------+----------+----+----+----+---------+
## |                          number_of_vehicles|         1|2446| Inf|   0|-3.314755|
## |                                            |         2|6388| Inf|   0|-3.736420|
## |                                            |         3| 571| Inf|   0|-2.340467|
## |                                            |         4| 110| Inf|   0|-2.991962|
## |                                            |         5|  22| Inf|    |     -Inf|
## |                                            |         6|   8| Inf|    |     -Inf|
## |                                            |         7|   3| Inf|    |         |
## |                                            |         8|   2| Inf|    |         |
## +--------------------------------------------+----------+----+----+----+---------+
## |                        number_of_casualties|         1|7598| Inf|   0|-3.547679|
## |                                            |    [2,17]|1952| Inf|   0|-2.998463|
## +--------------------------------------------+----------+----+----+----+---------+
## |                           first_road_number|         0|3880| Inf|   0|-3.374684|
## |                                            |[  1,  44)| 920| Inf|   0|-3.807914|
## |                                            |[ 44, 603)|2363| Inf|   0|-3.598057|
## |                                            |[603,9204]|2387| Inf|   0|-3.220051|
## +--------------------------------------------+----------+----+----+----+---------+
## |                                 speed_limit|        20|1654| Inf|   0|-3.460717|
## |                                            |        30|5736| Inf|   0|-3.762888|
## |                                            |        40| 857| Inf|   0|-2.990347|
## |                                            |        50| 374| Inf|   0|-2.934810|
## |                                            |        60| 781| Inf|   0|-2.680302|
## |                                            |        70| 148| Inf|    |     -Inf|
## +--------------------------------------------+----------+----+----+----+---------+
## |                             junction_detail|         3|4679| Inf|   0|-3.491274|
## |                                            |         1|1089| Inf|   0|-3.935456|
## |                                            |         2| 242| Inf|   0|-3.540034|
## |                                            |         5| 185| Inf|   0|-3.296415|
## |                                            |         6|1642| Inf|   0|-3.447044|
## |                                            |         7| 275| Inf|   0|-2.806646|
## |                                            |         8| 370| Inf|   0|-3.439233|
## |                                            |         9|1068| Inf|   0|-2.938883|
## +--------------------------------------------+----------+----+----+----+---------+
## |                            junction_control|         4|7546| Inf|   0|-3.376123|
## |                                            |         1| 125| Inf|    |     -Inf|
## |                                            |         2|1767| Inf|   0|-3.469085|
## |                                            |         3| 112| Inf|    |     -Inf|
## +--------------------------------------------+----------+----+----+----+---------+
## |                           second_road_class|         1|  41| Inf|    |     -Inf|
## |                                            |         2|   9| Inf|    |     -Inf|
## |                                            |         3|1500| Inf|   0|-3.391333|
## |                                            |         4| 685| Inf|   0|-4.278534|
## |                                            |         5| 402| Inf|   0|-4.928247|
## |                                            |         6|6913| Inf|   0|-3.312188|
## +--------------------------------------------+----------+----+----+----+---------+
## |                          second_road_number|         0|7315| Inf|   0|-3.357506|
## |                                            |  [1,6547]|2235| Inf|   0|-3.639830|
## +--------------------------------------------+----------+----+----+----+---------+
## |           pedestrian_crossing_human_control|         0|9289| Inf|   0|-3.389059|
## |                                            |         1|  53| Inf|    |     -Inf|
## |                                            |         2| 208| Inf|    |     -Inf|
## +--------------------------------------------+----------+----+----+----+---------+
## |                            light_conditions|         1|6963| Inf|   0|-3.705896|
## |                                            |         4|2208| Inf|   0|-2.952569|
## |                                            |         5|  57| Inf|   0|-2.849880|
## |                                            |         6| 235| Inf|   0|-3.178242|
## |                                            |         7|  87| Inf|   0|-2.180888|
## +--------------------------------------------+----------+----+----+----+---------+
## |                     road_surface_conditions|         1|7330| Inf|   0|-3.501883|
## |                                            |         2|2035| Inf|   0|-3.128152|
## |                                            |         3|  30| Inf|    |     -Inf|
## |                                            |         4| 151| Inf|   0|-3.573910|
## |                                            |         5|   4| Inf|   0| 0.000000|
## +--------------------------------------------+----------+----+----+----+---------+
## |did_police_officer_attend_scene_of_collision|         2|1314| Inf|   0|-5.300342|
## |                                            |         1|8236| Inf|   0|-3.365865|
## +--------------------------------------------+----------+----+----+----+---------+
## |                                     Overall|          |9550| Inf|   0|-3.408388|
## +--------------------------------------------+----------+----+----+----+---------+
#5.993961-1.0657146abs(5.993961-1.0657146) is maximum of s[, 4] - s[, 3]
5.993961-1.0657146
## [1] 4.928246
plot(s, which=1:3, pch=1:3, xlab='logit', main=' ', xlim=c(-5, 0))

#If y exceeds three levels, we need to change the '3' in 'which' to 'the number of categories' 
#Method 2: plot

# If the proportional odds assumption holds, for each of 13 predictors, distance between the symbols for each set of categories of the response, should remain similar.
#Looking at the coefficients for the variable 'pedestrian_crossing_human_control' we see that the distances between the two sets of coefficients are different (i.e., the markers are much further apart on the second line than on the first), suggesting that the proportional odds assumption may Not hold.

#Method 3: Brant test
library(brant)
#Test the parallel regression hypothesis using the Brant Test
#library(MASS)
#step_test <- polr(legacy_collision_severity ~ police_force + number_of_vehicles + number_of_casualties + first_road_number + speed_limit + junction_detail + junction_control + second_road_class + second_road_number + pedestrian_crossing_human_control + light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision, data = data4, Hess = TRUE)  
#brant_test <- brant(step_test, by.var=F)  
#brant_test
library(car)
step_test <- polr(legacy_collision_severity ~ police_force + number_of_vehicles + number_of_casualties + first_road_number + speed_limit + junction_detail + junction_control + second_road_class + second_road_number + pedestrian_crossing_human_control + light_conditions + road_surface_conditions + did_police_officer_attend_scene_of_collision, data = data4, Hess = TRUE) 
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#5. Test the Parallel Regression Assumption with a Subset
#Focus on variables suspected to be influential or causing issues:

step_test_subset1 <- polr(
  legacy_collision_severity ~ number_of_casualties + speed_limit + junction_detail + light_conditions,
  data = data4, Hess = TRUE)
subset1 <- brant(step_test_subset1)
## ---------------------------------------------------- 
## Test for     X2  df  probability 
## ---------------------------------------------------- 
## Omnibus          48.13   13  0
## number_of_casualties 4.37    1   0.04
## speed_limit      18.11   1   0
## junction_detail1 2.63    1   0.11
## junction_detail2 0   1   0.99
## junction_detail5 1.19    1   0.28
## junction_detail6 0   1   0.96
## junction_detail7 1.62    1   0.2
## junction_detail8 0   1   0.99
## junction_detail9 3.75    1   0.05
## light_conditions4    19.02   1   0
## light_conditions5    1.25    1   0.26
## light_conditions6    0.01    1   0.93
## light_conditions7    4.94    1   0.03
## ---------------------------------------------------- 
## 
## H0: Parallel Regression Assumption holds
## Warning in brant(step_test_subset1): 30 combinations in table(dv,ivs) do not
## occur. Because of that, the test results might be invalid.
subset1    #p<0.05,假设不成立
##                                X2 df  probability
## Omnibus              4.812670e+01 13 6.226739e-06
## number_of_casualties 4.366576e+00  1 3.665057e-02
## speed_limit          1.811111e+01  1 2.083819e-05
## junction_detail1     2.625992e+00  1 1.051268e-01
## junction_detail2     6.189444e-05  1 9.937229e-01
## junction_detail5     1.185039e+00  1 2.763326e-01
## junction_detail6     2.967106e-03  1 9.565598e-01
## junction_detail7     1.616852e+00  1 2.035312e-01
## junction_detail8     1.525929e-04  1 9.901441e-01
## junction_detail9     3.752251e+00  1 5.273644e-02
## light_conditions4    1.902495e+01  1 1.290201e-05
## light_conditions5    1.252328e+00  1 2.631084e-01
## light_conditions6    6.849784e-03  1 9.340397e-01
## light_conditions7    4.936616e+00  1 2.629347e-02
step_test_subset2 <- polr(
  legacy_collision_severity ~ police_force + number_of_vehicles  + second_road_number  + did_police_officer_attend_scene_of_collision,
  data = data4, Hess = TRUE)
subset2 <- brant(step_test_subset2)
## ------------------------------------------------------------------------------------ 
## Test for                     X2  df  probability 
## ------------------------------------------------------------------------------------ 
## Omnibus                          7.47    4   0.11
## police_force                     2.47    1   0.12
## number_of_vehicles                   0.81    1   0.37
## second_road_number                   0.39    1   0.53
## did_police_officer_attend_scene_of_collision2    3.63    1   0.06
## ------------------------------------------------------------------------------------ 
## 
## H0: Parallel Regression Assumption holds
subset2 #p<0.05,假设不成立
##                                                      X2 df probability
## Omnibus                                       7.4665098  4  0.11319517
## police_force                                  2.4734488  1  0.11578362
## number_of_vehicles                            0.8145733  1  0.36677159
## second_road_number                            0.3863730  1  0.53421209
## did_police_officer_attend_scene_of_collision2 3.6302488  1  0.05673833
step_test_subset3 <- polr(
  legacy_collision_severity ~ junction_control + second_road_class + pedestrian_crossing_human_control+ road_surface_conditions,
  data = data4, Hess = TRUE)
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
subset3 <- brant(step_test_subset3)
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## -------------------------------------------------------------------- 
## Test for             X2  df  probability 
## -------------------------------------------------------------------- 
## Omnibus                  1682.69 10  0
## junction_control1            0   1   0.99
## junction_control2            0.02    1   0.89
## junction_control3            0   1   0.99
## second_road_class            1.45    1   0.23
## pedestrian_crossing_human_control0   0   1   0.98
## pedestrian_crossing_human_control1   0   1   1
## road_surface_conditions2     2.93    1   0.09
## road_surface_conditions3     0   1   0.99
## road_surface_conditions4     0.01    1   0.91
## road_surface_conditions5     1053.21 1   0
## -------------------------------------------------------------------- 
## 
## H0: Parallel Regression Assumption holds
## Warning in brant(step_test_subset3): 124 combinations in table(dv,ivs) do not
## occur. Because of that, the test results might be invalid.
subset3  #p>0.05,假设成立
##                                              X2 df   probability
## Omnibus                            1.682688e+03 10  0.000000e+00
## junction_control1                  2.350416e-04  1  9.877681e-01
## junction_control2                  1.855091e-02  1  8.916618e-01
## junction_control3                  2.255954e-04  1  9.880164e-01
## second_road_class                  1.448086e+00  1  2.288353e-01
## pedestrian_crossing_human_control0 4.026090e-04  1  9.839914e-01
## pedestrian_crossing_human_control1 4.960485e-09  1  9.999438e-01
## road_surface_conditions2           2.930979e+00  1  8.689479e-02
## road_surface_conditions3           5.325632e-05  1  9.941773e-01
## road_surface_conditions4           1.281984e-02  1  9.098524e-01
## road_surface_conditions5           1.053212e+03  1 4.877837e-231
#Method 3: Brant test


#💚8 If we only pick 3 predictors(number_of_casualties,  pedestrian_crossing_human_control, did_police_officer_attend_scene_of_collision), plot all predicted probabilities for different conditions

#💛8_1. For example, we can vary 'number_of_casualties' for each level of 'pedestrian_crossing_human_control' and 'did_police_officer_attend_scene_of_collision' and calculate the probability of being in each category of severity. 

summary(data4$number_of_casualties)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   1.000   1.000   1.292   1.000  17.000
newdat <- data.frame(   #repeat 300 times
  pedestrian_crossing_human_control = rep(0:2, 100),
  did_police_officer_attend_scene_of_collision = rep(1:2, each = 150),
  number_of_casualties = rep(seq(from = 1, to = 17, length.out = 60), 5))
view(newdat) 
head(newdat)
##   pedestrian_crossing_human_control
## 1                                 0
## 2                                 1
## 3                                 2
## 4                                 0
## 5                                 1
## 6                                 2
##   did_police_officer_attend_scene_of_collision number_of_casualties
## 1                                            1             1.000000
## 2                                            1             1.271186
## 3                                            1             1.542373
## 4                                            1             1.813559
## 5                                            1             2.084746
## 6                                            1             2.355932
newdat$pedestrian_crossing_human_control[1]
## [1] 0
newdat$did_police_officer_attend_scene_of_collision[1]
## [1] 1
reduced_test4 <- polr(legacy_collision_severity ~  number_of_casualties +  pedestrian_crossing_human_control + did_police_officer_attend_scene_of_collision, data = data4, Hess = TRUE)  
summary(reduced_test4)
## Call:
## polr(formula = legacy_collision_severity ~ number_of_casualties + 
##     pedestrian_crossing_human_control + did_police_officer_attend_scene_of_collision, 
##     data = data4, Hess = TRUE)
## 
## Coefficients:
##                                                  Value Std. Error t value
## number_of_casualties                          -0.04235    0.03268  -1.296
## pedestrian_crossing_human_control0            -0.37587    0.17590  -2.137
## pedestrian_crossing_human_control1             0.14178    0.40506   0.350
## did_police_officer_attend_scene_of_collision2  0.88071    0.08518  10.340
## 
## Intercepts:
##     Value    Std. Error t value 
## 1|2  -4.8386   0.2027   -23.8743
## 2|3  -1.4223   0.1785    -7.9668
## 
## Residual Deviance: 11451.23 
## AIC: 11463.23
newdat$pedestrian_crossing_human_control <- as.factor(newdat$pedestrian_crossing_human_control)
newdat$did_police_officer_attend_scene_of_collision <- as.factor(newdat$did_police_officer_attend_scene_of_collision)

newdat <- cbind(newdat, predict(reduced_test4, newdat, type = "probs"))
view(newdat)   #Change number_of_casualties for each level of pedestrian_crossing_human_control and did_police_officer_attend_scene_of_collision and calculate the probability of belonging to each Severity category
head(newdat)
##   pedestrian_crossing_human_control
## 1                                 0
## 2                                 1
## 3                                 2
## 4                                 0
## 5                                 1
## 6                                 2
##   did_police_officer_attend_scene_of_collision number_of_casualties           1
## 1                                            1             1.000000 0.011887022
## 2                                            1             1.271186 0.007199495
## 3                                            1             1.542373 0.008381971
## 4                                            1             1.813559 0.012298565
## 5                                            1             2.084746 0.007449974
## 6                                            1             2.355932 0.008673231
##           2         3
## 1 0.2562492 0.7318638
## 2 0.1736995 0.8191010
## 3 0.1963456 0.7952724
## 4 0.2626522 0.7250492
## 5 0.1786102 0.8139398
## 6 0.2017207 0.7896061
#💛8_2. Plot all predicted probabilities for different conditions

library(reshape2)  
lnewdat <- melt(newdat, id.vars = c("pedestrian_crossing_human_control", "did_police_officer_attend_scene_of_collision", "number_of_casualties"),
  variable.name = "Level", value.name="Probability")
view(lnewdat)
head(lnewdat)
##   pedestrian_crossing_human_control
## 1                                 0
## 2                                 1
## 3                                 2
## 4                                 0
## 5                                 1
## 6                                 2
##   did_police_officer_attend_scene_of_collision number_of_casualties Level
## 1                                            1             1.000000     1
## 2                                            1             1.271186     1
## 3                                            1             1.542373     1
## 4                                            1             1.813559     1
## 5                                            1             2.084746     1
## 6                                            1             2.355932     1
##   Probability
## 1 0.011887022
## 2 0.007199495
## 3 0.008381971
## 4 0.012298565
## 5 0.007449974
## 6 0.008673231
ggplot(lnewdat, aes(x = number_of_casualties, y = Probability, colour = Level)) +  
  geom_line() + facet_grid(pedestrian_crossing_human_control ~ did_police_officer_attend_scene_of_collision, labeller="label_both")

#💚9 Table 4
#extracts parameter estimates and goodness-of-fit measures from the multinomial model (step_test2) and generates a table4 with the results.

library(broom)  # For tidying model output
library(AER)    # For goodness-of-fit measures

#💛9_1: Extract parameter estimates(including estimates, standard errors, p-values)  see Table 4_3

#Table 4
table4_ <- ctable[,c(1,5,2,4)]
table4_
##                                                       Value odds ratio
## police_force                                   2.803911e-03  1.0028078
## number_of_vehicles                             4.223909e-01  1.5256048
## number_of_casualties                          -8.624976e-02  0.9173651
## first_road_number                             -2.160612e-05  0.9999784
## speed_limit                                   -1.064822e-02  0.9894083
## junction_detail1                               3.816228e-01  1.4646595
## junction_detail2                               1.802745e-01  1.1975460
## junction_detail5                              -8.415701e-02  0.9192869
## junction_detail6                              -4.358178e-02  0.9573543
## junction_detail7                               2.872702e-01  1.3327843
## junction_detail8                               8.503491e-02  1.0887551
## junction_detail9                               1.785680e-01  1.1955041
## junction_control1                              6.040942e-01  1.8295942
## junction_control2                              2.583486e-01  1.2947901
## junction_control3                              4.060331e-02  1.0414389
## second_road_class                             -6.021036e-02  0.9415664
## second_road_number                            -4.883946e-05  0.9999512
## pedestrian_crossing_human_control1             5.855457e-01  1.7959708
## pedestrian_crossing_human_control2             2.941869e-01  1.3420347
## light_conditions4                             -2.276838e-01  0.7963761
## light_conditions5                             -7.794430e-01  0.4586614
## light_conditions6                              3.331103e-02  1.0338721
## light_conditions7                              3.449934e-01  1.4119806
## road_surface_conditions2                       2.179576e-01  1.2435344
## road_surface_conditions3                       7.776016e-01  2.1762466
## road_surface_conditions4                       4.717263e-01  1.6027586
## road_surface_conditions5                       9.462452e-02  1.0992460
## did_police_officer_attend_scene_of_collision1 -8.942235e-01  0.4089250
## 1|2                                           -5.221991e+00  1.0028078
## 2|3                                           -1.767972e+00  1.5256048
##                                                 Std. Error      p value
## police_force                                  1.348752e-03 3.762723e-02
## number_of_vehicles                            4.138042e-02 1.835193e-24
## number_of_casualties                          3.409343e-02 1.141256e-02
## first_road_number                             1.933466e-05 2.637887e-01
## speed_limit                                   2.159821e-03 8.217103e-07
## junction_detail1                              8.564934e-02 8.364238e-06
## junction_detail2                              1.593033e-02 1.088159e-29
## junction_detail5                              1.478322e-02 1.250165e-08
## junction_detail6                              6.785642e-02 5.207014e-01
## junction_detail7                              1.895339e-02 6.846003e-52
## junction_detail8                              1.231661e-01 4.899376e-01
## junction_detail9                              7.895421e-02 2.371811e-02
## junction_control1                             1.250450e-03 0.000000e+00
## junction_control2                             6.967706e-02 2.090675e-04
## junction_control3                             3.045438e-03 1.497836e-40
## second_road_class                             1.900684e-02 1.535831e-03
## second_road_number                            2.779943e-05 7.894314e-02
## pedestrian_crossing_human_control1            5.607103e-04 0.000000e+00
## pedestrian_crossing_human_control2            4.074396e-03 0.000000e+00
## light_conditions4                             5.773384e-02 8.024086e-05
## light_conditions5                             1.610522e-03 0.000000e+00
## light_conditions6                             7.572059e-03 1.086487e-05
## light_conditions7                             1.130846e-03 0.000000e+00
## road_surface_conditions2                      6.067263e-02 3.277032e-04
## road_surface_conditions3                      2.714258e-04 0.000000e+00
## road_surface_conditions4                      1.898218e-03 0.000000e+00
## road_surface_conditions5                      1.275162e-04 0.000000e+00
## did_police_officer_attend_scene_of_collision1 7.982335e-02 3.962518e-29
## 1|2                                           1.330876e-02 0.000000e+00
## 2|3                                           8.623728e-02 2.098531e-93
view(table4_)   

#💛9_2: Goodness-of-fit measures

#💙9_2_1 Log likelihood Null model and Full model
null_model_ol <- update(step_test2, .~1)   # Null model
logLik_null_ol <- logLik(null_model_ol)
logLik_null_ol
## 'log Lik.' -5793.893 (df=2)
logLik_full_ol <- logLik(step_test2)       # Full model
logLik_full_ol
## 'log Lik.' -5620.155 (df=30)
#💙9_2_2 McFadden's R2
R2McFadden_ol <- 1 - as.numeric(logLik_full_ol / logLik_null_ol)
R2McFadden_ol
## [1] 0.02998632
#💙9_2_3 AIC and BIC
AIC_value_ol <- AIC(step_test2)
BIC_value_ol <- BIC(step_test2)

#View the goodness-of-fit measures
cat("AIC:", AIC_value_ol, "\nBIC:", BIC_value_ol, "\n")
## AIC: 11300.31 
## BIC: 11515.24
#💙9_2_4 Organize goodness-of-fit measures into a data frame
#Table 4.4
goodness_of_fit <- data.frame(
  Metric = c("Log likelihood null model", "Log likelihood full model", "R2McFadden", "AIC", "BIC"),
  Value = c(as.numeric(logLik_null_ol), as.numeric(logLik_full_ol), R2McFadden_ol, AIC_value_ol, BIC_value_ol)
)
goodness_of_fit
##                      Metric         Value
## 1 Log likelihood null model -5.793893e+03
## 2 Log likelihood full model -5.620155e+03
## 3                R2McFadden  2.998632e-02
## 4                       AIC  1.130031e+04
## 5                       BIC  1.151524e+04
#This is Table 4.4 in article https://www.mdpi.com/2071-1050/14/6/3188 


#💚10. Table 8: The performances of both models were evaluated by the F-measure, the G-mean, and the AUC   #💛10_1: F-measure, the G-mean, and the AUC 

library(caret)      # For confusion matrix, F-measure, G-mean
## Loading required package: lattice
## 
## Attaching package: 'caret'
## The following object is masked from 'package:survival':
## 
##     cluster
## The following objects are masked from 'package:fabletools':
## 
##     MAE, RMSE
library(pROC)       # For AUC calculation
## Type 'citation("pROC")' for a citation.
## 
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
## 
##     cov, smooth, var
#💙10_1_0 Preparitions: 
#💜10_1_0_1 Divide training set and test set
set.seed(123)
train_index <- sample(seq_len(nrow(data4)), size = 0.70 * nrow(data4))   #用70%训练集的数据,来预测30%测试集的结果的正确性
train_data <- data4[train_index, ]
test_data <- data4[-train_index, ]
view(train_data)
view(test_data)

#fit MNL and OL best models on train data (12, 13 predictors respectively)

step_test_ <- multinom(legacy_collision_severity~., data = train_data)
## # weights:  180 (118 variable)
## initial  value 7344.223150 
## iter  10 value 4585.188378
## iter  20 value 4285.778911
## iter  30 value 4074.701391
## iter  40 value 3953.486038
## iter  50 value 3921.446975
## iter  60 value 3903.156134
## iter  70 value 3897.158965
## iter  80 value 3895.987299
## iter  90 value 3895.457695
## iter 100 value 3895.422299
## final  value 3895.422299 
## stopped after 100 iterations
step_test2_ <- polr(legacy_collision_severity ~ ., data = train_data, Hess = TRUE)
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
library(fpp3)
view(data02)
str(data02)
## 'data.frame':    49316 obs. of  36 variables:
##  $ collision_index                             : chr  "2023010419171" "2023010419183" "2023010419189" "2023010419191" ...
##  $ collision_year                              : int  2023 2023 2023 2023 2023 2023 2023 2023 2023 2023 ...
##  $ collision_reference                         : chr  "010419171" "010419183" "010419189" "010419191" ...
##  $ location_easting_osgr                       : chr  "525060" "535463" "508702" "520341" ...
##  $ location_northing_osgr                      : chr  "170416" "198745" "177696" "190175" ...
##  $ longitude                                   : chr  "-0.202878" "-0.042464" "-0.435789" "-0.263972" ...
##  $ latitude                                    : chr  "51.418974" "51.671155" "51.487777" "51.597575" ...
##  $ police_force                                : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ legacy_collision_severity                   : int  3 3 3 3 3 3 3 3 3 3 ...
##  $ number_of_vehicles                          : int  1 3 2 2 2 1 2 1 1 2 ...
##  $ number_of_casualties                        : int  1 2 1 1 1 1 1 1 1 1 ...
##  $ date                                        : chr  "01/01/2023" "01/01/2023" "01/01/2023" "01/01/2023" ...
##  $ day_of_week                                 : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ time                                        : chr  "01:24" "02:25" "03:50" "02:13" ...
##  $ local_authority_district                    : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ local_authority_ons_district                : chr  "E09000024" "E09000010" "E09000017" "E09000003" ...
##  $ local_authority_highway                     : chr  "E09000024" "E09000010" "E09000017" "E09000003" ...
##  $ first_road_class                            : int  5 6 3 3 3 3 3 3 3 5 ...
##  $ first_road_number                           : int  0 0 437 5 3220 5 3 406 10 0 ...
##  $ road_type                                   : int  2 6 1 6 6 6 6 3 6 6 ...
##  $ speed_limit                                 : int  20 30 30 30 30 30 20 50 20 20 ...
##  $ junction_detail                             : int  9 3 1 3 8 0 6 0 0 3 ...
##  $ junction_control                            : int  4 4 4 4 4 -1 2 -1 -1 4 ...
##  $ second_road_class                           : int  5 6 6 6 6 0 3 0 0 6 ...
##  $ second_road_number                          : int  0 0 0 0 0 -1 3202 -1 -1 0 ...
##  $ pedestrian_crossing_human_control           : int  2 0 0 0 0 2 0 0 0 1 ...
##  $ pedestrian_crossing_physical_facilities     : int  5 1 0 0 0 5 0 0 4 4 ...
##  $ light_conditions                            : int  4 4 4 4 4 4 4 1 4 1 ...
##  $ weather_conditions                          : int  8 1 1 9 1 1 1 1 1 1 ...
##  $ road_surface_conditions                     : int  2 1 1 1 1 1 2 1 1 1 ...
##  $ special_conditions_at_site                  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ carriageway_hazards                         : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ urban_or_rural_area                         : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ did_police_officer_attend_scene_of_collision: int  1 1 1 1 1 1 1 1 1 1 ...
##  $ trunk_road_flag                             : int  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
##  $ lsoa_of_collision_location                  : chr  "E01003383" "E01001547" "E01002448" "E01000129" ...
#make predictions on the test set
#决定了AUC
predictions1 <- predict(step_test_, newdata = test_data, type = "probs")   
predictions1 
##                 1            2            3
## 6    2.548035e-03 2.686960e-01 7.287560e-01
## 12   1.506044e-02 3.231856e-01 6.617540e-01
## 14   1.685106e-02 3.033349e-01 6.798140e-01
## 19   5.138084e-02 3.581751e-01 5.904441e-01
## 23   1.070685e-02 1.892302e-01 8.000629e-01
## 24   4.840208e-04 2.193911e-01 7.801249e-01
## 26   1.115354e-12 2.687426e-01 7.312574e-01
## 29   7.623624e-03 2.862490e-01 7.061274e-01
## 33   2.405694e-02 3.712045e-01 6.047385e-01
## 34   6.268199e-08 2.000728e-01 7.999272e-01
## 37   3.652411e-03 3.456446e-01 6.507030e-01
## 38   6.002098e-03 2.375908e-01 7.564071e-01
## 40   2.797537e-06 5.767565e-01 4.232408e-01
## 42   2.056394e-02 2.014031e-01 7.780330e-01
## 43   3.406688e-03 3.045181e-01 6.920752e-01
## 44   1.210593e-02 2.364536e-01 7.514404e-01
## 46   9.120544e-03 2.399221e-01 7.509573e-01
## 47   1.967919e-02 2.211458e-01 7.591750e-01
## 48   7.226254e-03 1.887799e-01 8.039938e-01
## 50   4.724354e-03 3.446962e-01 6.505794e-01
## 56   1.549182e-02 2.387653e-01 7.457429e-01
## 69   2.716968e-02 2.093292e-01 7.635011e-01
## 70   1.787437e-02 2.515943e-01 7.305313e-01
## 74   1.742712e-02 1.677643e-01 8.148086e-01
## 78   1.046674e-02 2.151332e-01 7.744001e-01
## 80   3.313686e-03 1.214751e-01 8.752112e-01
## 85   2.307795e-02 3.230828e-01 6.538392e-01
## 86   4.119034e-03 2.090699e-01 7.868111e-01
## 87   1.144903e-02 1.911453e-01 7.974057e-01
## 89   3.574696e-02 3.391984e-01 6.250547e-01
## 90   1.234013e-02 1.892327e-01 7.984272e-01
## 91   4.945130e-03 2.749610e-01 7.200939e-01
## 92   5.777369e-03 1.882771e-01 8.059456e-01
## 93   1.614978e-09 1.247156e-01 8.752844e-01
## 95   9.486076e-04 1.578324e-01 8.412190e-01
## 99   2.959622e-03 2.217713e-01 7.752690e-01
## 102  5.557656e-04 1.955706e-01 8.038736e-01
## 104  1.017662e-03 1.880117e-01 8.109706e-01
## 110  3.040155e-03 2.673269e-01 7.296329e-01
## 111  2.723975e-09 1.544715e-01 8.455285e-01
## 115  2.015412e-03 1.345423e-01 8.634423e-01
## 117  1.780290e-02 1.522717e-01 8.299254e-01
## 118  1.301535e-01 3.723156e-01 4.975309e-01
## 119  6.198068e-03 1.770712e-01 8.167308e-01
## 120  3.817716e-03 2.045265e-01 7.916558e-01
## 123  1.021576e-08 1.660817e-01 8.339183e-01
## 124  7.369851e-08 2.969501e-01 7.030498e-01
## 130  5.956242e-03 1.679186e-01 8.261251e-01
## 138  2.434774e-02 3.947762e-01 5.808761e-01
## 140  2.274922e-02 2.209967e-01 7.562541e-01
## 141  8.572814e-03 2.126877e-01 7.787395e-01
## 146  4.059239e-09 1.525867e-01 8.474133e-01
## 148  3.353557e-02 2.963839e-01 6.700805e-01
## 157  5.692014e-03 2.016497e-01 7.926583e-01
## 158  1.160766e-02 2.193482e-01 7.690442e-01
## 160  6.280260e-03 3.548746e-01 6.388452e-01
## 166  2.057081e-02 2.691748e-01 7.102544e-01
## 167  1.502085e-02 3.417934e-01 6.431857e-01
## 168  1.955085e-02 3.527870e-01 6.276622e-01
## 169  4.215498e-03 3.534031e-01 6.423814e-01
## 174  3.327790e-11 1.051187e-01 8.948813e-01
## 176  1.974436e-03 1.942161e-01 8.038095e-01
## 177  4.204035e-03 2.437552e-01 7.520408e-01
## 189  3.864181e-02 3.544831e-01 6.068750e-01
## 190  7.560910e-03 3.521216e-01 6.403175e-01
## 197  5.959966e-03 2.827593e-01 7.112807e-01
## 199  1.156660e-03 2.200664e-01 7.787770e-01
## 202  2.225843e-02 3.577994e-01 6.199422e-01
## 205  1.369366e-02 1.146187e-01 8.716877e-01
## 211  3.800543e-03 2.911322e-01 7.050673e-01
## 212  3.557188e-03 2.331579e-01 7.632849e-01
## 214  4.680928e-03 3.441844e-01 6.511347e-01
## 219  1.279602e-02 3.020177e-01 6.851863e-01
## 220  1.147056e-02 3.587055e-01 6.298239e-01
## 225  7.750182e-03 2.372778e-01 7.549720e-01
## 226  7.845473e-03 1.938657e-01 7.982888e-01
## 228  3.770056e-03 2.665514e-01 7.296786e-01
## 233  6.707007e-08 1.132444e-01 8.867555e-01
## 235  3.423814e-02 2.053140e-01 7.604478e-01
## 239  6.152375e-12 4.141983e-01 5.858017e-01
## 240  2.908033e-03 2.476956e-01 7.493963e-01
## 241  9.246847e-03 3.057503e-01 6.850028e-01
## 247  1.817124e-03 2.148149e-01 7.833679e-01
## 248  3.922625e-15 1.238702e-01 8.761298e-01
## 254  4.776817e-09 3.774879e-01 6.225121e-01
## 266  2.187658e-03 2.329426e-01 7.648697e-01
## 268  1.180184e-02 2.667202e-01 7.214780e-01
## 280  5.999837e-03 1.440722e-01 8.499280e-01
## 283  5.274465e-03 1.536455e-01 8.410800e-01
## 285  3.790952e-03 2.648555e-01 7.313535e-01
## 289  7.975413e-04 9.127497e-02 9.079275e-01
## 292  1.834923e-02 1.623581e-01 8.192927e-01
## 293  7.837739e-03 3.204823e-01 6.716799e-01
## 301  6.186983e-03 1.837306e-01 8.100824e-01
## 310  9.561856e-09 1.760476e-01 8.239524e-01
## 312  7.145715e-03 2.385431e-01 7.543111e-01
## 313  4.529098e-03 1.525374e-01 8.429335e-01
## 320  6.822150e-10 1.230512e-01 8.769488e-01
## 322  1.423961e-02 2.999597e-01 6.858007e-01
## 332  1.135215e-02 2.088068e-01 7.798411e-01
## 337  1.061390e-03 3.092564e-01 6.896822e-01
## 347  2.751600e-03 2.461779e-01 7.510705e-01
## 349  6.911232e-03 3.644430e-01 6.286457e-01
## 356  5.271381e-09 2.786146e-01 7.213854e-01
## 357  3.934455e-03 2.575311e-01 7.385345e-01
## 358  1.527573e-03 2.333292e-01 7.651433e-01
## 360  1.665217e-03 2.377547e-01 7.605801e-01
## 363  3.009646e-02 2.602536e-01 7.096500e-01
## 376  2.402307e-02 3.803995e-01 5.955774e-01
## 377  9.074200e-03 2.708025e-01 7.201233e-01
## 378  1.740208e-02 2.786069e-01 7.039910e-01
## 387  6.167034e-08 2.500515e-01 7.499484e-01
## 388  4.281143e-04 1.386084e-01 8.609635e-01
## 389  2.148750e-02 2.903057e-01 6.882068e-01
## 392  6.375416e-03 4.320871e-01 5.615374e-01
## 395  1.969832e-02 2.232741e-01 7.570275e-01
## 396  9.326484e-09 2.116251e-01 7.883749e-01
## 397  1.455194e-02 2.549602e-01 7.304879e-01
## 399  9.340555e-03 3.488463e-01 6.418132e-01
## 404  1.648688e-02 3.097032e-01 6.738099e-01
## 406  1.381239e-02 2.916629e-01 6.945247e-01
## 409  1.035417e-02 2.360108e-01 7.536350e-01
## 411  1.103539e-02 3.045367e-01 6.844279e-01
## 412  3.344950e-03 1.784857e-01 8.181693e-01
## 416  2.764685e-03 2.927882e-01 7.044472e-01
## 419  1.820610e-09 1.829921e-01 8.170079e-01
## 425  1.174533e-02 2.966745e-01 6.915802e-01
## 430  1.094455e-03 2.111342e-01 7.877714e-01
## 431  3.946006e-03 2.285721e-01 7.674819e-01
## 439  3.238634e-03 2.137185e-01 7.830429e-01
## 440  1.763221e-03 2.284964e-01 7.697404e-01
## 441  3.238435e-02 2.804803e-01 6.871353e-01
## 443  5.349328e-03 2.318195e-01 7.628311e-01
## 446  4.424881e-03 3.321432e-01 6.634319e-01
## 449  4.693714e-02 3.163076e-01 6.367553e-01
## 450  1.221672e-02 2.587278e-01 7.290555e-01
## 452  3.838753e-09 1.888296e-01 8.111704e-01
## 463  1.998967e-02 1.682760e-01 8.117343e-01
## 465  3.208831e-02 4.021238e-01 5.657879e-01
## 468  5.372987e-09 1.544979e-01 8.455021e-01
## 471  1.631600e-03 3.353064e-01 6.630620e-01
## 475  5.515610e-03 2.136778e-01 7.808066e-01
## 476  6.903888e-03 2.181243e-01 7.749718e-01
## 477  2.637174e-02 3.202068e-01 6.534214e-01
## 478  6.408084e-03 2.073202e-01 7.862717e-01
## 480  4.664827e-10 7.483458e-02 9.251654e-01
## 483  2.908438e-03 2.020559e-01 7.950356e-01
## 487  1.691555e-03 3.467637e-01 6.515447e-01
## 488  8.430197e-03 2.403819e-01 7.511879e-01
## 493  5.489087e-03 2.190429e-01 7.754680e-01
## 494  1.802707e-02 4.122468e-01 5.697262e-01
## 497  4.542060e-03 1.865728e-01 8.088851e-01
## 499  4.843104e-03 3.386475e-01 6.565094e-01
## 501  4.843104e-03 3.386475e-01 6.565094e-01
## 503  1.535102e-03 2.538910e-01 7.445739e-01
## 507  3.168316e-03 2.529118e-01 7.439198e-01
## 508  7.026888e-03 2.232739e-01 7.696992e-01
## 510  3.383163e-03 1.722906e-01 8.243262e-01
## 514  5.088153e-03 2.908370e-01 7.040748e-01
## 515  4.462598e-03 2.868452e-01 7.086922e-01
## 516  7.136167e-09 2.198341e-01 7.801659e-01
## 519  9.209689e-03 2.420104e-01 7.487799e-01
## 521  9.445120e-03 1.868442e-01 8.037106e-01
## 524  3.929378e-04 2.164585e-01 7.831486e-01
## 530  4.241784e-03 2.649115e-01 7.308467e-01
## 531  4.510035e-03 2.419324e-01 7.535575e-01
## 533  8.120549e-04 2.996887e-01 6.994993e-01
## 540  5.836979e-03 3.468252e-01 6.473378e-01
## 544  3.672409e-03 2.701585e-01 7.261691e-01
## 545  7.496218e-03 2.751139e-01 7.173899e-01
## 550  4.753643e-03 2.683265e-01 7.269198e-01
## 554  1.688002e-02 1.955285e-01 7.875914e-01
## 556  4.663032e-04 2.926311e-01 7.069026e-01
## 557  4.356797e-07 1.014135e-01 8.985860e-01
## 565  1.533708e-02 3.046586e-01 6.800043e-01
## 566  2.108824e-02 3.257738e-01 6.531380e-01
## 571  4.056007e-03 3.480007e-01 6.479433e-01
## 573  3.845592e-03 3.715607e-01 6.245937e-01
## 576  2.960691e-02 2.041365e-01 7.662566e-01
## 579  5.628746e-03 2.624804e-01 7.318909e-01
## 580  7.828094e-10 9.841418e-02 9.015858e-01
## 582  7.651087e-03 1.978530e-01 7.944959e-01
## 585  4.007481e-03 3.476127e-01 6.483798e-01
## 591  3.150903e-03 2.359182e-01 7.609309e-01
## 592  4.306819e-02 2.861924e-01 6.707394e-01
## 593  2.276540e-02 2.181073e-01 7.591273e-01
## 594  1.880164e-02 2.763441e-01 7.048542e-01
## 595  7.180108e-09 1.911952e-01 8.088048e-01
## 596  3.916480e-03 2.235950e-01 7.724885e-01
## 598  1.891224e-08 1.769327e-01 8.230673e-01
## 611  6.319174e-03 3.001436e-01 6.935372e-01
## 622  1.331752e-02 3.901032e-01 5.965793e-01
## 626  3.680075e-03 2.567345e-01 7.395854e-01
## 627  8.714432e-03 2.753519e-01 7.159337e-01
## 629  2.346366e-03 1.827802e-01 8.148734e-01
## 635  2.217283e-02 1.212063e-01 8.566208e-01
## 642  1.008123e-02 3.682097e-01 6.217090e-01
## 648  5.934893e-03 2.816895e-01 7.123756e-01
## 650  1.339385e-02 3.037723e-01 6.828339e-01
## 654  1.463002e-02 2.557254e-01 7.296446e-01
## 658  1.048425e-02 2.755782e-01 7.139375e-01
## 661  5.921455e-03 3.440411e-01 6.500374e-01
## 662  1.993860e-03 2.482185e-01 7.497876e-01
## 667  4.656629e-03 3.409094e-01 6.544339e-01
## 670  5.583067e-03 2.751535e-01 7.192635e-01
## 673  1.306008e-03 2.022684e-01 7.964255e-01
## 676  9.716142e-03 2.433374e-01 7.469465e-01
## 679  9.630761e-03 1.893413e-01 8.010279e-01
## 681  1.552499e-03 1.982726e-01 8.001749e-01
## 687  2.204199e-02 2.476561e-01 7.303019e-01
## 696  8.633478e-04 2.151839e-01 7.839528e-01
## 698  2.676372e-08 2.096886e-01 7.903114e-01
## 699  1.864863e-02 3.142149e-01 6.671364e-01
## 702  5.642810e-03 3.293226e-01 6.650346e-01
## 709  6.995775e-03 3.592894e-01 6.337149e-01
## 717  2.702838e-02 2.956518e-01 6.773199e-01
## 722  6.767352e-03 2.813185e-01 7.119142e-01
## 725  1.588017e-09 1.676957e-01 8.323043e-01
## 726  3.939908e-08 2.608307e-01 7.391693e-01
## 728  1.034946e-07 4.269098e-01 5.730901e-01
## 731  7.833922e-03 2.720280e-01 7.201380e-01
## 732  7.753221e-03 2.857711e-01 7.064757e-01
## 734  2.050090e-08 1.101463e-01 8.898537e-01
## 736  8.575383e-03 3.005574e-01 6.908672e-01
## 738  4.842868e-03 2.560899e-01 7.390673e-01
## 746  5.551326e-03 2.689974e-01 7.254513e-01
## 747  1.590573e-02 2.517394e-01 7.323548e-01
## 749  1.643604e-02 3.807282e-01 6.028357e-01
## 753  5.055381e-03 3.576888e-01 6.372558e-01
## 757  6.125491e-03 2.277180e-01 7.661565e-01
## 758  5.432510e-03 2.439306e-01 7.506369e-01
## 759  8.488168e-03 3.717778e-01 6.197340e-01
## 760  7.846403e-03 2.420259e-01 7.501277e-01
## 763  2.790352e-02 2.335134e-01 7.385830e-01
## 765  2.162731e-03 2.930028e-01 7.048344e-01
## 766  6.705474e-03 2.250686e-01 7.682259e-01
## 768  1.313583e-03 1.362040e-01 8.624824e-01
## 770  1.869619e-02 2.769150e-01 7.043888e-01
## 771  5.317208e-03 3.427338e-01 6.519490e-01
## 775  1.869826e-02 3.385650e-01 6.427367e-01
## 776  1.854941e-02 1.523250e-01 8.291256e-01
## 778  6.402801e-03 2.301373e-01 7.634599e-01
## 787  8.284481e-03 1.936122e-01 7.981033e-01
## 791  3.419117e-08 1.575863e-01 8.424136e-01
## 794  1.267734e-08 2.456523e-01 7.543477e-01
## 802  2.297561e-02 2.855901e-01 6.914343e-01
## 803  6.596288e-03 2.042912e-01 7.891125e-01
## 806  1.484180e-02 3.640617e-01 6.210965e-01
## 809  7.396508e-03 2.839477e-01 7.086558e-01
## 811  4.016378e-03 2.108978e-01 7.850859e-01
## 813  1.799840e-02 3.651666e-01 6.168350e-01
## 814  1.724783e-02 3.876348e-01 5.951174e-01
## 815  3.567030e-08 2.305524e-01 7.694476e-01
## 823  6.065259e-03 1.821793e-01 8.117554e-01
## 824  8.115301e-03 3.051875e-01 6.866972e-01
## 833  2.932074e-08 1.225837e-01 8.774162e-01
## 835  2.766746e-02 2.224259e-01 7.499067e-01
## 837  1.000005e-02 2.221750e-01 7.678250e-01
## 841  4.063214e-03 2.627538e-01 7.331830e-01
## 844  7.947163e-03 1.952984e-01 7.967544e-01
## 846  1.508704e-02 2.444870e-01 7.404260e-01
## 848  7.005603e-03 1.637771e-01 8.292173e-01
## 853  7.052173e-03 2.352492e-01 7.576986e-01
## 857  5.081128e-08 1.632396e-01 8.367603e-01
## 861  5.843375e-03 2.024319e-01 7.917247e-01
## 865  3.807084e-03 2.028151e-01 7.933778e-01
## 868  4.198031e-03 2.177438e-01 7.780581e-01
## 869  7.320654e-03 3.465970e-01 6.460823e-01
## 876  2.983878e-03 2.958047e-01 7.012114e-01
## 877  1.435337e-03 2.615485e-01 7.370161e-01
## 878  2.529342e-03 9.434264e-02 9.031280e-01
## 879  5.282747e-03 3.468313e-01 6.478859e-01
## 880  1.682781e-03 2.334846e-01 7.648326e-01
## 886  1.172384e-03 1.700677e-01 8.287599e-01
## 888  2.578213e-03 2.078614e-01 7.895603e-01
## 889  9.665085e-03 1.495855e-01 8.407495e-01
## 895  5.576749e-03 2.795903e-01 7.148330e-01
## 900  3.976913e-03 2.908555e-01 7.051676e-01
## 902  4.349203e-03 3.860516e-01 6.095992e-01
## 907  2.132623e-02 2.357749e-01 7.428988e-01
## 909  8.168527e-03 1.027667e-01 8.890648e-01
## 921  1.317673e-02 2.292678e-01 7.575555e-01
## 924  3.352141e-03 2.580416e-01 7.386063e-01
## 928  2.467187e-03 2.651869e-01 7.323459e-01
## 934  3.368775e-03 1.688211e-01 8.278101e-01
## 935  2.320391e-03 2.044476e-01 7.932320e-01
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## 1871 1.202160e-08 2.192967e-01 7.807033e-01
## 1875 7.794850e-03 2.335324e-01 7.586727e-01
## 1889 3.177929e-03 1.688044e-01 8.280176e-01
## 1890 1.270986e-03 2.288099e-01 7.699192e-01
## 1893 2.896839e-03 1.608099e-01 8.362933e-01
## 1894 7.820831e-03 2.990307e-01 6.931485e-01
## 1897 4.528823e-03 3.045969e-01 6.908743e-01
## 1898 1.160057e-02 1.866976e-01 8.017018e-01
## 1901 1.920264e-06 1.489156e-01 8.510825e-01
## 1902 4.017922e-03 2.413083e-01 7.546738e-01
## 1903 3.291672e-03 2.833018e-01 7.134065e-01
## 1908 6.096616e-09 2.434622e-01 7.565378e-01
## 1910 5.325755e-03 2.817483e-01 7.129259e-01
## 1911 1.034696e-03 2.585416e-01 7.404237e-01
## 1915 5.521114e-03 3.448752e-01 6.496037e-01
## 1917 4.858259e-03 2.636248e-01 7.315169e-01
## 1919 4.643287e-03 2.721292e-01 7.232275e-01
## 1929 4.488134e-03 2.535294e-01 7.419825e-01
## 1930 3.073596e-03 1.695644e-01 8.273621e-01
## 1931 1.429458e-03 2.309302e-01 7.676404e-01
## 1933 4.399419e-03 3.517780e-01 6.438226e-01
## 1938 5.337431e-03 2.261446e-01 7.685180e-01
## 1945 2.608780e-03 3.221315e-01 6.752597e-01
## 1951 1.366281e-09 1.999115e-01 8.000885e-01
## 1954 4.293554e-02 3.482672e-01 6.087973e-01
## 1955 1.587845e-08 1.343918e-01 8.656082e-01
## 1958 8.397363e-03 2.523469e-01 7.392558e-01
## 1966 9.190985e-03 3.641621e-01 6.266469e-01
## 1975 3.319741e-03 2.173654e-01 7.793149e-01
## 1977 7.962738e-03 3.757679e-01 6.162694e-01
## 1978 3.392790e-03 2.542513e-01 7.423560e-01
## 1980 7.444136e-03 3.622252e-01 6.303307e-01
## 1983 6.245823e-04 1.579160e-01 8.414594e-01
## 1985 3.309922e-03 1.694223e-01 8.272678e-01
## 1986 4.783034e-03 3.407187e-01 6.544983e-01
## 1990 2.923534e-09 2.203292e-01 7.796708e-01
## 1992 4.823947e-04 2.185830e-01 7.809346e-01
## 1997 1.109447e-02 3.222527e-01 6.666528e-01
## 2005 5.393018e-03 3.274846e-01 6.671224e-01
## 2010 6.328082e-03 1.892159e-01 8.044560e-01
## 2011 1.267784e-02 2.533878e-01 7.339344e-01
## 2019 4.874061e-03 2.446830e-01 7.504430e-01
## 2020 9.831996e-04 2.637426e-01 7.352742e-01
## 2030 2.889870e-03 2.946520e-01 7.024582e-01
## 2031 1.377517e-03 1.526026e-01 8.460199e-01
## 2039 8.769879e-03 3.046189e-01 6.866112e-01
## 2040 3.773826e-03 2.402260e-01 7.560002e-01
## 2042 4.466378e-14 1.846807e-01 8.153193e-01
## 2043 9.656795e-03 2.436389e-01 7.467043e-01
## 2045 2.218160e-02 2.666956e-01 7.111228e-01
## 2048 3.865863e-03 2.633830e-01 7.327512e-01
## 2052 1.353043e-02 2.577130e-01 7.287565e-01
## 2053 5.275348e-03 2.773588e-01 7.173658e-01
## 2054 9.124901e-04 2.696712e-01 7.294163e-01
## 2061 1.495449e-03 2.657697e-01 7.327348e-01
## 2064 9.762884e-05 2.236469e-01 7.762555e-01
## 2066 7.197976e-03 3.561135e-01 6.366885e-01
## 2068 8.622276e-04 3.405957e-01 6.585421e-01
## 2071 2.570267e-03 3.640015e-01 6.334282e-01
## 2072 3.231269e-09 2.215381e-01 7.784619e-01
## 2073 2.999718e-03 1.980161e-01 7.989842e-01
## 2074 2.533705e-08 2.886272e-01 7.113728e-01
## 2079 1.817841e-02 2.320607e-01 7.497609e-01
## 2088 1.373573e-03 2.826732e-01 7.159532e-01
## 2089 3.592218e-03 2.647108e-01 7.316970e-01
## 2091 3.361245e-04 1.241287e-01 8.755352e-01
## 2092 2.030442e-02 3.173392e-01 6.623563e-01
## 2093 1.252369e-02 1.927970e-01 7.946793e-01
## 2094 4.871127e-02 2.865361e-01 6.647526e-01
## 2097 5.027323e-03 2.808688e-01 7.141039e-01
## 2098 6.033598e-03 2.977074e-01 6.962590e-01
## 2102 4.263364e-03 3.343979e-01 6.613387e-01
## 2103 1.439955e-03 1.854737e-01 8.130864e-01
## 2105 5.687503e-03 2.312403e-01 7.630722e-01
## 2106 1.910357e-02 2.524251e-01 7.284713e-01
## 2114 2.844033e-03 1.703101e-01 8.268458e-01
## 2119 3.678320e-04 3.224612e-01 6.771710e-01
## 2123 5.812837e-03 2.785106e-01 7.156766e-01
## 2124 7.841403e-04 2.120159e-01 7.871999e-01
## 2128 6.103652e-06 1.594195e-01 8.405744e-01
## 2134 5.262906e-02 2.959502e-01 6.514208e-01
## 2137 2.961197e-02 3.120467e-01 6.583413e-01
## 2141 1.350241e-03 2.764227e-01 7.222271e-01
## 2152 3.540856e-03 2.599385e-01 7.365206e-01
## 2155 2.996112e-03 2.861861e-01 7.108177e-01
## 2156 1.147790e-15 6.789713e-02 9.321029e-01
## 2159 5.937879e-03 4.290185e-01 5.650436e-01
## 2160 7.056288e-03 2.427996e-01 7.501441e-01
## 2161 1.438575e-02 3.322110e-01 6.534032e-01
## 2162 6.136539e-03 2.787885e-01 7.150749e-01
## 2164 3.502229e-03 2.683413e-01 7.281565e-01
## 2167 1.438079e-02 1.915981e-01 7.940211e-01
## 2168 5.437055e-03 3.056173e-01 6.889457e-01
## 2171 4.461149e-02 3.062351e-01 6.491534e-01
## 2174 1.510150e-03 2.810363e-01 7.174536e-01
## 2176 3.035935e-03 3.079244e-01 6.890397e-01
## 2179 1.103480e-02 3.813647e-01 6.076005e-01
## 2184 1.894259e-02 2.435413e-01 7.375161e-01
## 2188 4.222195e-09 1.252909e-01 8.747091e-01
## 2197 3.613617e-14 2.446709e-01 7.553291e-01
## 2205 7.577781e-10 1.656309e-01 8.343691e-01
## 2206 6.590114e-03 2.838213e-01 7.095886e-01
## 2207 1.814073e-02 3.532600e-01 6.285993e-01
## 2209 4.399213e-03 3.044869e-01 6.911139e-01
## 2212 8.317568e-03 3.727082e-01 6.189743e-01
## 2214 2.220910e-03 2.040059e-01 7.937732e-01
## 2218 3.233595e-02 3.466244e-01 6.210397e-01
## 2223 3.795166e-10 1.465746e-01 8.534254e-01
## 2227 1.184586e-02 2.072972e-01 7.808570e-01
## 2230 6.662275e-03 3.021053e-01 6.912324e-01
## 2234 1.561691e-03 2.712325e-01 7.272058e-01
## 2235 1.352372e-03 3.270136e-01 6.716340e-01
## 2237 6.124315e-03 2.766755e-01 7.172002e-01
## 2238 8.348633e-03 3.646266e-01 6.270247e-01
## 2240 4.687156e-03 2.725800e-01 7.227329e-01
## 2246 1.111745e-02 2.449462e-01 7.439364e-01
## 2248 2.110416e-03 1.612036e-01 8.366860e-01
## 2250 4.187111e-03 1.854075e-01 8.104054e-01
## 2252 1.668457e-03 2.739972e-01 7.243343e-01
## 2256 6.359339e-03 4.152993e-01 5.783413e-01
## 2259 1.742103e-02 2.411827e-01 7.413963e-01
## 2260 5.547167e-03 2.879877e-01 7.064652e-01
## 2261 2.154941e-02 2.031287e-01 7.753218e-01
## 2263 1.430792e-03 2.573540e-01 7.412152e-01
## 2264 2.443283e-03 2.796807e-01 7.178760e-01
## 2270 9.369206e-04 1.622773e-01 8.367857e-01
## 2271 5.892828e-03 2.371957e-01 7.569115e-01
## 2274 3.856454e-09 2.404495e-01 7.595505e-01
## 2277 7.566353e-03 2.345744e-01 7.578592e-01
## 2283 1.980713e-02 2.986750e-01 6.815178e-01
## 2284 2.571717e-02 2.133739e-01 7.609090e-01
## 2297 1.815900e-14 1.770083e-01 8.229917e-01
## 2303 3.150561e-02 3.516150e-01 6.168793e-01
## 2307 2.584772e-13 3.292689e-01 6.707311e-01
## 2308 4.670354e-14 3.504397e-01 6.495603e-01
## 2309 2.519468e-09 1.327925e-01 8.672075e-01
## 2310 8.368662e-02 2.474552e-01 6.688582e-01
## 2319 6.329858e-12 1.019435e-01 8.980565e-01
## 2326 6.368678e-09 2.165839e-01 7.834161e-01
## 2328 2.291501e-03 1.471258e-01 8.505827e-01
## 2333 8.193931e-03 2.351459e-01 7.566602e-01
## 2335 1.425826e-02 2.968886e-01 6.888532e-01
## 2336 2.348380e-17 1.612631e-01 8.387369e-01
## 2342 9.073450e-13 1.166401e-01 8.833599e-01
## 2344 2.547042e-03 2.442303e-01 7.532227e-01
## 2347 2.014414e-02 1.886007e-01 7.912552e-01
## 2352 5.708466e-03 2.616999e-01 7.325916e-01
## 2361 4.993111e-03 2.791607e-01 7.158462e-01
## 2371 1.500342e-02 3.198297e-01 6.651669e-01
## 2376 4.090148e-02 4.291296e-01 5.299689e-01
## 2379 4.479125e-03 2.864147e-01 7.091062e-01
## 2380 2.424964e-11 1.292101e-01 8.707899e-01
## 2388 4.440136e-12 1.551898e-01 8.448102e-01
## 2394 2.289216e-11 1.565663e-01 8.434337e-01
## 2397 9.150141e-03 2.867444e-01 7.041055e-01
## 2400 1.053167e-02 2.931821e-01 6.962862e-01
## 2402 9.298947e-09 2.931958e-01 7.068042e-01
## 2404 1.337982e-03 1.657454e-01 8.329167e-01
## 2408 2.089048e-03 2.200002e-01 7.779107e-01
## 2414 1.011693e-02 2.434356e-01 7.464475e-01
## 2415 7.450224e-03 2.319344e-01 7.606153e-01
## 2426 4.017213e-06 2.605537e-01 7.394423e-01
## 2427 1.054768e-17 1.652052e-01 8.347948e-01
## 2429 8.061639e-03 3.223208e-01 6.696176e-01
## 2431 1.759551e-03 2.715697e-01 7.266707e-01
## 2439 1.273232e-08 2.350798e-01 7.649202e-01
## 2441 2.455190e-03 1.972759e-01 8.002689e-01
## 2443 1.143693e-02 3.183486e-01 6.702144e-01
## 2446 7.895516e-12 2.172271e-01 7.827729e-01
## 2448 5.161186e-02 2.461189e-01 7.022693e-01
## 2452 3.769144e-12 1.620460e-01 8.379540e-01
## 2453 7.925149e-03 2.838490e-01 7.082259e-01
## 2454 3.267695e-12 7.910369e-02 9.208963e-01
## 2456 2.635254e-02 2.191403e-01 7.545072e-01
## 2471 1.416795e-08 2.202140e-01 7.797860e-01
## 2476 9.675917e-12 1.632560e-01 8.367440e-01
## 2481 5.711634e-03 1.914926e-01 8.027957e-01
## 2485 3.942527e-03 2.593290e-01 7.367285e-01
## 2488 5.031786e-02 3.529791e-01 5.967031e-01
## 2489 9.033152e-12 2.201655e-01 7.798345e-01
## 2494 3.781592e-02 1.596276e-01 8.025564e-01
## 2495 3.493968e-03 2.259639e-01 7.705421e-01
## 2500 2.282814e-02 3.792105e-01 5.979614e-01
## 2501 3.660563e-12 1.177570e-01 8.822430e-01
## 2513 2.062556e-12 1.347349e-01 8.652651e-01
## 2515 5.940692e-09 2.396977e-01 7.603023e-01
## 2519 1.862316e-08 2.081912e-01 7.918088e-01
## 2525 4.337785e-03 2.713104e-01 7.243518e-01
## 2526 4.984941e-03 2.550849e-01 7.399301e-01
## 2529 2.846096e-02 3.663459e-01 6.051931e-01
## 2531 8.166362e-02 1.770451e-01 7.412913e-01
## 2532 4.048807e-29 1.319031e-01 8.680969e-01
## 2535 9.769074e-12 1.397895e-01 8.602105e-01
## 2538 3.123536e-02 2.853129e-01 6.834517e-01
## 2540 2.767558e-02 2.740264e-01 6.982980e-01
## 2541 2.917391e-03 2.020621e-01 7.950205e-01
## 2543 1.961791e-12 1.351393e-01 8.648607e-01
## 2546 4.397030e-12 1.113699e-01 8.886301e-01
## 2549 6.896036e-03 2.388051e-01 7.542989e-01
## 2551 6.814020e-13 9.700783e-02 9.029922e-01
## 2556 6.331467e-12 1.619238e-01 8.380762e-01
## 2559 3.236931e-02 2.677450e-01 6.998857e-01
## 2560 4.171928e-19 5.556546e-02 9.444345e-01
## 2561 5.389530e-03 3.044243e-01 6.901862e-01
## 2563 3.229387e-02 2.747867e-01 6.929195e-01
## 2564 1.125544e-02 2.852161e-01 7.035284e-01
## 2566 1.506090e-08 2.115475e-01 7.884525e-01
## 2568 1.729102e-02 3.159252e-01 6.667838e-01
## 2569 8.115520e-03 2.311165e-01 7.607679e-01
## 2570 3.075686e-18 4.813663e-02 9.518634e-01
## 2574 1.179145e-07 2.074922e-01 7.925077e-01
## 2575 1.401673e-03 2.528605e-01 7.457378e-01
## 2582 1.230906e-02 3.400173e-01 6.476736e-01
## 2587 2.600050e-12 1.362467e-01 8.637533e-01
## 2588 2.372239e-02 2.204452e-01 7.558324e-01
## 2595 1.374384e-02 3.179763e-01 6.682798e-01
## 2602 9.999997e-14 1.073311e-01 8.926689e-01
## 2604 7.739813e-12 2.075351e-01 7.924649e-01
## 2607 5.134186e-03 2.160900e-01 7.787759e-01
## 2613 9.080672e-03 3.091389e-01 6.817804e-01
## 2614 1.117027e-02 2.114668e-01 7.773629e-01
## 2622 5.519286e-03 2.766081e-01 7.178726e-01
## 2625 4.390082e-12 1.472827e-01 8.527173e-01
## 2626 5.444362e-03 2.506184e-01 7.439372e-01
## 2632 3.981886e-12 1.449168e-01 8.550832e-01
## 2642 3.456393e-12 1.481727e-01 8.518273e-01
## 2654 6.749119e-03 3.601973e-01 6.330536e-01
## 2666 1.477994e-03 2.250302e-01 7.734918e-01
## 2667 3.012361e-03 2.725126e-01 7.244750e-01
## 2668 4.210124e-12 1.457126e-01 8.542874e-01
## 2671 4.403678e-03 1.516847e-01 8.439117e-01
## 2672 7.058244e-03 2.478053e-01 7.451364e-01
## 2676 2.704517e-02 2.596389e-01 7.133159e-01
## 2679 4.822863e-04 2.993370e-01 7.001807e-01
## 2680 5.037918e-12 1.100331e-01 8.899669e-01
## 2682 1.972085e-03 2.833713e-01 7.146566e-01
## 2685 8.347107e-03 2.747815e-01 7.168714e-01
## 2694 6.533621e-03 3.137386e-01 6.797278e-01
## 2696 5.207246e-03 2.777817e-01 7.170111e-01
## 2697 1.236281e-02 2.932722e-01 6.943650e-01
## 2699 4.807652e-12 1.680021e-01 8.319979e-01
## 2701 2.729526e-13 1.093265e-01 8.906735e-01
## 2702 7.800690e-03 2.425839e-01 7.496154e-01
## 2704 2.026863e-03 2.782585e-01 7.197147e-01
## 2713 1.000291e-02 3.733828e-01 6.166143e-01
## 2714 7.287163e-03 2.901084e-01 7.026045e-01
## 2716 2.984299e-02 3.178253e-01 6.523317e-01
## 2720 6.930298e-03 2.777832e-01 7.152865e-01
## 2723 7.284926e-03 3.046774e-01 6.880376e-01
## 2725 5.581707e-03 3.590313e-01 6.353870e-01
## 2727 1.002814e-11 2.120037e-01 7.879963e-01
## 2730 8.336978e-03 2.207391e-01 7.709239e-01
## 2732 5.034704e-03 2.678499e-01 7.271154e-01
## 2733 7.283273e-03 2.770886e-01 7.156281e-01
## 2735 6.025009e-14 7.930345e-02 9.206965e-01
## 2736 8.634305e-03 3.571926e-01 6.341731e-01
## 2746 1.197588e-02 3.683562e-01 6.196679e-01
## 2749 3.894119e-03 1.557972e-01 8.403087e-01
## 2755 3.146788e-12 1.169518e-01 8.830482e-01
## 2759 6.268089e-12 1.326344e-01 8.673656e-01
## 2763 1.702718e-03 2.818882e-01 7.164091e-01
## 2766 1.006037e-12 7.249882e-02 9.275012e-01
## 2771 5.500527e-02 2.399899e-01 7.050048e-01
## 2772 1.903792e-02 3.040573e-01 6.769048e-01
## 2781 5.835923e-03 2.411155e-01 7.530485e-01
## 2782 2.709565e-12 1.348021e-01 8.651979e-01
## 2791 3.137053e-03 2.585520e-01 7.383109e-01
## 2794 1.348354e-02 2.872131e-01 6.993034e-01
## 2796 4.935920e-03 1.611037e-01 8.339604e-01
## 2800 4.640994e-09 3.300368e-01 6.699632e-01
## 2802 2.577839e-03 4.102741e-01 5.871481e-01
## 2803 5.117736e-18 1.439696e-01 8.560304e-01
## 2805 6.417160e-12 2.028804e-01 7.971196e-01
## 2807 5.551884e-12 1.983188e-01 8.016812e-01
## 2811 6.886830e-03 3.403852e-01 6.527280e-01
## 2814 1.150621e-12 1.202611e-01 8.797389e-01
## 2816 7.004080e-03 2.286855e-01 7.643104e-01
## 2818 1.936992e-03 1.679066e-01 8.301564e-01
## 2819 1.106870e-12 1.443510e-01 8.556490e-01
## 2821 1.870847e-03 2.490814e-01 7.490477e-01
## 2822 9.227606e-03 1.929465e-01 7.978259e-01
## 2823 7.615665e-09 2.567944e-01 7.432056e-01
## 2827 5.119930e-03 2.421072e-01 7.527728e-01
## 2828 1.591097e-03 2.242135e-01 7.741954e-01
## 2829 2.453062e-03 2.600650e-01 7.374819e-01
## 2832 8.460157e-03 3.027697e-01 6.887702e-01
## 2837 9.170865e-03 2.120565e-01 7.787726e-01
## 2839 3.749914e-03 2.275467e-01 7.687034e-01
## 2843 8.242985e-03 3.551690e-01 6.365881e-01
## 2844 3.636576e-12 1.422071e-01 8.577929e-01
## 2854 9.969735e-04 2.333955e-01 7.656075e-01
## 2856 4.579178e-03 2.642749e-01 7.311459e-01
## 2861 2.046946e-03 2.782822e-01 7.196708e-01
## 2862 2.350206e-03 2.907939e-01 7.068559e-01
## 2867 1.963057e-12 1.356022e-01 8.643978e-01
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## 8731 6.709389e-04 1.965533e-01 8.027757e-01
## 8733 6.653848e-12 1.325576e-01 8.674424e-01
## 8735 3.097936e-02 2.905670e-01 6.784536e-01
## 8740 1.490103e-02 2.713076e-01 7.137913e-01
## 8742 8.901985e-03 2.028575e-01 7.882405e-01
## 8745 3.559186e-02 2.890015e-01 6.754066e-01
## 8746 3.837287e-03 2.483930e-01 7.477697e-01
## 8752 6.328319e-04 1.543007e-01 8.450665e-01
## 8754 8.329049e-03 2.453190e-01 7.463520e-01
## 8755 1.780883e-12 9.344371e-02 9.065563e-01
## 8762 3.034457e-03 2.460817e-01 7.508839e-01
## 8769 2.759586e-02 1.725157e-01 7.998885e-01
## 8777 2.387226e-11 1.255296e-01 8.744704e-01
## 8779 1.012271e-02 2.585980e-01 7.312793e-01
## 8783 9.034093e-02 3.245119e-01 5.851472e-01
## 8788 5.935884e-02 2.950610e-01 6.455802e-01
## 8789 4.888082e-02 2.658682e-01 6.852510e-01
## 8796 9.253264e-03 2.175264e-01 7.732203e-01
## 8797 9.848170e-03 2.056981e-01 7.844537e-01
## 8798 6.346945e-02 2.514695e-01 6.850610e-01
## 8810 2.150519e-08 1.996835e-01 8.003165e-01
## 8815 4.773282e-02 3.706657e-01 5.816015e-01
## 8816 6.044113e-12 1.342034e-01 8.657966e-01
## 8823 9.784413e-03 2.107083e-01 7.795073e-01
## 8824 3.819705e-02 3.021472e-01 6.596557e-01
## 8834 2.474553e-02 2.697863e-01 7.054682e-01
## 8836 7.806740e-03 1.871528e-01 8.050405e-01
## 8838 3.262091e-03 1.866575e-01 8.100804e-01
## 8839 8.339978e-03 2.104681e-01 7.811920e-01
## 8840 1.265783e-02 3.269749e-01 6.603672e-01
## 8842 2.757331e-11 1.583301e-01 8.416699e-01
## 8844 1.055365e-02 2.536070e-01 7.358393e-01
## 8845 1.419262e-02 2.811406e-01 7.046668e-01
## 8849 1.463776e-02 2.691650e-01 7.161973e-01
## 8852 1.522202e-02 2.788473e-01 7.059307e-01
## 8853 3.212313e-02 2.413107e-01 7.265661e-01
## 8854 3.753702e-02 2.901347e-01 6.723282e-01
## 8868 1.153391e-02 3.232084e-01 6.652577e-01
## 8870 4.121950e-02 2.903390e-01 6.684415e-01
## 8875 1.684982e-03 2.419544e-01 7.563606e-01
## 8877 5.954480e-03 2.534767e-01 7.405689e-01
## 8880 8.885298e-03 2.077305e-01 7.833842e-01
## 8887 3.914498e-12 9.335612e-02 9.066439e-01
## 8889 2.634136e-03 1.532274e-01 8.441385e-01
## 8890 1.312834e-02 2.628096e-01 7.240621e-01
## 8895 1.157691e-02 2.605600e-01 7.278631e-01
## 8902 4.684212e-02 3.097955e-01 6.433623e-01
## 8906 5.567473e-03 2.757441e-01 7.186884e-01
## 8907 6.056371e-03 1.882683e-01 8.056754e-01
## 8911 3.173474e-02 2.422502e-01 7.260150e-01
## 8916 2.278428e-02 2.983587e-01 6.788570e-01
## 8917 2.127415e-12 1.118080e-01 8.881920e-01
## 8918 1.680595e-08 8.291476e-02 9.170852e-01
## 8921 3.412626e-02 2.818594e-01 6.840144e-01
## 8922 6.814924e-03 2.472152e-01 7.459699e-01
## 8924 1.253196e-02 2.300688e-01 7.573992e-01
## 8925 3.980414e-03 5.263211e-02 9.433875e-01
## 8930 4.795472e-02 2.988269e-01 6.532184e-01
## 8942 3.051891e-02 3.032804e-01 6.662007e-01
## 8945 3.274909e-04 1.328258e-01 8.668467e-01
## 8953 1.870976e-02 1.870473e-01 7.942430e-01
## 8956 6.130353e-03 2.351152e-01 7.587545e-01
## 8958 1.020859e-02 2.018598e-01 7.879316e-01
## 8959 5.014752e-03 2.819505e-01 7.130347e-01
## 8962 4.705710e-08 2.496545e-01 7.503455e-01
## 8963 2.495336e-03 1.455162e-01 8.519885e-01
## 8968 3.953891e-02 2.937727e-01 6.666884e-01
## 8969 1.639224e-02 2.348953e-01 7.487124e-01
## 8972 6.915024e-02 2.768365e-01 6.540132e-01
## 8975 1.434652e-13 9.740818e-02 9.025918e-01
## 8980 3.635982e-02 2.181528e-01 7.454874e-01
## 8981 5.895438e-03 1.092160e-01 8.848886e-01
## 8982 1.390435e-02 2.655767e-01 7.205190e-01
## 8988 2.389618e-04 1.957060e-01 8.040550e-01
## 8990 6.402649e-03 1.301202e-01 8.634771e-01
## 8993 1.493505e-02 2.159962e-01 7.690687e-01
## 8996 4.901737e-13 1.069087e-01 8.930913e-01
## 9000 1.030792e-02 2.478347e-01 7.418574e-01
## 9007 1.125629e-02 3.192423e-01 6.695014e-01
## 9019 3.344313e-02 2.790717e-01 6.874852e-01
## 9023 3.183730e-02 2.946644e-01 6.734983e-01
## 9024 1.271505e-03 2.284859e-01 7.702426e-01
## 9027 3.946920e-02 2.288543e-01 7.316765e-01
## 9029 3.175024e-02 2.972521e-01 6.709976e-01
## 9030 1.320847e-02 2.660065e-01 7.207851e-01
## 9033 1.496104e-02 2.224362e-01 7.626027e-01
## 9035 9.356910e-03 2.468659e-01 7.437772e-01
## 9037 4.840518e-03 2.169830e-01 7.781765e-01
## 9038 1.383886e-02 2.606456e-01 7.255155e-01
## 9040 2.787166e-03 2.832035e-01 7.140094e-01
## 9043 1.130545e-02 2.534632e-01 7.352314e-01
## 9047 3.624292e-03 1.831567e-01 8.132190e-01
## 9049 7.984524e-09 1.108881e-01 8.891119e-01
## 9054 3.198122e-02 2.930068e-01 6.750120e-01
## 9070 6.457459e-03 1.450931e-01 8.484495e-01
## 9072 2.165648e-02 3.059368e-01 6.724068e-01
## 9073 3.277861e-02 1.484877e-01 8.187336e-01
## 9085 3.631904e-12 1.665094e-01 8.334906e-01
## 9086 4.013260e-02 2.894047e-01 6.704627e-01
## 9089 7.115265e-03 2.600884e-01 7.327964e-01
## 9090 8.957585e-03 2.275342e-01 7.635082e-01
## 9092 2.035878e-02 2.483880e-01 7.312532e-01
## 9093 4.778250e-02 1.907258e-01 7.614917e-01
## 9096 2.455958e-02 2.485653e-01 7.268751e-01
## 9098 8.920178e-02 3.471720e-01 5.636262e-01
## 9102 9.845350e-03 1.923334e-01 7.978212e-01
## 9103 4.351105e-03 1.285736e-01 8.670753e-01
## 9105 1.093691e-02 2.527092e-01 7.363539e-01
## 9106 5.111139e-09 1.396953e-01 8.603047e-01
## 9111 3.165189e-03 1.008235e-01 8.960113e-01
## 9112 2.220239e-11 1.521351e-01 8.478649e-01
## 9113 8.599492e-03 2.775389e-01 7.138616e-01
## 9115 4.374928e-02 2.184740e-01 7.377767e-01
## 9116 4.965257e-02 3.599299e-01 5.904175e-01
## 9117 1.342661e-02 2.153470e-01 7.712264e-01
## 9122 2.287098e-02 2.339852e-01 7.431438e-01
## 9123 3.500524e-02 3.531287e-01 6.118660e-01
## 9126 2.905776e-02 2.774487e-01 6.934935e-01
## 9128 9.964094e-03 2.179891e-01 7.720468e-01
## 9132 1.753522e-02 2.197222e-01 7.627426e-01
## 9141 8.302033e-03 2.212839e-01 7.704141e-01
## 9143 1.103823e-01 2.947183e-01 5.948995e-01
## 9144 2.003934e-11 1.233027e-01 8.766973e-01
## 9150 2.194129e-03 2.120003e-01 7.858055e-01
## 9151 6.018141e-03 2.770500e-01 7.169318e-01
## 9152 5.485017e-02 2.398455e-01 7.053043e-01
## 9156 7.728882e-03 2.778591e-01 7.144120e-01
## 9159 1.735568e-05 7.375401e-01 2.624426e-01
## 9163 3.404450e-02 2.845869e-01 6.813686e-01
## 9164 5.936951e-03 2.036048e-01 7.904582e-01
## 9176 1.018779e-02 2.570819e-01 7.327303e-01
## 9183 1.365793e-02 3.260290e-01 6.603131e-01
## 9185 3.457450e-02 1.747787e-01 7.906468e-01
## 9186 2.468060e-03 1.178423e-01 8.796897e-01
## 9190 3.832955e-02 2.251537e-01 7.365168e-01
## 9194 6.840265e-03 2.372538e-01 7.559060e-01
## 9197 2.527385e-02 2.955657e-01 6.791605e-01
## 9199 3.608249e-02 3.005830e-01 6.633345e-01
## 9207 4.306813e-03 1.968733e-01 7.988199e-01
## 9208 1.550530e-02 2.175904e-01 7.669043e-01
## 9211 9.395524e-03 2.497364e-01 7.408681e-01
## 9212 3.068086e-02 2.932942e-01 6.760250e-01
## 9215 1.577835e-02 2.176337e-01 7.665880e-01
## 9220 1.444603e-03 1.084963e-01 8.900591e-01
## 9221 6.448448e-03 1.757878e-01 8.177637e-01
## 9229 4.607912e-08 1.798220e-01 8.201779e-01
## 9231 4.324878e-02 2.091738e-01 7.475774e-01
## 9233 1.973374e-02 2.744864e-01 7.057799e-01
## 9235 5.774607e-02 2.771716e-01 6.650824e-01
## 9238 2.716745e-11 1.101771e-01 8.898229e-01
## 9242 2.057709e-02 2.138859e-01 7.655371e-01
## 9245 9.435013e-03 3.118489e-01 6.787161e-01
## 9248 4.617375e-02 2.870701e-01 6.667562e-01
## 9253 1.083872e-02 2.437275e-01 7.454338e-01
## 9263 5.755109e-03 1.888507e-01 8.053942e-01
## 9268 1.005424e-11 1.790738e-01 8.209262e-01
## 9272 1.188850e-02 2.492810e-01 7.388305e-01
## 9275 8.180903e-03 2.423829e-01 7.494361e-01
## 9277 1.531734e-02 2.061055e-01 7.785772e-01
## 9281 1.240255e-02 1.472520e-01 8.403454e-01
## 9282 8.990931e-03 2.536984e-01 7.373106e-01
## 9286 1.038633e-02 2.451712e-01 7.444425e-01
## 9292 6.029864e-12 1.300606e-01 8.699394e-01
## 9294 5.041767e-03 1.290124e-01 8.659458e-01
## 9299 4.196160e-02 2.300293e-01 7.280091e-01
## 9302 1.000000e+00 1.376835e-08 1.989381e-08
## 9303 3.126805e-02 2.740750e-01 6.946570e-01
## 9306 3.764612e-02 2.419185e-01 7.204354e-01
## 9313 6.296292e-12 2.015706e-01 7.984294e-01
## 9316 1.346246e-02 2.019655e-01 7.845721e-01
## 9317 3.286787e-02 2.905713e-01 6.765608e-01
## 9320 1.540877e-02 2.638656e-01 7.207257e-01
## 9321 3.358134e-02 2.679815e-01 6.984371e-01
## 9327 5.462072e-02 2.984026e-01 6.469767e-01
## 9328 9.909747e-03 2.422002e-01 7.478901e-01
## 9331 6.565837e-03 1.990678e-01 7.943664e-01
## 9333 1.445733e-02 2.066107e-01 7.789320e-01
## 9337 9.909747e-03 2.422002e-01 7.478901e-01
## 9338 3.127250e-02 3.754488e-01 5.932787e-01
## 9343 1.914934e-02 1.955595e-01 7.852912e-01
## 9346 2.673243e-02 2.776714e-01 6.955962e-01
## 9350 9.697866e-03 2.408410e-01 7.494611e-01
## 9351 3.892215e-09 1.651387e-01 8.348613e-01
## 9354 5.577376e-02 3.280413e-01 6.161849e-01
## 9356 5.259790e-02 3.387709e-01 6.086312e-01
## 9361 2.559753e-02 3.350059e-01 6.393966e-01
## 9364 1.189447e-02 2.546757e-01 7.334299e-01
## 9365 3.091998e-03 1.717745e-01 8.251335e-01
## 9367 9.713824e-03 2.493566e-01 7.409296e-01
## 9374 1.347814e-02 2.443193e-01 7.422026e-01
## 9378 1.326474e-06 2.268752e-01 7.731234e-01
## 9380 1.060444e-02 2.158898e-01 7.735057e-01
## 9381 4.206935e-06 3.906280e-01 6.093677e-01
## 9383 6.112004e-02 2.886244e-01 6.502556e-01
## 9385 1.300298e-02 2.791930e-01 7.078040e-01
## 9387 7.293318e-03 2.074468e-01 7.852599e-01
## 9389 2.942943e-02 2.870689e-01 6.835017e-01
## 9393 3.095983e-03 2.344153e-01 7.624887e-01
## 9395 6.008021e-02 2.089125e-01 7.310073e-01
## 9398 8.594769e-03 2.094817e-01 7.819235e-01
## 9399 1.615504e-03 1.451921e-01 8.531924e-01
## 9401 1.600534e-02 2.198142e-01 7.641805e-01
## 9408 1.405400e-12 1.091980e-01 8.908020e-01
## 9409 7.542076e-03 2.996329e-01 6.928250e-01
## 9415 7.134705e-03 2.407820e-01 7.520833e-01
## 9416 2.765296e-03 1.940026e-01 8.032321e-01
## 9420 7.341107e-03 1.793394e-01 8.133195e-01
## 9421 1.932429e-03 1.562988e-01 8.417688e-01
## 9423 2.897014e-02 3.761374e-01 5.948925e-01
## 9424 4.467766e-03 1.812627e-01 8.142695e-01
## 9425 5.101639e-04 2.247165e-01 7.747733e-01
## 9426 2.956106e-02 2.941061e-01 6.763329e-01
## 9430 4.111124e-02 3.526821e-01 6.062067e-01
## 9431 1.362648e-03 2.717252e-01 7.269122e-01
## 9434 1.383204e-02 3.185783e-01 6.675897e-01
## 9437 1.837111e-02 3.400812e-01 6.415477e-01
## 9441 8.669153e-10 1.518092e-01 8.481908e-01
## 9442 6.482697e-03 2.144761e-01 7.790412e-01
## 9447 5.981417e-03 2.319785e-01 7.620401e-01
## 9455 1.538861e-02 2.633237e-01 7.212877e-01
## 9457 1.642203e-02 1.648039e-01 8.187740e-01
## 9459 1.544951e-01 2.480266e-01 5.974783e-01
## 9461 8.626528e-12 1.342463e-01 8.657537e-01
## 9473 3.609410e-03 2.784728e-01 7.179178e-01
## 9476 9.483935e-03 1.776750e-01 8.128410e-01
## 9480 7.824079e-03 1.817755e-01 8.104004e-01
## 9481 1.401671e-02 2.424289e-01 7.435544e-01
## 9482 5.489853e-02 2.959587e-01 6.491428e-01
## 9487 1.717532e-02 2.163565e-01 7.664682e-01
## 9490 2.527917e-03 2.102159e-01 7.872562e-01
## 9494 2.938860e-03 1.804764e-01 8.165847e-01
## 9496 7.558706e-03 2.401634e-01 7.522779e-01
## 9497 3.865408e-02 3.367290e-01 6.246169e-01
## 9499 7.300036e-02 3.067460e-01 6.202537e-01
## 9503 1.419090e-02 2.577527e-01 7.280564e-01
## 9507 3.358497e-06 1.602904e-01 8.397063e-01
## 9510 1.621695e-02 2.064917e-01 7.772913e-01
## 9511 1.305753e-02 2.044141e-01 7.825284e-01
## 9516 3.172791e-02 3.414342e-01 6.268379e-01
## 9520 2.622376e-02 2.772116e-01 6.965647e-01
## 9521 7.660203e-03 1.563811e-01 8.359587e-01
## 9524 2.855737e-02 2.914340e-01 6.800087e-01
## 9526 8.150941e-02 3.641950e-01 5.542955e-01
## 9533 1.391547e-02 2.940999e-01 6.919846e-01
## 9535 7.813152e-02 2.864972e-01 6.353713e-01
## 9540 4.662876e-03 1.606012e-01 8.347360e-01
## 9541 1.464250e-02 2.668894e-01 7.184681e-01
## 9547 2.333759e-02 2.846544e-01 6.920080e-01
view(predictions1)

predictions2 <- predict(step_test2_, newdata = test_data, type = "probs")
predictions2 
##                 1            2            3
## 6    1.172861e-02 2.591351e-01 7.291363e-01
## 12   1.630640e-02 3.253153e-01 6.583783e-01
## 14   1.505021e-02 3.084970e-01 6.764528e-01
## 19   2.167765e-02 3.878602e-01 5.904622e-01
## 23   8.043181e-03 1.943871e-01 7.975698e-01
## 24   8.257051e-03 1.984786e-01 7.932643e-01
## 26   9.920757e-03 2.288420e-01 7.612373e-01
## 29   1.319902e-02 2.819212e-01 7.048798e-01
## 33   2.076379e-02 3.781768e-01 6.010594e-01
## 34   1.003961e-02 2.309163e-01 7.590440e-01
## 37   1.615775e-02 3.233732e-01 6.604690e-01
## 38   1.014737e-02 2.327867e-01 7.570660e-01
## 40   3.631214e-02 5.048608e-01 4.588271e-01
## 42   9.410389e-03 2.197947e-01 7.707949e-01
## 43   1.379887e-02 2.907790e-01 6.954221e-01
## 44   1.076213e-02 2.432703e-01 7.459676e-01
## 46   1.087237e-02 2.451173e-01 7.440104e-01
## 47   1.022292e-02 2.340920e-01 7.556851e-01
## 48   7.837816e-03 1.904158e-01 8.017464e-01
## 50   1.636023e-02 3.260154e-01 6.576244e-01
## 56   1.098976e-02 2.470735e-01 7.419368e-01
## 69   9.776458e-03 2.263071e-01 7.639164e-01
## 70   1.182033e-02 2.606029e-01 7.275768e-01
## 74   7.442153e-03 1.826450e-01 8.099129e-01
## 78   9.580280e-03 2.228318e-01 7.675879e-01
## 80   4.613420e-03 1.220840e-01 8.733026e-01
## 85   1.680923e-02 3.317918e-01 6.513989e-01
## 86   8.685879e-03 2.065495e-01 7.847647e-01
## 87   8.379239e-03 2.007962e-01 7.908245e-01
## 89   1.899134e-02 3.583338e-01 6.226749e-01
## 90   8.131547e-03 1.960830e-01 7.957854e-01
## 91   1.233872e-02 2.687806e-01 7.188807e-01
## 92   7.833873e-03 1.903391e-01 8.018270e-01
## 93   4.394311e-03 1.169928e-01 8.786129e-01
## 95   5.777574e-03 1.481274e-01 8.460950e-01
## 99   9.015723e-03 2.126393e-01 7.783450e-01
## 102  7.269444e-03 1.792027e-01 8.135279e-01
## 104  7.074884e-03 1.752875e-01 8.176376e-01
## 110  1.126098e-02 2.515506e-01 7.371884e-01
## 111  5.462130e-03 1.412333e-01 8.533046e-01
## 115  5.207576e-03 1.355831e-01 8.592094e-01
## 117  6.525973e-03 1.640237e-01 8.294503e-01
## 118  3.052519e-02 4.658445e-01 5.036303e-01
## 119  7.301737e-03 1.798487e-01 8.128496e-01
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## 1096 6.118651e-03 1.554510e-01 8.384303e-01
## 1097 1.015587e-02 2.329338e-01 7.569103e-01
## 1100 6.000266e-03 1.529242e-01 8.410755e-01
## 1113 1.283377e-02 2.764064e-01 7.107599e-01
## 1115 1.004340e-02 2.309822e-01 7.589744e-01
## 1116 1.088498e-02 2.453280e-01 7.437870e-01
## 1117 1.332090e-02 2.837407e-01 7.029383e-01
## 1118 7.735502e-03 1.884215e-01 8.038430e-01
## 1121 8.934169e-03 2.111430e-01 7.799229e-01
## 1122 8.908128e-03 2.106639e-01 7.804280e-01
## 1124 2.508633e-02 4.210375e-01 5.538762e-01
## 1125 1.604005e-02 3.218266e-01 6.621333e-01
## 1127 7.865878e-03 1.909609e-01 8.011732e-01
## 1130 8.516098e-03 2.033751e-01 7.881088e-01
## 1131 1.840483e-02 3.514395e-01 6.301557e-01
## 1134 8.091886e-03 1.953228e-01 7.965853e-01
## 1136 7.569919e-03 1.851717e-01 8.072584e-01
## 1141 1.096888e-02 2.467263e-01 7.423048e-01
## 1144 5.296542e-03 1.375667e-01 8.571367e-01
## 1145 7.301002e-03 1.798340e-01 8.128650e-01
## 1148 1.487819e-02 3.061201e-01 6.790017e-01
## 1150 1.420489e-02 2.966381e-01 6.891570e-01
## 1156 7.819253e-03 1.900547e-01 8.021260e-01
## 1159 1.249991e-02 2.712829e-01 7.162172e-01
## 1168 1.028822e-03 3.020172e-02 9.687695e-01
## 1172 2.599743e-02 4.291893e-01 5.448133e-01
## 1173 1.203507e-02 2.640147e-01 7.239502e-01
## 1174 1.747656e-02 3.401724e-01 6.423510e-01
## 1180 1.240146e-02 2.697567e-01 7.178418e-01
## 1182 5.561913e-03 1.434268e-01 8.510113e-01
## 1183 1.473182e-02 3.040831e-01 6.811851e-01
## 1187 8.571987e-03 2.044230e-01 7.870050e-01
## 1188 1.226456e-02 2.676229e-01 7.201126e-01
## 1189 1.461539e-02 3.024533e-01 6.829313e-01
## 1192 5.294967e-03 1.375317e-01 8.571733e-01
## 1197 9.782062e-03 2.264059e-01 7.638120e-01
## 1200 9.831529e-03 2.272767e-01 7.628918e-01
## 1208 1.975515e-02 3.670629e-01 6.131819e-01
## 1210 1.719115e-02 3.366176e-01 6.461913e-01
## 1218 1.402368e-02 2.940364e-01 6.919399e-01
## 1220 7.706506e-03 1.878545e-01 8.044390e-01
## 1221 8.294639e-03 1.991931e-01 7.925122e-01
## 1229 1.031284e-02 2.356394e-01 7.540478e-01
## 1231 8.207988e-03 1.975440e-01 7.942481e-01
## 1237 1.032495e-02 2.358473e-01 7.538278e-01
## 1242 2.675475e-03 7.479173e-02 9.225328e-01
## 1244 3.211999e-03 8.841213e-02 9.083759e-01
## 1247 1.203762e-02 2.640550e-01 7.239074e-01
## 1250 8.930294e-03 2.110717e-01 7.799980e-01
## 1253 1.458733e-02 3.020592e-01 6.833535e-01
## 1254 6.736899e-03 1.683906e-01 8.248725e-01
## 1255 1.060919e-02 2.406913e-01 7.486995e-01
## 1257 9.000997e-03 2.123696e-01 7.786294e-01
## 1262 1.102866e-02 2.477192e-01 7.412522e-01
## 1265 4.461630e-03 1.185636e-01 8.769748e-01
## 1266 1.540475e-02 3.133387e-01 6.712565e-01
## 1269 1.406513e-02 2.946334e-01 6.913015e-01
## 1273 1.060362e-02 2.405971e-01 7.487993e-01
## 1277 9.194805e-03 2.159036e-01 7.749016e-01
## 1279 1.573549e-02 3.177873e-01 6.664772e-01
## 1281 9.574446e-03 2.227279e-01 7.676976e-01
## 1282 1.644806e-02 3.271542e-01 6.563977e-01
## 1283 9.033442e-03 2.129636e-01 7.780030e-01
## 1287 1.656789e-02 3.287010e-01 6.547311e-01
## 1292 2.428181e-02 4.135995e-01 5.621187e-01
## 1293 1.894281e-02 3.577698e-01 6.232874e-01
## 1295 1.011091e-02 2.321549e-01 7.577342e-01
## 1302 6.997182e-03 1.737127e-01 8.192901e-01
## 1303 1.141649e-02 2.540917e-01 7.344918e-01
## 1305 1.443976e-02 2.999784e-01 6.855818e-01
## 1310 1.376834e-02 2.903340e-01 6.958977e-01
## 1311 1.369765e-02 2.893013e-01 6.970010e-01
## 1317 2.245472e-02 3.958193e-01 5.817260e-01
## 1320 1.562761e-02 3.163434e-01 6.680290e-01
## 1321 2.212942e-02 3.925173e-01 5.853532e-01
## 1326 1.519409e-02 3.104711e-01 6.743348e-01
## 1329 1.779634e-02 3.441041e-01 6.380996e-01
## 1332 2.749924e-02 4.420307e-01 5.304701e-01
## 1336 1.094713e-02 2.463643e-01 7.426886e-01
## 1343 8.374068e-03 2.006984e-01 7.909275e-01
## 1346 1.018931e-02 2.335120e-01 7.562987e-01
## 1348 1.310440e-02 2.805015e-01 7.063941e-01
## 1353 5.791667e-03 1.484327e-01 8.457756e-01
## 1355 1.817421e-02 3.486815e-01 6.331443e-01
## 1357 7.334938e-03 1.805117e-01 8.121534e-01
## 1359 2.420939e-03 6.817999e-02 9.293991e-01
## 1367 1.613541e-02 3.230803e-01 6.607843e-01
## 1369 1.099083e-02 2.470912e-01 7.419180e-01
## 1373 1.490802e-02 3.065336e-01 6.785584e-01
## 1374 1.305764e-02 2.797976e-01 7.071448e-01
## 1375 6.103012e-03 1.551181e-01 8.387789e-01
## 1377 5.769502e-03 1.479525e-01 8.462780e-01
## 1378 1.168083e-02 2.583678e-01 7.299514e-01
## 1379 1.146151e-02 2.548237e-01 7.337147e-01
## 1382 6.389514e-03 1.611724e-01 8.324381e-01
## 1383 1.050758e-02 2.389674e-01 7.505250e-01
## 1384 1.285008e-02 2.766547e-01 7.104952e-01
## 1387 1.240469e-02 2.698070e-01 7.177883e-01
## 1388 1.099687e-02 2.471916e-01 7.418116e-01
## 1390 9.753372e-03 2.258999e-01 7.643467e-01
## 1392 1.426760e-02 2.975334e-01 6.881990e-01
## 1393 1.004852e-02 2.310713e-01 7.588801e-01
## 1395 1.134739e-02 2.529649e-01 7.356878e-01
## 1396 1.030686e-02 2.355367e-01 7.541565e-01
## 1398 1.849749e-02 3.525400e-01 6.289625e-01
## 1407 1.026717e-02 2.348544e-01 7.548784e-01
## 1416 9.222797e-03 2.164112e-01 7.743660e-01
## 1418 1.464789e-02 3.029091e-01 6.824430e-01
## 1422 1.194343e-02 2.625630e-01 7.254935e-01
## 1433 1.199181e-02 2.633301e-01 7.246780e-01
## 1438 1.053537e-02 2.394398e-01 7.500248e-01
## 1439 1.077598e-02 2.435028e-01 7.457212e-01
## 1443 1.020032e-02 2.337020e-01 7.560977e-01
## 1450 1.057512e-02 2.401143e-01 7.493106e-01
## 1451 1.109347e-02 2.487923e-01 7.401142e-01
## 1455 1.640214e-02 3.265594e-01 6.570385e-01
## 1460 1.407772e-02 2.948145e-01 6.911078e-01
## 1461 6.826404e-03 1.702290e-01 8.229446e-01
## 1463 8.783502e-03 2.083624e-01 7.828541e-01
## 1471 6.836564e-03 1.704371e-01 8.227263e-01
## 1473 5.924051e-03 1.512890e-01 8.427869e-01
## 1480 8.109073e-03 1.956524e-01 7.962385e-01
## 1484 1.532019e-01 6.967183e-01 1.500798e-01
## 1485 8.448907e-03 2.021112e-01 7.894399e-01
## 1486 1.247591e-02 2.709115e-01 7.166126e-01
## 1487 1.004090e-02 2.309388e-01 7.590203e-01
## 1490 1.404528e-02 2.943477e-01 6.916070e-01
## 1491 1.512763e-02 3.095608e-01 6.753116e-01
## 1493 1.246762e-02 2.707831e-01 7.167493e-01
## 1496 1.003240e-02 2.307909e-01 7.591767e-01
## 1499 1.322253e-02 2.822729e-01 7.045045e-01
## 1502 6.398677e-03 1.613645e-01 8.322368e-01
## 1503 1.316706e-02 2.814423e-01 7.053906e-01
## 1509 7.957331e-03 1.927320e-01 7.993106e-01
## 1510 1.272520e-02 2.747490e-01 7.125258e-01
## 1511 6.081024e-03 1.546496e-01 8.392693e-01
## 1515 1.336122e-02 2.843405e-01 7.022983e-01
## 1521 7.766140e-03 1.890198e-01 8.032140e-01
## 1523 1.136650e-02 2.532770e-01 7.353565e-01
## 1525 8.531603e-03 2.036661e-01 7.878023e-01
## 1527 8.562142e-03 2.042386e-01 7.871992e-01
## 1528 8.415536e-03 2.014819e-01 7.901025e-01
## 1530 2.113002e-02 3.821004e-01 5.967696e-01
## 1531 8.208479e-03 1.975533e-01 7.942382e-01
## 1534 7.773989e-03 1.891729e-01 8.030531e-01
## 1536 8.320392e-03 1.996819e-01 7.919978e-01
## 1537 8.987672e-03 2.121253e-01 7.788870e-01
## 1538 1.351664e-02 2.866416e-01 6.998417e-01
## 1539 1.127642e-02 2.518038e-01 7.369198e-01
## 1541 1.063967e-02 2.412069e-01 7.481534e-01
## 1544 5.259600e-03 1.367442e-01 8.579962e-01
## 1547 8.216013e-03 1.976970e-01 7.940870e-01
## 1550 3.957949e-03 1.066661e-01 8.893759e-01
## 1554 5.004192e-03 1.310118e-01 8.639840e-01
## 1558 1.205717e-02 2.643638e-01 7.235790e-01
## 1559 1.221094e-02 2.667833e-01 7.210058e-01
## 1563 1.829080e-02 3.500792e-01 6.316299e-01
## 1568 3.076395e-03 8.500940e-02 9.119142e-01
## 1570 6.033844e-03 1.536425e-01 8.403236e-01
## 1576 2.094251e-02 3.800988e-01 5.989587e-01
## 1580 1.354198e-02 2.870154e-01 6.994426e-01
## 1585 1.382640e-02 2.911797e-01 6.949939e-01
## 1586 3.022015e-03 8.363736e-02 9.133406e-01
## 1591 1.802173e-02 3.468433e-01 6.351349e-01
## 1592 2.010973e-02 3.710224e-01 6.088678e-01
## 1594 7.879778e-03 1.912306e-01 8.008896e-01
## 1595 8.488389e-03 2.028544e-01 7.886572e-01
## 1596 9.354738e-03 2.187943e-01 7.718510e-01
## 1601 1.826548e-02 3.497763e-01 6.319582e-01
## 1602 2.116435e-02 3.824652e-01 5.963704e-01
## 1615 1.271024e-02 2.745200e-01 7.127698e-01
## 1617 1.380616e-02 2.908851e-01 6.953087e-01
## 1621 9.592257e-03 2.230450e-01 7.673628e-01
## 1624 1.542809e-02 3.136548e-01 6.709171e-01
## 1626 8.101056e-03 1.954987e-01 7.964002e-01
## 1628 1.806344e-02 3.473474e-01 6.345892e-01
## 1633 1.210094e-02 2.650544e-01 7.228447e-01
## 1635 1.643096e-02 3.269329e-01 6.566362e-01
## 1638 2.269142e-02 3.981953e-01 5.791133e-01
## 1642 9.546196e-03 2.222245e-01 7.682293e-01
## 1644 6.922190e-03 1.721868e-01 8.208910e-01
## 1645 7.046784e-03 1.747188e-01 8.182345e-01
## 1649 8.457765e-03 2.022781e-01 7.892641e-01
## 1650 1.822494e-03 5.223958e-02 9.459379e-01
## 1657 9.849575e-03 2.275938e-01 7.625566e-01
## 1659 9.523592e-03 2.218213e-01 7.686552e-01
## 1671 1.052072e-02 2.391908e-01 7.502885e-01
## 1680 9.961524e-03 2.295549e-01 7.604836e-01
## 1688 1.277681e-02 2.755379e-01 7.116852e-01
## 1691 2.038561e-02 3.740634e-01 6.055509e-01
## 1692 1.114436e-02 2.496326e-01 7.392230e-01
## 1704 1.159407e-02 2.569702e-01 7.314357e-01
## 1715 1.163440e-02 2.576207e-01 7.307449e-01
## 1719 1.114115e-02 2.495797e-01 7.392792e-01
## 1725 1.016318e-02 2.330602e-01 7.567766e-01
## 1727 2.807333e-03 7.817844e-02 9.190142e-01
## 1728 1.299566e-02 2.788621e-01 7.081422e-01
## 1730 1.107976e-02 2.485657e-01 7.403546e-01
## 1732 9.194805e-03 2.159036e-01 7.749016e-01
## 1737 1.401620e-02 2.939286e-01 6.920552e-01
## 1740 7.155104e-03 1.769066e-01 8.159383e-01
## 1742 1.695526e-02 3.336464e-01 6.493984e-01
## 1749 5.016304e-03 1.312855e-01 8.636982e-01
## 1759 9.132878e-03 2.147781e-01 7.760890e-01
## 1763 7.851568e-03 1.906830e-01 8.014654e-01
## 1765 1.381482e-02 2.910111e-01 6.951741e-01
## 1769 1.729710e-02 3.379423e-01 6.447606e-01
## 1771 1.164147e-02 2.577345e-01 7.306240e-01
## 1772 9.522371e-03 2.217995e-01 7.686782e-01
## 1778 7.970011e-03 1.929769e-01 7.990531e-01
## 1779 7.384328e-03 1.814959e-01 8.111198e-01
## 1782 1.459572e-02 3.021771e-01 6.832272e-01
## 1785 7.304447e-03 1.799028e-01 8.127927e-01
## 1788 3.198508e-02 4.764399e-01 4.915751e-01
## 1791 1.569006e-02 3.171800e-01 6.671299e-01
## 1798 9.865085e-03 2.278661e-01 7.622688e-01
## 1800 9.645190e-03 2.239854e-01 7.663694e-01
## 1801 1.287113e-02 2.769748e-01 7.101541e-01
## 1806 9.405509e-03 2.197071e-01 7.708874e-01
## 1810 8.048947e-03 1.944980e-01 7.974531e-01
## 1811 7.692628e-03 1.875827e-01 8.047246e-01
## 1813 1.049409e-02 2.387379e-01 7.507680e-01
## 1814 7.712020e-03 1.879624e-01 8.043256e-01
## 1816 8.885873e-03 2.102540e-01 7.808602e-01
## 1817 1.190381e-02 2.619334e-01 7.261628e-01
## 1818 6.200272e-03 1.571838e-01 8.366159e-01
## 1819 1.478336e-02 3.048019e-01 6.804148e-01
## 1822 9.298578e-03 2.177819e-01 7.729196e-01
## 1824 1.220302e-02 2.666592e-01 7.211378e-01
## 1825 1.033102e-02 2.359514e-01 7.537176e-01
## 1826 1.502422e-02 3.081390e-01 6.768368e-01
## 1828 9.974092e-03 2.297743e-01 7.602516e-01
## 1830 1.133079e-02 2.526937e-01 7.359755e-01
## 1837 7.480123e-03 1.833976e-01 8.091222e-01
## 1846 9.705862e-03 2.250604e-01 7.652337e-01
## 1848 1.112554e-02 2.493222e-01 7.395523e-01
## 1851 9.556559e-03 2.224093e-01 7.680342e-01
## 1852 8.566941e-03 2.043285e-01 7.871045e-01
## 1856 1.267996e-02 2.740558e-01 7.132642e-01
## 1857 1.083494e-02 2.444913e-01 7.446738e-01
## 1858 9.509383e-03 2.215675e-01 7.689231e-01
## 1859 1.021893e-02 2.340233e-01 7.557578e-01
## 1861 8.775979e-03 2.082230e-01 7.830010e-01
## 1867 7.807355e-03 1.898232e-01 8.023695e-01
## 1871 8.741649e-03 2.075863e-01 7.836721e-01
## 1875 1.027570e-02 2.350012e-01 7.547231e-01
## 1889 6.826454e-03 1.702300e-01 8.229436e-01
## 1890 9.075683e-03 2.137355e-01 7.771888e-01
## 1893 6.290240e-03 1.590850e-01 8.346247e-01
## 1894 1.393319e-02 2.927292e-01 6.933376e-01
## 1897 1.405650e-02 2.945092e-01 6.914343e-01
## 1898 8.329155e-03 1.998480e-01 7.918228e-01
## 1901 5.081736e-03 1.327607e-01 8.621576e-01
## 1902 1.028669e-02 2.351901e-01 7.545232e-01
## 1903 1.234919e-02 2.689437e-01 7.187071e-01
## 1908 9.666835e-03 2.243693e-01 7.659639e-01
## 1910 1.257591e-02 2.724563e-01 7.149678e-01
## 1911 1.033576e-02 2.360328e-01 7.536314e-01
## 1915 1.646779e-02 3.274095e-01 6.561227e-01
## 1917 1.159736e-02 2.570234e-01 7.313793e-01
## 1919 1.185721e-02 2.611914e-01 7.269514e-01
## 1929 1.094847e-02 2.463867e-01 7.426649e-01
## 1930 6.706672e-03 1.677677e-01 8.255256e-01
## 1931 9.041446e-03 2.131100e-01 7.778486e-01
## 1933 1.682499e-02 3.319926e-01 6.511824e-01
## 1938 9.753772e-03 2.259070e-01 7.643393e-01
## 1945 1.443580e-02 2.999225e-01 6.856417e-01
## 1951 7.166967e-03 1.771455e-01 8.156875e-01
## 1954 2.087361e-02 3.793595e-01 5.997669e-01
## 1955 5.532565e-03 1.427829e-01 8.516846e-01
## 1958 1.121088e-02 2.507279e-01 7.380612e-01
## 1966 1.862414e-02 3.540373e-01 6.273385e-01
## 1975 8.944332e-03 2.113298e-01 7.797259e-01
## 1977 1.938477e-02 3.628647e-01 6.177506e-01
## 1978 1.067888e-02 2.418688e-01 7.474523e-01
## 1980 1.819163e-02 3.488909e-01 6.329175e-01
## 1983 5.699097e-03 1.464233e-01 8.478776e-01
## 1985 6.698831e-03 1.676060e-01 8.256951e-01
## 1986 1.637384e-02 3.261922e-01 6.574340e-01
## 1990 8.674665e-03 2.063406e-01 7.849847e-01
## 1992 8.216265e-03 1.977018e-01 7.940819e-01
## 1997 1.589090e-02 3.198552e-01 6.642539e-01
## 2005 1.557082e-02 3.155805e-01 6.688487e-01
## 2010 7.902778e-03 1.916765e-01 8.004207e-01
## 2011 1.155701e-02 2.563716e-01 7.320714e-01
## 2019 1.058513e-02 2.402840e-01 7.491309e-01
## 2020 1.061106e-02 2.407230e-01 7.486659e-01
## 2030 1.289922e-02 2.774015e-01 7.096993e-01
## 2031 5.637401e-03 1.450784e-01 8.492842e-01
## 2039 1.435975e-02 2.988445e-01 6.867957e-01
## 2040 1.011493e-02 2.322247e-01 7.576604e-01
## 2042 7.107776e-03 1.759522e-01 8.169400e-01
## 2043 1.097791e-02 2.468765e-01 7.421456e-01
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## 8911 1.218906e-02 2.664401e-01 7.213709e-01
## 8916 1.520948e-02 3.106815e-01 6.741090e-01
## 8917 3.962347e-03 1.067714e-01 8.892662e-01
## 8918 2.820240e-03 7.850857e-02 9.186712e-01
## 8921 1.443734e-02 2.999442e-01 6.856185e-01
## 8922 1.070167e-02 2.422532e-01 7.470452e-01
## 8924 1.031201e-02 2.356252e-01 7.540628e-01
## 8925 1.938369e-03 5.537028e-02 9.426913e-01
## 8930 1.667696e-02 3.301018e-01 6.532212e-01
## 8942 1.606191e-02 3.221145e-01 6.618236e-01
## 8945 4.668316e-03 1.233498e-01 8.719818e-01
## 8953 8.357274e-03 2.003807e-01 7.912620e-01
## 8956 9.992041e-03 2.300876e-01 7.599204e-01
## 8958 8.648536e-03 2.058536e-01 7.854979e-01
## 8959 1.265992e-02 2.737484e-01 7.135917e-01
## 8962 1.140400e-02 2.538883e-01 7.347077e-01
## 8963 5.552310e-03 1.432162e-01 8.512315e-01
## 8968 1.579235e-02 3.185454e-01 6.656622e-01
## 8969 1.070505e-02 2.423100e-01 7.469850e-01
## 8972 1.568376e-02 3.170957e-01 6.672205e-01
## 8975 3.004595e-03 8.319691e-02 9.137985e-01
## 8980 1.063384e-02 2.411083e-01 7.482579e-01
## 8981 4.328665e-03 1.154554e-01 8.802160e-01
## 8982 1.242235e-02 2.700812e-01 7.174964e-01
## 8988 7.069191e-03 1.751724e-01 8.177584e-01
## 8990 5.117806e-03 1.335717e-01 8.613105e-01
## 8993 1.000485e-02 2.303109e-01 7.596843e-01
## 8996 3.658197e-03 9.942386e-02 8.969179e-01
## 9000 1.112642e-02 2.493366e-01 7.395369e-01
## 9007 1.558648e-02 3.157911e-01 6.686224e-01
## 9019 1.429573e-02 2.979343e-01 6.877700e-01
## 9023 1.553045e-02 3.150371e-01 6.694325e-01
## 9024 9.469777e-03 2.208593e-01 7.696709e-01
## 9027 1.143474e-02 2.543886e-01 7.341767e-01
## 9029 1.566644e-02 3.168639e-01 6.674697e-01
## 9030 1.238220e-02 2.694574e-01 7.181603e-01
## 9033 1.001974e-02 2.305703e-01 7.594099e-01
## 9035 1.095954e-02 2.465708e-01 7.424696e-01
## 9037 9.025443e-03 2.128172e-01 7.781573e-01
## 9038 1.219431e-02 2.665226e-01 7.212831e-01
## 9040 1.311093e-02 2.805996e-01 7.062895e-01
## 9043 1.149536e-02 2.553732e-01 7.331315e-01
## 9047 7.283023e-03 1.794744e-01 8.132425e-01
## 9049 4.267885e-03 1.140268e-01 8.817053e-01
## 9054 1.524032e-02 3.111027e-01 6.736570e-01
## 9070 5.932965e-03 1.514806e-01 8.425864e-01
## 9072 1.565867e-02 3.167598e-01 6.675815e-01
## 9073 6.977233e-03 1.733074e-01 8.197154e-01
## 9085 6.324363e-03 1.598038e-01 8.338719e-01
## 9086 1.545390e-02 3.140039e-01 6.705422e-01
## 9089 1.149587e-02 2.553814e-01 7.331227e-01
## 9090 1.004916e-02 2.310824e-01 7.588684e-01
## 9092 1.172243e-02 2.590358e-01 7.292417e-01
## 9093 9.319125e-03 2.181526e-01 7.725283e-01
## 9096 1.202333e-02 2.638291e-01 7.241476e-01
## 9098 2.267822e-02 3.980634e-01 5.792584e-01
## 9102 8.209384e-03 1.975706e-01 7.942200e-01
## 9103 5.018779e-03 1.313414e-01 8.636398e-01
## 9105 1.193830e-02 2.624816e-01 7.255801e-01
## 9106 5.094640e-03 1.330510e-01 8.618543e-01
## 9111 3.846187e-03 1.039802e-01 8.921736e-01
## 9112 6.086123e-03 1.547583e-01 8.391555e-01
## 9113 1.317513e-02 2.815633e-01 7.052616e-01
## 9115 1.081337e-02 2.441299e-01 7.450567e-01
## 9116 2.148412e-02 3.858391e-01 5.926767e-01
## 9117 9.559619e-03 2.224638e-01 7.679766e-01
## 9122 1.113383e-02 2.494589e-01 7.394073e-01
## 9123 2.025226e-02 3.725978e-01 6.071499e-01
## 9126 1.401673e-02 2.939363e-01 6.920470e-01
## 9128 9.630008e-03 2.237159e-01 7.666541e-01
## 9132 1.010875e-02 2.321174e-01 7.577738e-01
## 9141 9.528194e-03 2.219034e-01 7.685684e-01
## 9143 1.883936e-02 3.565636e-01 6.245970e-01
## 9144 4.819982e-03 1.268272e-01 8.683528e-01
## 9150 8.606437e-03 2.050675e-01 7.863260e-01
## 9151 1.267320e-02 2.739522e-01 7.133746e-01
## 9152 1.250633e-02 2.713822e-01 7.161114e-01
## 9156 1.249622e-02 2.712258e-01 7.162779e-01
## 9159 7.732453e-02 6.466803e-01 2.759952e-01
## 9163 1.499244e-02 3.077008e-01 6.773068e-01
## 9164 8.538443e-03 2.037944e-01 7.876671e-01
## 9176 1.161326e-02 2.572799e-01 7.311068e-01
## 9183 1.630375e-02 3.252808e-01 6.584154e-01
## 9185 8.144167e-03 1.963246e-01 7.955312e-01
## 9186 4.396907e-03 1.170535e-01 8.785496e-01
## 9190 1.116325e-02 2.499441e-01 7.388927e-01
## 9194 1.018203e-02 2.333861e-01 7.564319e-01
## 9197 1.517523e-02 3.102130e-01 6.746117e-01
## 9199 1.613405e-02 3.230625e-01 6.608035e-01
## 9207 8.106384e-03 1.956009e-01 7.962928e-01
## 9208 9.822079e-03 2.271105e-01 7.630674e-01
## 9211 1.115760e-02 2.498510e-01 7.389914e-01
## 9212 1.527994e-02 3.116430e-01 6.730770e-01
## 9215 1.006704e-02 2.313934e-01 7.585395e-01
## 9220 3.951971e-03 1.065229e-01 8.895252e-01
## 9221 7.087928e-03 1.755513e-01 8.173608e-01
## 9229 7.584442e-03 1.854579e-01 8.069577e-01
## 9231 1.025413e-02 2.346299e-01 7.551160e-01
## 9233 1.335269e-02 2.842136e-01 7.024337e-01
## 9235 1.530504e-02 3.119848e-01 6.727102e-01
## 9238 4.661132e-03 1.231844e-01 8.721545e-01
## 9242 9.825144e-03 2.271644e-01 7.630105e-01
## 9245 1.487953e-02 3.061387e-01 6.789818e-01
## 9248 1.554931e-02 3.152910e-01 6.691597e-01
## 9253 1.093133e-02 2.461012e-01 7.429674e-01
## 9263 7.696159e-03 1.876519e-01 8.046519e-01
## 9268 6.950564e-03 1.727649e-01 8.202846e-01
## 9272 1.129388e-02 2.520898e-01 7.366163e-01
## 9275 1.060148e-02 2.405609e-01 7.488376e-01
## 9277 9.264097e-03 2.171588e-01 7.735771e-01
## 9281 6.245156e-03 1.581334e-01 8.356214e-01
## 9282 1.134534e-02 2.529314e-01 7.357232e-01
## 9286 1.089207e-02 2.454464e-01 7.436615e-01
## 9292 4.745038e-03 1.251126e-01 8.701424e-01
## 9294 5.145557e-03 1.341945e-01 8.606599e-01
## 9299 1.147506e-02 2.550438e-01 7.334811e-01
## 9302 1.000000e+00 1.117959e-09 3.689404e-11
## 9303 1.398849e-02 2.935287e-01 6.924828e-01
## 9306 1.203747e-02 2.640527e-01 7.239099e-01
## 9313 7.875454e-03 1.911468e-01 8.009778e-01
## 9316 8.876194e-03 2.100755e-01 7.810483e-01
## 9317 1.515257e-02 3.099027e-01 6.749447e-01
## 9320 1.243835e-02 2.703294e-01 7.172322e-01
## 9321 1.363950e-02 2.884493e-01 6.979112e-01
## 9327 1.677653e-02 3.313749e-01 6.518486e-01
## 9328 1.074016e-02 2.429010e-01 7.463588e-01
## 9331 8.382048e-03 2.008493e-01 7.907686e-01
## 9333 9.408128e-03 2.197541e-01 7.708377e-01
## 9337 1.074016e-02 2.429010e-01 7.463588e-01
## 9338 2.173352e-02 3.884407e-01 5.898258e-01
## 9343 8.904531e-03 2.105977e-01 7.804978e-01
## 9346 1.415883e-02 2.959788e-01 6.898623e-01
## 9350 1.061475e-02 2.407854e-01 7.485998e-01
## 9351 6.089677e-03 1.548341e-01 8.390763e-01
## 9354 1.904635e-02 3.589718e-01 6.219818e-01
## 9356 2.054391e-02 3.757930e-01 6.036631e-01
## 9361 1.803837e-02 3.470444e-01 6.349172e-01
## 9364 1.160505e-02 2.571475e-01 7.312475e-01
## 9365 6.768145e-03 1.690333e-01 8.241985e-01
## 9367 1.112526e-02 2.493175e-01 7.395573e-01
## 9374 1.130122e-02 2.522100e-01 7.364887e-01
## 9378 1.107905e-02 2.485538e-01 7.403671e-01
## 9380 9.374122e-03 2.191430e-01 7.714828e-01
## 9381 2.027486e-02 3.728468e-01 6.068783e-01
## 9383 1.617811e-02 3.236401e-01 6.601818e-01
## 9385 1.339525e-02 2.848458e-01 7.017590e-01
## 9387 8.809331e-03 2.088406e-01 7.823501e-01
## 9389 1.503287e-02 3.082582e-01 6.767089e-01
## 9393 1.010077e-02 2.319791e-01 7.579201e-01
## 9395 1.166205e-02 2.580658e-01 7.302721e-01
## 9398 9.068080e-03 2.135967e-01 7.773352e-01
## 9399 5.469765e-03 1.414015e-01 8.531287e-01
## 9401 9.898900e-03 2.284592e-01 7.616419e-01
## 9408 3.775936e-03 1.022832e-01 8.939409e-01
## 9409 1.400672e-02 2.937919e-01 6.922014e-01
## 9415 1.039814e-02 2.371011e-01 7.525007e-01
## 9416 7.829259e-03 1.902494e-01 8.019214e-01
## 9420 7.343690e-03 1.806863e-01 8.119700e-01
## 9421 5.895567e-03 1.506762e-01 8.434283e-01
## 9423 2.214953e-02 3.927227e-01 5.851277e-01
## 9424 7.314565e-03 1.801050e-01 8.125805e-01
## 9425 8.732319e-03 2.074130e-01 7.838547e-01
## 9426 1.564316e-02 3.165519e-01 6.678049e-01
## 9430 2.055165e-02 3.758772e-01 6.035711e-01
## 9431 1.146666e-02 2.549074e-01 7.336260e-01
## 9434 1.579047e-02 3.185205e-01 6.656890e-01
## 9437 1.772617e-02 3.432460e-01 6.390279e-01
## 9441 5.418614e-03 1.402729e-01 8.543085e-01
## 9442 9.074412e-03 2.137123e-01 7.772133e-01
## 9447 9.805555e-03 2.268197e-01 7.633747e-01
## 9455 1.238019e-02 2.694261e-01 7.181937e-01
## 9457 7.130637e-03 1.764135e-01 8.164558e-01
## 9459 1.578044e-02 3.183868e-01 6.658328e-01
## 9461 4.996682e-03 1.308421e-01 8.641613e-01
## 9473 1.205812e-02 2.643789e-01 7.235630e-01
## 9476 7.658396e-03 1.869117e-01 8.054299e-01
## 9480 7.526513e-03 1.843152e-01 8.081583e-01
## 9481 1.142826e-02 2.542832e-01 7.342886e-01
## 9482 1.664641e-02 3.297101e-01 6.536435e-01
## 9487 9.803392e-03 2.267816e-01 7.634150e-01
## 9490 8.611001e-03 2.051528e-01 7.862362e-01
## 9494 7.081787e-03 1.754271e-01 8.174911e-01
## 9496 1.040648e-02 2.372436e-01 7.523499e-01
## 9497 1.898620e-02 3.582741e-01 6.227397e-01
## 9499 1.843952e-02 3.518520e-01 6.297084e-01
## 9503 1.198513e-02 2.632243e-01 7.247906e-01
## 9507 6.564559e-03 1.648262e-01 8.286093e-01
## 9510 9.555579e-03 2.223918e-01 7.680526e-01
## 9511 9.000937e-03 2.123685e-01 7.786306e-01
## 9516 1.887983e-02 3.570360e-01 6.240842e-01
## 9520 1.388828e-02 2.920785e-01 6.940333e-01
## 9521 6.398136e-03 1.613531e-01 8.322487e-01
## 9524 1.506410e-02 3.086882e-01 6.762477e-01
## 9526 2.368761e-02 4.079557e-01 5.683567e-01
## 9533 1.416367e-02 2.960482e-01 6.897881e-01
## 9535 1.701658e-02 3.344217e-01 6.485618e-01
## 9540 6.373079e-03 1.608276e-01 8.327993e-01
## 9541 1.259126e-02 2.726928e-01 7.147160e-01
## 9547 1.423021e-02 2.969999e-01 6.887699e-01
view(predictions2)
#MNL best model of train data
# Convert the probability value into a category 
pred_class1_1 <- ifelse(predictions1[,1] > 0.002, 1, 0 )
pred_class1_1 #. If the probability is greater than 0.01, the prediction is a positive class (1), otherwise negative class (0)
##    6   12   14   19   23   24   26   29   33   34   37   38   40   42   43   44 
##    1    1    1    1    1    0    0    1    1    0    1    1    0    1    1    1 
##   46   47   48   50   56   69   70   74   78   80   85   86   87   89   90   91 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   92   93   95   99  102  104  110  111  115  117  118  119  120  123  124  130 
##    1    0    0    1    0    0    1    0    1    1    1    1    1    0    0    1 
##  138  140  141  146  148  157  158  160  166  167  168  169  174  176  177  189 
##    1    1    1    0    1    1    1    1    1    1    1    1    0    0    1    1 
##  190  197  199  202  205  211  212  214  219  220  225  226  228  233  235  239 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    0    1    0 
##  240  241  247  248  254  266  268  280  283  285  289  292  293  301  310  312 
##    1    1    0    0    0    1    1    1    1    1    0    1    1    1    0    1 
##  313  320  322  332  337  347  349  356  357  358  360  363  376  377  378  387 
##    1    0    1    1    0    1    1    0    1    0    0    1    1    1    1    0 
##  388  389  392  395  396  397  399  404  406  409  411  412  416  419  425  430 
##    0    1    1    1    0    1    1    1    1    1    1    1    1    0    1    0 
##  431  439  440  441  443  446  449  450  452  463  465  468  471  475  476  477 
##    1    1    0    1    1    1    1    1    0    1    1    0    0    1    1    1 
##  478  480  483  487  488  493  494  497  499  501  503  507  508  510  514  515 
##    1    0    1    0    1    1    1    1    1    1    0    1    1    1    1    1 
##  516  519  521  524  530  531  533  540  544  545  550  554  556  557  565  566 
##    0    1    1    0    1    1    0    1    1    1    1    1    0    0    1    1 
##  571  573  576  579  580  582  585  591  592  593  594  595  596  598  611  622 
##    1    1    1    1    0    1    1    1    1    1    1    0    1    0    1    1 
##  626  627  629  635  642  648  650  654  658  661  662  667  670  673  676  679 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    0    1    1 
##  681  687  696  698  699  702  709  717  722  725  726  728  731  732  734  736 
##    0    1    0    0    1    1    1    1    1    0    0    0    1    1    0    1 
##  738  746  747  749  753  757  758  759  760  763  765  766  768  770  771  775 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  776  778  787  791  794  802  803  806  809  811  813  814  815  823  824  833 
##    1    1    1    0    0    1    1    1    1    1    1    1    0    1    1    0 
##  835  837  841  844  846  848  853  857  861  865  868  869  876  877  878  879 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    0    1    1 
##  880  886  888  889  895  900  902  907  909  921  924  928  934  935  937  941 
##    0    0    1    1    1    1    1    1    1    1    1    1    1    1    0    0 
##  944  945  951  952  953  955  962  965  968  971  973  975  977  980  983  989 
##    1    0    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
##  992  993  994  996  998 1011 1012 1013 1014 1018 1020 1022 1032 1034 1035 1036 
##    1    0    1    1    1    1    0    1    1    1    1    1    1    0    1    0 
## 1038 1052 1061 1062 1064 1069 1072 1076 1077 1090 1092 1096 1097 1100 1113 1115 
##    0    1    1    1    1    1    1    1    1    1    0    0    0    1    1    1 
## 1116 1117 1118 1121 1122 1124 1125 1127 1130 1131 1134 1136 1141 1144 1145 1148 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    0    1    1 
## 1150 1156 1159 1168 1172 1173 1174 1180 1182 1183 1187 1188 1189 1192 1197 1200 
##    0    1    1    0    1    1    1    1    1    1    0    1    1    0    1    0 
## 1208 1210 1218 1220 1221 1229 1231 1237 1242 1244 1247 1250 1253 1254 1255 1257 
##    1    1    0    1    0    0    1    1    0    1    1    1    1    1    1    1 
## 1262 1265 1266 1269 1273 1277 1279 1281 1282 1283 1287 1292 1293 1295 1302 1303 
##    0    1    1    1    1    1    1    1    1    1    1    1    0    1    1    0 
## 1305 1310 1311 1317 1320 1321 1326 1329 1332 1336 1343 1346 1348 1353 1355 1357 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    0    1    0 
## 1359 1367 1369 1373 1374 1375 1377 1378 1379 1382 1383 1384 1387 1388 1390 1392 
##    0    1    1    1    1    1    0    1    1    1    0    1    1    1    0    1 
## 1393 1395 1396 1398 1407 1416 1418 1422 1433 1438 1439 1443 1450 1451 1455 1460 
##    1    1    1    0    1    1    1    1    1    1    1    1    0    0    1    1 
## 1461 1463 1471 1473 1480 1484 1485 1486 1487 1490 1491 1493 1496 1499 1502 1503 
##    0    0    0    0    1    0    1    1    1    1    0    1    1    0    1    1 
## 1509 1510 1511 1515 1521 1523 1525 1527 1528 1530 1531 1534 1536 1537 1538 1539 
##    0    1    1    1    1    1    1    1    1    1    1    0    0    1    1    1 
## 1541 1544 1547 1550 1554 1558 1559 1563 1568 1570 1576 1580 1585 1586 1591 1592 
##    1    0    1    0    0    1    1    1    0    0    1    1    1    0    1    1 
## 1594 1595 1596 1601 1602 1615 1617 1621 1624 1626 1628 1633 1635 1638 1642 1644 
##    0    0    0    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 1645 1649 1650 1657 1659 1671 1680 1688 1691 1692 1704 1715 1719 1725 1727 1728 
##    0    0    0    1    1    0    1    1    1    1    1    1    1    1    0    1 
## 1730 1732 1737 1740 1742 1749 1759 1763 1765 1769 1771 1772 1778 1779 1782 1785 
##    1    1    1    1    1    0    1    0    1    1    1    1    0    1    1    0 
## 1788 1791 1798 1800 1801 1806 1810 1811 1813 1814 1816 1817 1818 1819 1822 1824 
##    0    1    1    1    1    0    0    0    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    0    1    0    1    1    1    1    1    1    1    1 
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##    1    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1 
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##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 9547 
##    1
#225个0,775个1
library(fpp3)
view(pred_class1_1)
pred_class1_1
##    6   12   14   19   23   24   26   29   33   34   37   38   40   42   43   44 
##    1    1    1    1    1    0    0    1    1    0    1    1    0    1    1    1 
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## 7033 7037 7038 7041 7043 7044 7047 7049 7052 7054 7058 7061 7062 7063 7072 7077 
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##    0    0    1    0    1    1    1    0    1    1    0    0    0    1    1    0 
## 8059 8062 8063 8065 8067 8069 8075 8080 8096 8097 8102 8105 8106 8109 8111 8117 
##    1    1    1    1    1    1    0    1    1    0    1    1    0    0    0    1 
## 8119 8120 8123 8130 8132 8134 8136 8139 8142 8144 8145 8148 8150 8151 8154 8156 
##    1    1    1    1    1    1    1    1    1    1    1    0    0    1    1    1 
## 8161 8162 8168 8170 8171 8175 8180 8184 8187 8188 8189 8192 8201 8204 8206 8207 
##    1    1    1    1    1    1    0    0    1    0    1    1    0    0    1    1 
## 8208 8210 8212 8219 8220 8228 8233 8239 8240 8243 8245 8249 8250 8251 8252 8253 
##    1    0    1    1    0    1    1    1    1    1    0    1    1    0    1    1 
## 8254 8256 8257 8258 8267 8273 8274 8278 8282 8285 8286 8288 8289 8292 8295 8302 
##    0    0    1    1    1    1    1    1    1    0    1    1    1    1    0    1 
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##    0    1    0    1    1    1    0    0    0    0    0    0    1    0    0    1 
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##    1    1    0    1    1    1    0    1    1    0    0    1    1    1    1    1 
## 8436 8437 8440 8446 8451 8453 8456 8460 8461 8462 8464 8465 8466 8474 8476 8478 
##    1    0    1    1    0    1    1    1    0    1    1    1    1    1    1    1 
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##    0    0    1    1    1    1    1    0    1    0    0    1    0    1    1    0 
## 8560 8561 8563 8565 8567 8573 8574 8575 8576 8581 8582 8585 8586 8589 8592 8595 
##    0    1    0    0    1    1    0    1    1    1    1    1    1    1    1    0 
## 8600 8602 8604 8605 8607 8609 8612 8617 8618 8619 8622 8625 8626 8627 8632 8647 
##    1    0    1    1    1    1    1    0    1    1    1    0    1    0    0    0 
## 8648 8649 8651 8653 8656 8659 8662 8669 8670 8674 8676 8678 8680 8682 8688 8695 
##    1    1    0    1    1    1    0    1    0    0    0    1    0    1    1    1 
## 8696 8697 8699 8700 8705 8711 8713 8715 8725 8731 8733 8735 8740 8742 8745 8746 
##    1    1    1    1    1    0    0    0    1    0    0    1    1    1    1    1 
## 8752 8754 8755 8762 8769 8777 8779 8783 8788 8789 8796 8797 8798 8810 8815 8816 
##    0    1    0    1    1    0    1    1    1    1    1    1    1    0    1    0 
## 8823 8824 8834 8836 8838 8839 8840 8842 8844 8845 8849 8852 8853 8854 8868 8870 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8875 8877 8880 8887 8889 8890 8895 8902 8906 8907 8911 8916 8917 8918 8921 8922 
##    0    1    1    0    1    1    1    1    1    1    1    1    0    0    1    1 
## 8924 8925 8930 8942 8945 8953 8956 8958 8959 8962 8963 8968 8969 8972 8975 8980 
##    1    1    1    1    0    1    1    1    1    0    1    1    1    1    0    1 
## 8981 8982 8988 8990 8993 8996 9000 9007 9019 9023 9024 9027 9029 9030 9033 9035 
##    1    1    0    1    1    0    1    1    1    1    0    1    1    1    1    1 
## 9037 9038 9040 9043 9047 9049 9054 9070 9072 9073 9085 9086 9089 9090 9092 9093 
##    1    1    1    1    1    0    1    1    1    1    0    1    1    1    1    1 
## 9096 9098 9102 9103 9105 9106 9111 9112 9113 9115 9116 9117 9122 9123 9126 9128 
##    1    1    1    1    1    0    1    0    1    1    1    1    1    1    1    1 
## 9132 9141 9143 9144 9150 9151 9152 9156 9159 9163 9164 9176 9183 9185 9186 9190 
##    1    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1 
## 9194 9197 9199 9207 9208 9211 9212 9215 9220 9221 9229 9231 9233 9235 9238 9242 
##    1    1    1    1    1    1    1    1    0    1    0    1    1    1    0    1 
## 9245 9248 9253 9263 9268 9272 9275 9277 9281 9282 9286 9292 9294 9299 9302 9303 
##    1    1    1    1    0    1    1    1    1    1    1    0    1    1    1    1 
## 9306 9313 9316 9317 9320 9321 9327 9328 9331 9333 9337 9338 9343 9346 9350 9351 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 9354 9356 9361 9364 9365 9367 9374 9378 9380 9381 9383 9385 9387 9389 9393 9395 
##    1    1    1    1    1    1    1    0    1    0    1    1    1    1    1    1 
## 9398 9399 9401 9408 9409 9415 9416 9420 9421 9423 9424 9425 9426 9430 9431 9434 
##    1    0    1    0    1    1    1    1    0    1    1    0    1    1    0    1 
## 9437 9441 9442 9447 9455 9457 9459 9461 9473 9476 9480 9481 9482 9487 9490 9494 
##    1    0    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 9496 9497 9499 9503 9507 9510 9511 9516 9520 9521 9524 9526 9533 9535 9540 9541 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 9547 
##    1
pred_class1_2 <- ifelse(predictions1[,2] > 0.1126, 1, 0 )
pred_class1_2 #. If the probability is greater than 0.24, the prediction is a positive class (1), otherwise negative class (0)
##    6   12   14   19   23   24   26   29   33   34   37   38   40   42   43   44 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   46   47   48   50   56   69   70   74   78   80   85   86   87   89   90   91 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   92   93   95   99  102  104  110  111  115  117  118  119  120  123  124  130 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  138  140  141  146  148  157  158  160  166  167  168  169  174  176  177  189 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  190  197  199  202  205  211  212  214  219  220  225  226  228  233  235  239 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  240  241  247  248  254  266  268  280  283  285  289  292  293  301  310  312 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  313  320  322  332  337  347  349  356  357  358  360  363  376  377  378  387 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  388  389  392  395  396  397  399  404  406  409  411  412  416  419  425  430 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  431  439  440  441  443  446  449  450  452  463  465  468  471  475  476  477 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  478  480  483  487  488  493  494  497  499  501  503  507  508  510  514  515 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  516  519  521  524  530  531  533  540  544  545  550  554  556  557  565  566 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
##  571  573  576  579  580  582  585  591  592  593  594  595  596  598  611  622 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
##  626  627  629  635  642  648  650  654  658  661  662  667  670  673  676  679 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  681  687  696  698  699  702  709  717  722  725  726  728  731  732  734  736 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  738  746  747  749  753  757  758  759  760  763  765  766  768  770  771  775 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  776  778  787  791  794  802  803  806  809  811  813  814  815  823  824  833 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  835  837  841  844  846  848  853  857  861  865  868  869  876  877  878  879 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  880  886  888  889  895  900  902  907  909  921  924  928  934  935  937  941 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
##  944  945  951  952  953  955  962  965  968  971  973  975  977  980  983  989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  992  993  994  996  998 1011 1012 1013 1014 1018 1020 1022 1032 1034 1035 1036 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1038 1052 1061 1062 1064 1069 1072 1076 1077 1090 1092 1096 1097 1100 1113 1115 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1116 1117 1118 1121 1122 1124 1125 1127 1130 1131 1134 1136 1141 1144 1145 1148 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1150 1156 1159 1168 1172 1173 1174 1180 1182 1183 1187 1188 1189 1192 1197 1200 
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## 7384 7387 7394 7399 7400 7401 7404 7408 7414 7417 7418 7420 7422 7424 7430 7436 
##    0    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 7440 7442 7449 7451 7456 7473 7476 7482 7485 7489 7494 7495 7496 7498 7503 7504 
##    1    0    1    1    1    0    1    1    0    1    1    1    1    1    1    1 
## 7505 7507 7509 7512 7515 7525 7528 7532 7535 7539 7540 7543 7546 7552 7561 7563 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 7565 7573 7574 7578 7579 7582 7586 7589 7590 7591 7603 7606 7609 7611 7612 7630 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7631 7637 7640 7649 7658 7664 7665 7671 7673 7675 7682 7683 7687 7688 7689 7694 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 7695 7697 7698 7706 7713 7715 7721 7724 7732 7738 7739 7745 7749 7754 7755 7758 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7767 7768 7769 7771 7772 7773 7776 7784 7786 7790 7792 7793 7795 7798 7801 7822 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7830 7832 7836 7841 7845 7848 7862 7865 7870 7874 7884 7885 7887 7890 7891 7893 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 7894 7898 7899 7902 7908 7909 7911 7922 7923 7927 7928 7936 7938 7951 7954 7957 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7960 7961 7963 7966 7970 7971 7976 7982 7986 7988 7991 7992 7999 8001 8002 8004 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 8008 8010 8013 8017 8019 8020 8021 8022 8025 8033 8034 8035 8040 8043 8047 8056 
##    0    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 8059 8062 8063 8065 8067 8069 8075 8080 8096 8097 8102 8105 8106 8109 8111 8117 
##    1    1    1    1    1    1    1    1    1    0    1    1    0    1    1    1 
## 8119 8120 8123 8130 8132 8134 8136 8139 8142 8144 8145 8148 8150 8151 8154 8156 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8161 8162 8168 8170 8171 8175 8180 8184 8187 8188 8189 8192 8201 8204 8206 8207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8208 8210 8212 8219 8220 8228 8233 8239 8240 8243 8245 8249 8250 8251 8252 8253 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8254 8256 8257 8258 8267 8273 8274 8278 8282 8285 8286 8288 8289 8292 8295 8302 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8306 8314 8319 8320 8329 8337 8339 8340 8342 8345 8353 8354 8360 8362 8364 8366 
##    0    1    0    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 8367 8369 8378 8380 8381 8383 8386 8391 8396 8397 8398 8415 8417 8418 8424 8425 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8436 8437 8440 8446 8451 8453 8456 8460 8461 8462 8464 8465 8466 8474 8476 8478 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8483 8484 8498 8499 8504 8505 8506 8511 8515 8522 8524 8534 8545 8547 8556 8559 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8560 8561 8563 8565 8567 8573 8574 8575 8576 8581 8582 8585 8586 8589 8592 8595 
##    0    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8600 8602 8604 8605 8607 8609 8612 8617 8618 8619 8622 8625 8626 8627 8632 8647 
##    1    1    1    1    1    0    1    1    1    1    1    0    1    1    1    1 
## 8648 8649 8651 8653 8656 8659 8662 8669 8670 8674 8676 8678 8680 8682 8688 8695 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8696 8697 8699 8700 8705 8711 8713 8715 8725 8731 8733 8735 8740 8742 8745 8746 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8752 8754 8755 8762 8769 8777 8779 8783 8788 8789 8796 8797 8798 8810 8815 8816 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8823 8824 8834 8836 8838 8839 8840 8842 8844 8845 8849 8852 8853 8854 8868 8870 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8875 8877 8880 8887 8889 8890 8895 8902 8906 8907 8911 8916 8917 8918 8921 8922 
##    1    1    1    0    1    1    1    1    1    1    1    1    0    0    1    1 
## 8924 8925 8930 8942 8945 8953 8956 8958 8959 8962 8963 8968 8969 8972 8975 8980 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 8981 8982 8988 8990 8993 8996 9000 9007 9019 9023 9024 9027 9029 9030 9033 9035 
##    0    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 9037 9038 9040 9043 9047 9049 9054 9070 9072 9073 9085 9086 9089 9090 9092 9093 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 9096 9098 9102 9103 9105 9106 9111 9112 9113 9115 9116 9117 9122 9123 9126 9128 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 9132 9141 9143 9144 9150 9151 9152 9156 9159 9163 9164 9176 9183 9185 9186 9190 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9194 9197 9199 9207 9208 9211 9212 9215 9220 9221 9229 9231 9233 9235 9238 9242 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    0    1 
## 9245 9248 9253 9263 9268 9272 9275 9277 9281 9282 9286 9292 9294 9299 9302 9303 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 9306 9313 9316 9317 9320 9321 9327 9328 9331 9333 9337 9338 9343 9346 9350 9351 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9354 9356 9361 9364 9365 9367 9374 9378 9380 9381 9383 9385 9387 9389 9393 9395 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9398 9399 9401 9408 9409 9415 9416 9420 9421 9423 9424 9425 9426 9430 9431 9434 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 9437 9441 9442 9447 9455 9457 9459 9461 9473 9476 9480 9481 9482 9487 9490 9494 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9496 9497 9499 9503 9507 9510 9511 9516 9520 9521 9524 9526 9533 9535 9540 9541 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9547 
##    1
#25个0,975个1
view(pred_class1_2)  

#19个0,981个1
pred_class1_3 <- ifelse(predictions1[,3] > 0.6, 1, 0 )
pred_class1_3 #. If the probability is greater than 0.75, the prediction is a positive class (1), otherwise negative class (0)
##    6   12   14   19   23   24   26   29   33   34   37   38   40   42   43   44 
##    1    1    1    0    1    1    1    1    1    1    1    1    0    1    1    1 
##   46   47   48   50   56   69   70   74   78   80   85   86   87   89   90   91 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   92   93   95   99  102  104  110  111  115  117  118  119  120  123  124  130 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  138  140  141  146  148  157  158  160  166  167  168  169  174  176  177  189 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  190  197  199  202  205  211  212  214  219  220  225  226  228  233  235  239 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
##  240  241  247  248  254  266  268  280  283  285  289  292  293  301  310  312 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  313  320  322  332  337  347  349  356  357  358  360  363  376  377  378  387 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  388  389  392  395  396  397  399  404  406  409  411  412  416  419  425  430 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  431  439  440  441  443  446  449  450  452  463  465  468  471  475  476  477 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  478  480  483  487  488  493  494  497  499  501  503  507  508  510  514  515 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
##  516  519  521  524  530  531  533  540  544  545  550  554  556  557  565  566 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  571  573  576  579  580  582  585  591  592  593  594  595  596  598  611  622 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
##  626  627  629  635  642  648  650  654  658  661  662  667  670  673  676  679 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  681  687  696  698  699  702  709  717  722  725  726  728  731  732  734  736 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
##  738  746  747  749  753  757  758  759  760  763  765  766  768  770  771  775 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  776  778  787  791  794  802  803  806  809  811  813  814  815  823  824  833 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
##  835  837  841  844  846  848  853  857  861  865  868  869  876  877  878  879 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  880  886  888  889  895  900  902  907  909  921  924  928  934  935  937  941 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  944  945  951  952  953  955  962  965  968  971  973  975  977  980  983  989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  992  993  994  996  998 1011 1012 1013 1014 1018 1020 1022 1032 1034 1035 1036 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1038 1052 1061 1062 1064 1069 1072 1076 1077 1090 1092 1096 1097 1100 1113 1115 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1116 1117 1118 1121 1122 1124 1125 1127 1130 1131 1134 1136 1141 1144 1145 1148 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 1150 1156 1159 1168 1172 1173 1174 1180 1182 1183 1187 1188 1189 1192 1197 1200 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 1208 1210 1218 1220 1221 1229 1231 1237 1242 1244 1247 1250 1253 1254 1255 1257 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1262 1265 1266 1269 1273 1277 1279 1281 1282 1283 1287 1292 1293 1295 1302 1303 
##    1    1    1    1    1    1    1    1    1    1    1    0    0    1    1    1 
## 1305 1310 1311 1317 1320 1321 1326 1329 1332 1336 1343 1346 1348 1353 1355 1357 
##    1    1    1    0    1    0    1    1    0    1    1    1    1    1    1    1 
## 1359 1367 1369 1373 1374 1375 1377 1378 1379 1382 1383 1384 1387 1388 1390 1392 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1393 1395 1396 1398 1407 1416 1418 1422 1433 1438 1439 1443 1450 1451 1455 1460 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 1461 1463 1471 1473 1480 1484 1485 1486 1487 1490 1491 1493 1496 1499 1502 1503 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 1509 1510 1511 1515 1521 1523 1525 1527 1528 1530 1531 1534 1536 1537 1538 1539 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1541 1544 1547 1550 1554 1558 1559 1563 1568 1570 1576 1580 1585 1586 1591 1592 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1594 1595 1596 1601 1602 1615 1617 1621 1624 1626 1628 1633 1635 1638 1642 1644 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    0    1    1 
## 1645 1649 1650 1657 1659 1671 1680 1688 1691 1692 1704 1715 1719 1725 1727 1728 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1730 1732 1737 1740 1742 1749 1759 1763 1765 1769 1771 1772 1778 1779 1782 1785 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1788 1791 1798 1800 1801 1806 1810 1811 1813 1814 1816 1817 1818 1819 1822 1824 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1825 1826 1828 1830 1837 1846 1848 1851 1852 1856 1857 1858 1859 1861 1867 1871 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1875 1889 1890 1893 1894 1897 1898 1901 1902 1903 1908 1910 1911 1915 1917 1919 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1929 1930 1931 1933 1938 1945 1951 1954 1955 1958 1966 1975 1977 1978 1980 1983 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1985 1986 1990 1992 1997 2005 2010 2011 2019 2020 2030 2031 2039 2040 2042 2043 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2045 2048 2052 2053 2054 2061 2064 2066 2068 2071 2072 2073 2074 2079 2088 2089 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2091 2092 2093 2094 2097 2098 2102 2103 2105 2106 2114 2119 2123 2124 2128 2134 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2137 2141 2152 2155 2156 2159 2160 2161 2162 2164 2167 2168 2171 2174 2176 2179 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 2184 2188 2197 2205 2206 2207 2209 2212 2214 2218 2223 2227 2230 2234 2235 2237 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2238 2240 2246 2248 2250 2252 2256 2259 2260 2261 2263 2264 2270 2271 2274 2277 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 2283 2284 2297 2303 2307 2308 2309 2310 2319 2326 2328 2333 2335 2336 2342 2344 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2347 2352 2361 2371 2376 2379 2380 2388 2394 2397 2400 2402 2404 2408 2414 2415 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 2426 2427 2429 2431 2439 2441 2443 2446 2448 2452 2453 2454 2456 2471 2476 2481 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2485 2488 2489 2494 2495 2500 2501 2513 2515 2519 2525 2526 2529 2531 2532 2535 
##    1    0    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 2538 2540 2541 2543 2546 2549 2551 2556 2559 2560 2561 2563 2564 2566 2568 2569 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2570 2574 2575 2582 2587 2588 2595 2602 2604 2607 2613 2614 2622 2625 2626 2632 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2642 2654 2666 2667 2668 2671 2672 2676 2679 2680 2682 2685 2694 2696 2697 2699 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2701 2702 2704 2713 2714 2716 2720 2723 2725 2727 2730 2732 2733 2735 2736 2746 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2749 2755 2759 2763 2766 2771 2772 2781 2782 2791 2794 2796 2800 2802 2803 2805 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 2807 2811 2814 2816 2818 2819 2821 2822 2823 2827 2828 2829 2832 2837 2839 2843 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2844 2854 2856 2861 2862 2867 2869 2875 2878 2884 2886 2889 2891 2895 2896 2897 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2899 2900 2901 2902 2906 2915 2918 2922 2924 2927 2934 2937 2942 2953 2955 2956 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2957 2958 2964 2966 2967 2968 2975 2978 2988 2993 2995 2996 2999 3005 3006 3011 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 3013 3020 3022 3025 3026 3027 3029 3030 3034 3037 3042 3044 3046 3050 3051 3053 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3054 3057 3062 3065 3067 3068 3070 3071 3072 3074 3077 3081 3092 3093 3094 3095 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 3096 3097 3098 3100 3102 3107 3113 3115 3121 3122 3123 3130 3132 3133 3134 3136 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3138 3143 3145 3153 3157 3158 3160 3161 3163 3164 3166 3168 3173 3177 3179 3183 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3186 3188 3191 3194 3209 3210 3212 3217 3227 3228 3229 3232 3243 3246 3248 3250 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 3251 3258 3262 3264 3269 3274 3279 3286 3287 3289 3291 3292 3293 3305 3308 3324 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3326 3328 3330 3331 3333 3334 3336 3343 3347 3351 3356 3357 3361 3364 3370 3372 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3377 3379 3384 3394 3398 3403 3407 3413 3415 3417 3418 3422 3430 3434 3437 3438 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3442 3443 3456 3457 3465 3469 3470 3472 3475 3476 3477 3482 3489 3490 3492 3498 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 3499 3502 3505 3512 3518 3520 3524 3528 3534 3535 3537 3538 3539 3541 3542 3544 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 3546 3548 3549 3555 3561 3572 3573 3575 3578 3583 3588 3589 3591 3596 3597 3599 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3600 3601 3606 3611 3613 3615 3621 3633 3634 3636 3637 3638 3644 3647 3650 3655 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 3656 3657 3659 3660 3663 3676 3681 3689 3694 3695 3701 3704 3706 3708 3711 3714 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 3715 3718 3719 3725 3729 3736 3738 3741 3745 3757 3759 3764 3766 3778 3780 3781 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3789 3792 3793 3803 3807 3810 3811 3812 3816 3824 3840 3841 3843 3850 3856 3859 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3860 3866 3868 3869 3871 3873 3874 3877 3881 3883 3888 3891 3892 3893 3895 3896 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 3897 3898 3900 3904 3905 3914 3915 3917 3922 3929 3936 3943 3947 3954 3967 3970 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    0 
## 3972 3974 3977 3979 3981 3985 3986 3987 3989 3990 3992 3994 3997 4003 4004 4011 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4012 4013 4019 4020 4021 4026 4028 4030 4034 4037 4038 4039 4041 4043 4047 4051 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4054 4056 4057 4058 4059 4064 4068 4073 4074 4087 4092 4099 4100 4107 4111 4117 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4118 4124 4125 4127 4128 4129 4139 4140 4141 4142 4144 4145 4149 4154 4155 4156 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 4158 4161 4162 4164 4168 4169 4170 4171 4177 4180 4181 4189 4191 4196 4199 4201 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4206 4207 4209 4211 4221 4222 4223 4227 4231 4236 4242 4246 4252 4254 4262 4264 
##    1    0    1    1    1    1    1    1    0    1    1    1    0    1    1    1 
## 4270 4272 4273 4279 4284 4285 4286 4301 4305 4306 4310 4315 4317 4320 4322 4323 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4324 4329 4331 4332 4339 4345 4348 4350 4352 4354 4361 4363 4368 4369 4380 4381 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4384 4386 4396 4398 4400 4404 4406 4412 4413 4420 4424 4428 4431 4435 4441 4442 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4443 4444 4445 4450 4451 4452 4458 4460 4461 4462 4465 4468 4474 4478 4481 4487 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4493 4495 4496 4497 4498 4505 4506 4508 4511 4513 4517 4522 4523 4533 4540 4542 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4544 4549 4554 4555 4557 4560 4566 4569 4573 4582 4584 4586 4591 4595 4597 4600 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4606 4615 4624 4629 4630 4631 4633 4634 4636 4637 4641 4646 4652 4653 4654 4659 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4660 4661 4662 4667 4670 4672 4680 4686 4687 4689 4692 4693 4694 4703 4704 4707 
##    1    1    1    1    1    0    1    1    1    0    1    1    1    1    1    0 
## 4709 4711 4714 4718 4727 4731 4735 4740 4742 4743 4745 4746 4748 4752 4755 4764 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4768 4777 4780 4783 4786 4788 4791 4794 4795 4799 4802 4805 4810 4813 4814 4818 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 4820 4823 4827 4832 4839 4844 4845 4847 4851 4853 4858 4860 4862 4870 4871 4872 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 4874 4876 4880 4884 4888 4889 4894 4896 4899 4902 4904 4908 4914 4919 4920 4922 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4923 4926 4932 4935 4936 4940 4947 4951 4954 4955 4956 4959 4965 4967 4970 4973 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4974 4977 4978 4979 4980 4983 4984 4985 4988 4989 4994 4998 5007 5013 5014 5018 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5021 5034 5035 5036 5045 5048 5051 5052 5053 5054 5056 5057 5058 5059 5062 5064 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5069 5071 5074 5079 5080 5092 5095 5096 5100 5104 5109 5114 5116 5119 5123 5125 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5132 5134 5136 5140 5149 5150 5153 5155 5159 5161 5164 5171 5175 5181 5182 5184 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5186 5187 5191 5196 5198 5204 5205 5207 5208 5211 5212 5220 5226 5228 5234 5237 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5239 5241 5244 5245 5246 5253 5254 5262 5267 5268 5271 5272 5273 5274 5277 5282 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5286 5296 5299 5304 5305 5310 5311 5313 5319 5321 5324 5326 5327 5332 5333 5341 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5342 5350 5355 5357 5359 5360 5365 5366 5367 5374 5375 5377 5381 5388 5391 5394 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5399 5400 5401 5403 5406 5410 5414 5416 5418 5419 5420 5424 5426 5430 5432 5444 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    0 
## 5447 5451 5460 5467 5470 5474 5480 5485 5491 5492 5493 5494 5498 5499 5500 5504 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 5510 5511 5513 5514 5522 5523 5526 5530 5538 5539 5540 5541 5547 5550 5554 5557 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 5558 5559 5566 5568 5571 5573 5575 5577 5597 5598 5605 5607 5609 5615 5616 5617 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 5619 5621 5623 5625 5626 5631 5641 5642 5644 5645 5650 5653 5654 5659 5661 5663 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5667 5672 5676 5679 5682 5685 5686 5690 5691 5692 5695 5697 5703 5706 5709 5716 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 5718 5726 5729 5745 5753 5757 5759 5765 5767 5768 5770 5772 5773 5775 5778 5779 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5780 5782 5787 5790 5795 5796 5797 5798 5800 5802 5803 5804 5805 5808 5810 5820 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5824 5825 5829 5830 5839 5841 5842 5843 5846 5847 5853 5855 5860 5863 5865 5867 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5874 5880 5885 5888 5889 5890 5894 5896 5898 5902 5907 5909 5910 5914 5919 5921 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5924 5931 5935 5936 5940 5941 5942 5943 5948 5954 5959 5962 5963 5966 5969 5972 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5973 5974 5986 5987 5992 5996 5999 6000 6002 6005 6010 6011 6012 6014 6021 6030 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6031 6032 6042 6044 6048 6049 6051 6053 6056 6059 6060 6063 6067 6068 6070 6074 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6079 6084 6092 6094 6096 6097 6099 6102 6104 6106 6110 6112 6113 6114 6115 6117 
##    0    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 6130 6135 6136 6141 6146 6151 6153 6156 6157 6158 6160 6169 6171 6173 6178 6182 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 6190 6191 6193 6196 6198 6205 6206 6212 6214 6220 6221 6223 6225 6226 6227 6230 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 6231 6232 6234 6237 6238 6244 6248 6252 6254 6256 6266 6268 6272 6275 6277 6280 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6281 6284 6290 6293 6301 6306 6310 6321 6322 6323 6329 6334 6335 6338 6342 6357 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6358 6360 6361 6363 6366 6368 6371 6372 6375 6376 6377 6378 6384 6390 6393 6398 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6399 6401 6404 6405 6410 6413 6418 6420 6421 6422 6429 6433 6434 6436 6442 6448 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6449 6450 6456 6463 6473 6481 6484 6486 6487 6489 6503 6507 6508 6510 6530 6533 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 6535 6536 6538 6542 6547 6548 6549 6555 6557 6562 6570 6579 6580 6582 6584 6587 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6589 6594 6595 6596 6598 6605 6607 6608 6610 6620 6625 6626 6631 6632 6634 6637 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6640 6641 6645 6646 6651 6655 6658 6659 6661 6662 6665 6671 6673 6675 6677 6679 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6681 6682 6683 6686 6688 6696 6714 6715 6716 6717 6719 6720 6724 6725 6728 6729 
##    1    1    1    1    1    1    0    1    1    0    1    1    1    1    1    1 
## 6731 6735 6737 6738 6744 6747 6748 6752 6753 6754 6762 6765 6767 6768 6770 6776 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6782 6788 6793 6798 6800 6811 6814 6816 6822 6824 6831 6832 6835 6836 6838 6839 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6842 6843 6848 6850 6852 6853 6856 6857 6858 6859 6862 6867 6872 6873 6874 6884 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6885 6887 6889 6892 6893 6895 6900 6903 6904 6913 6915 6919 6923 6925 6929 6930 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6931 6933 6936 6938 6939 6942 6944 6948 6949 6951 6952 6954 6957 6968 6969 6970 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6974 6975 6976 6981 6987 6989 6990 6994 6999 7001 7006 7007 7009 7011 7012 7013 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7033 7037 7038 7041 7043 7044 7047 7049 7052 7054 7058 7061 7062 7063 7072 7077 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7079 7081 7084 7087 7088 7092 7093 7094 7096 7099 7100 7105 7106 7107 7115 7116 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 7125 7128 7135 7137 7141 7149 7150 7153 7154 7157 7160 7162 7164 7165 7166 7168 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 7169 7171 7174 7177 7180 7188 7197 7199 7203 7206 7207 7208 7209 7212 7215 7219 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7221 7222 7224 7227 7232 7233 7235 7238 7239 7248 7250 7251 7256 7257 7262 7264 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 7265 7271 7273 7275 7276 7277 7282 7287 7291 7292 7295 7297 7301 7303 7308 7309 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7311 7312 7317 7318 7323 7329 7330 7331 7332 7333 7334 7335 7336 7338 7339 7340 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7344 7347 7350 7351 7354 7356 7358 7360 7361 7362 7368 7369 7375 7379 7381 7382 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 7384 7387 7394 7399 7400 7401 7404 7408 7414 7417 7418 7420 7422 7424 7430 7436 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7440 7442 7449 7451 7456 7473 7476 7482 7485 7489 7494 7495 7496 7498 7503 7504 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 7505 7507 7509 7512 7515 7525 7528 7532 7535 7539 7540 7543 7546 7552 7561 7563 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7565 7573 7574 7578 7579 7582 7586 7589 7590 7591 7603 7606 7609 7611 7612 7630 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7631 7637 7640 7649 7658 7664 7665 7671 7673 7675 7682 7683 7687 7688 7689 7694 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7695 7697 7698 7706 7713 7715 7721 7724 7732 7738 7739 7745 7749 7754 7755 7758 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7767 7768 7769 7771 7772 7773 7776 7784 7786 7790 7792 7793 7795 7798 7801 7822 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7830 7832 7836 7841 7845 7848 7862 7865 7870 7874 7884 7885 7887 7890 7891 7893 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 7894 7898 7899 7902 7908 7909 7911 7922 7923 7927 7928 7936 7938 7951 7954 7957 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 7960 7961 7963 7966 7970 7971 7976 7982 7986 7988 7991 7992 7999 8001 8002 8004 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8008 8010 8013 8017 8019 8020 8021 8022 8025 8033 8034 8035 8040 8043 8047 8056 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8059 8062 8063 8065 8067 8069 8075 8080 8096 8097 8102 8105 8106 8109 8111 8117 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8119 8120 8123 8130 8132 8134 8136 8139 8142 8144 8145 8148 8150 8151 8154 8156 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8161 8162 8168 8170 8171 8175 8180 8184 8187 8188 8189 8192 8201 8204 8206 8207 
##    0    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 8208 8210 8212 8219 8220 8228 8233 8239 8240 8243 8245 8249 8250 8251 8252 8253 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8254 8256 8257 8258 8267 8273 8274 8278 8282 8285 8286 8288 8289 8292 8295 8302 
##    1    1    1    1    1    1    0    1    1    1    0    1    1    1    1    1 
## 8306 8314 8319 8320 8329 8337 8339 8340 8342 8345 8353 8354 8360 8362 8364 8366 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8367 8369 8378 8380 8381 8383 8386 8391 8396 8397 8398 8415 8417 8418 8424 8425 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8436 8437 8440 8446 8451 8453 8456 8460 8461 8462 8464 8465 8466 8474 8476 8478 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8483 8484 8498 8499 8504 8505 8506 8511 8515 8522 8524 8534 8545 8547 8556 8559 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8560 8561 8563 8565 8567 8573 8574 8575 8576 8581 8582 8585 8586 8589 8592 8595 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8600 8602 8604 8605 8607 8609 8612 8617 8618 8619 8622 8625 8626 8627 8632 8647 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8648 8649 8651 8653 8656 8659 8662 8669 8670 8674 8676 8678 8680 8682 8688 8695 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8696 8697 8699 8700 8705 8711 8713 8715 8725 8731 8733 8735 8740 8742 8745 8746 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8752 8754 8755 8762 8769 8777 8779 8783 8788 8789 8796 8797 8798 8810 8815 8816 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    0    1 
## 8823 8824 8834 8836 8838 8839 8840 8842 8844 8845 8849 8852 8853 8854 8868 8870 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8875 8877 8880 8887 8889 8890 8895 8902 8906 8907 8911 8916 8917 8918 8921 8922 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8924 8925 8930 8942 8945 8953 8956 8958 8959 8962 8963 8968 8969 8972 8975 8980 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8981 8982 8988 8990 8993 8996 9000 9007 9019 9023 9024 9027 9029 9030 9033 9035 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9037 9038 9040 9043 9047 9049 9054 9070 9072 9073 9085 9086 9089 9090 9092 9093 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9096 9098 9102 9103 9105 9106 9111 9112 9113 9115 9116 9117 9122 9123 9126 9128 
##    1    0    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 9132 9141 9143 9144 9150 9151 9152 9156 9159 9163 9164 9176 9183 9185 9186 9190 
##    1    1    0    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 9194 9197 9199 9207 9208 9211 9212 9215 9220 9221 9229 9231 9233 9235 9238 9242 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9245 9248 9253 9263 9268 9272 9275 9277 9281 9282 9286 9292 9294 9299 9302 9303 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 9306 9313 9316 9317 9320 9321 9327 9328 9331 9333 9337 9338 9343 9346 9350 9351 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 9354 9356 9361 9364 9365 9367 9374 9378 9380 9381 9383 9385 9387 9389 9393 9395 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9398 9399 9401 9408 9409 9415 9416 9420 9421 9423 9424 9425 9426 9430 9431 9434 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 9437 9441 9442 9447 9455 9457 9459 9461 9473 9476 9480 9481 9482 9487 9490 9494 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 9496 9497 9499 9503 9507 9510 9511 9516 9520 9521 9524 9526 9533 9535 9540 9541 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 9547 
##    1
view(pred_class1_3)  #0.5时全是1

pred_class1 <- cbind(pred_class1_1, pred_class1_2,pred_class1_3)
pred_class1
##      pred_class1_1 pred_class1_2 pred_class1_3
## 6                1             1             1
## 12               1             1             1
## 14               1             1             1
## 19               1             1             0
## 23               1             1             1
## 24               0             1             1
## 26               0             1             1
## 29               1             1             1
## 33               1             1             1
## 34               0             1             1
## 37               1             1             1
## 38               1             1             1
## 40               0             1             0
## 42               1             1             1
## 43               1             1             1
## 44               1             1             1
## 46               1             1             1
## 47               1             1             1
## 48               1             1             1
## 50               1             1             1
## 56               1             1             1
## 69               1             1             1
## 70               1             1             1
## 74               1             1             1
## 78               1             1             1
## 80               1             1             1
## 85               1             1             1
## 86               1             1             1
## 87               1             1             1
## 89               1             1             1
## 90               1             1             1
## 91               1             1             1
## 92               1             1             1
## 93               0             1             1
## 95               0             1             1
## 99               1             1             1
## 102              0             1             1
## 104              0             1             1
## 110              1             1             1
## 111              0             1             1
## 115              1             1             1
## 117              1             1             1
## 118              1             1             0
## 119              1             1             1
## 120              1             1             1
## 123              0             1             1
## 124              0             1             1
## 130              1             1             1
## 138              1             1             0
## 140              1             1             1
## 141              1             1             1
## 146              0             1             1
## 148              1             1             1
## 157              1             1             1
## 158              1             1             1
## 160              1             1             1
## 166              1             1             1
## 167              1             1             1
## 168              1             1             1
## 169              1             1             1
## 174              0             0             1
## 176              0             1             1
## 177              1             1             1
## 189              1             1             1
## 190              1             1             1
## 197              1             1             1
## 199              0             1             1
## 202              1             1             1
## 205              1             1             1
## 211              1             1             1
## 212              1             1             1
## 214              1             1             1
## 219              1             1             1
## 220              1             1             1
## 225              1             1             1
## 226              1             1             1
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## 9496             1             1             1
## 9497             1             1             1
## 9499             1             1             1
## 9503             1             1             1
## 9507             0             1             1
## 9510             1             1             1
## 9511             1             1             1
## 9516             1             1             1
## 9520             1             1             1
## 9521             1             1             1
## 9524             1             1             1
## 9526             1             1             0
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## 9540             1             1             1
## 9541             1             1             1
## 9547             1             1             1
view(pred_class1)


#repeat
#OL best model of train data
# Convert the probability value into a category
pred_class2_1 <- ifelse(predictions2[,1] > 0.0044, 1, 0 )
pred_class2_1 #. If the probability is greater than 0.01, the prediction is a positive class (1), otherwise negative class (0)
##    6   12   14   19   23   24   26   29   33   34   37   38   40   42   43   44 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   46   47   48   50   56   69   70   74   78   80   85   86   87   89   90   91 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   92   93   95   99  102  104  110  111  115  117  118  119  120  123  124  130 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  138  140  141  146  148  157  158  160  166  167  168  169  174  176  177  189 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  190  197  199  202  205  211  212  214  219  220  225  226  228  233  235  239 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
##  240  241  247  248  254  266  268  280  283  285  289  292  293  301  310  312 
##    1    1    1    0    1    1    1    1    1    1    0    1    1    1    1    1 
##  313  320  322  332  337  347  349  356  357  358  360  363  376  377  378  387 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  388  389  392  395  396  397  399  404  406  409  411  412  416  419  425  430 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  431  439  440  441  443  446  449  450  452  463  465  468  471  475  476  477 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  478  480  483  487  488  493  494  497  499  501  503  507  508  510  514  515 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  516  519  521  524  530  531  533  540  544  545  550  554  556  557  565  566 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
##  571  573  576  579  580  582  585  591  592  593  594  595  596  598  611  622 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
##  626  627  629  635  642  648  650  654  658  661  662  667  670  673  676  679 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  681  687  696  698  699  702  709  717  722  725  726  728  731  732  734  736 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  738  746  747  749  753  757  758  759  760  763  765  766  768  770  771  775 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  776  778  787  791  794  802  803  806  809  811  813  814  815  823  824  833 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  835  837  841  844  846  848  853  857  861  865  868  869  876  877  878  879 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  880  886  888  889  895  900  902  907  909  921  924  928  934  935  937  941 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
##  944  945  951  952  953  955  962  965  968  971  973  975  977  980  983  989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  992  993  994  996  998 1011 1012 1013 1014 1018 1020 1022 1032 1034 1035 1036 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1038 1052 1061 1062 1064 1069 1072 1076 1077 1090 1092 1096 1097 1100 1113 1115 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1116 1117 1118 1121 1122 1124 1125 1127 1130 1131 1134 1136 1141 1144 1145 1148 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1150 1156 1159 1168 1172 1173 1174 1180 1182 1183 1187 1188 1189 1192 1197 1200 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 1208 1210 1218 1220 1221 1229 1231 1237 1242 1244 1247 1250 1253 1254 1255 1257 
##    1    1    1    1    1    1    1    1    0    0    1    1    1    1    1    1 
## 1262 1265 1266 1269 1273 1277 1279 1281 1282 1283 1287 1292 1293 1295 1302 1303 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1305 1310 1311 1317 1320 1321 1326 1329 1332 1336 1343 1346 1348 1353 1355 1357 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1359 1367 1369 1373 1374 1375 1377 1378 1379 1382 1383 1384 1387 1388 1390 1392 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1393 1395 1396 1398 1407 1416 1418 1422 1433 1438 1439 1443 1450 1451 1455 1460 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9547 
##    1
view(pred_class2_1)
#39个0,961个1
pred_class2_1
##    6   12   14   19   23   24   26   29   33   34   37   38   40   42   43   44 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  190  197  199  202  205  211  212  214  219  220  225  226  228  233  235  239 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
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##    1    1    1    0    1    1    1    1    1    1    0    1    1    1    1    1 
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##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  388  389  392  395  396  397  399  404  406  409  411  412  416  419  425  430 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##  738  746  747  749  753  757  758  759  760  763  765  766  768  770  771  775 
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##  776  778  787  791  794  802  803  806  809  811  813  814  815  823  824  833 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  835  837  841  844  846  848  853  857  861  865  868  869  876  877  878  879 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
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##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    0    1    1    1    1    0    1    1    1    1    0    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2137 2141 2152 2155 2156 2159 2160 2161 2162 2164 2167 2168 2171 2174 2176 2179 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    0    1 
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##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
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##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    0    1 
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##    1    1    1    1    0    1    0    1    1    0    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
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##    1    0    1    1    1    1    1    1    1    1    1    1    1    0    0    0 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    0    1    1    0    1    1    1    1    0    1    1    0    1    0 
## 5667 5672 5676 5679 5682 5685 5686 5690 5691 5692 5695 5697 5703 5706 5709 5716 
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##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 5874 5880 5885 5888 5889 5890 5894 5896 5898 5902 5907 5909 5910 5914 5919 5921 
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## 5924 5931 5935 5936 5940 5941 5942 5943 5948 5954 5959 5962 5963 5966 5969 5972 
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## 5973 5974 5986 5987 5992 5996 5999 6000 6002 6005 6010 6011 6012 6014 6021 6030 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 6031 6032 6042 6044 6048 6049 6051 6053 6056 6059 6060 6063 6067 6068 6070 6074 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6079 6084 6092 6094 6096 6097 6099 6102 6104 6106 6110 6112 6113 6114 6115 6117 
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##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 6190 6191 6193 6196 6198 6205 6206 6212 6214 6220 6221 6223 6225 6226 6227 6230 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6231 6232 6234 6237 6238 6244 6248 6252 6254 6256 6266 6268 6272 6275 6277 6280 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6281 6284 6290 6293 6301 6306 6310 6321 6322 6323 6329 6334 6335 6338 6342 6357 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6358 6360 6361 6363 6366 6368 6371 6372 6375 6376 6377 6378 6384 6390 6393 6398 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 6399 6401 6404 6405 6410 6413 6418 6420 6421 6422 6429 6433 6434 6436 6442 6448 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6449 6450 6456 6463 6473 6481 6484 6486 6487 6489 6503 6507 6508 6510 6530 6533 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6535 6536 6538 6542 6547 6548 6549 6555 6557 6562 6570 6579 6580 6582 6584 6587 
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## 6589 6594 6595 6596 6598 6605 6607 6608 6610 6620 6625 6626 6631 6632 6634 6637 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6640 6641 6645 6646 6651 6655 6658 6659 6661 6662 6665 6671 6673 6675 6677 6679 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6681 6682 6683 6686 6688 6696 6714 6715 6716 6717 6719 6720 6724 6725 6728 6729 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6731 6735 6737 6738 6744 6747 6748 6752 6753 6754 6762 6765 6767 6768 6770 6776 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 6782 6788 6793 6798 6800 6811 6814 6816 6822 6824 6831 6832 6835 6836 6838 6839 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6842 6843 6848 6850 6852 6853 6856 6857 6858 6859 6862 6867 6872 6873 6874 6884 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 6885 6887 6889 6892 6893 6895 6900 6903 6904 6913 6915 6919 6923 6925 6929 6930 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6931 6933 6936 6938 6939 6942 6944 6948 6949 6951 6952 6954 6957 6968 6969 6970 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6974 6975 6976 6981 6987 6989 6990 6994 6999 7001 7006 7007 7009 7011 7012 7013 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7033 7037 7038 7041 7043 7044 7047 7049 7052 7054 7058 7061 7062 7063 7072 7077 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7079 7081 7084 7087 7088 7092 7093 7094 7096 7099 7100 7105 7106 7107 7115 7116 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 7125 7128 7135 7137 7141 7149 7150 7153 7154 7157 7160 7162 7164 7165 7166 7168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7169 7171 7174 7177 7180 7188 7197 7199 7203 7206 7207 7208 7209 7212 7215 7219 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7221 7222 7224 7227 7232 7233 7235 7238 7239 7248 7250 7251 7256 7257 7262 7264 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7265 7271 7273 7275 7276 7277 7282 7287 7291 7292 7295 7297 7301 7303 7308 7309 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7311 7312 7317 7318 7323 7329 7330 7331 7332 7333 7334 7335 7336 7338 7339 7340 
##    1    1    1    1    1    1    0    1    1    1    1    0    1    1    1    1 
## 7344 7347 7350 7351 7354 7356 7358 7360 7361 7362 7368 7369 7375 7379 7381 7382 
##    1    1    0    0    1    1    1    1    1    1    1    1    1    1    1    0 
## 7384 7387 7394 7399 7400 7401 7404 7408 7414 7417 7418 7420 7422 7424 7430 7436 
##    0    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 7440 7442 7449 7451 7456 7473 7476 7482 7485 7489 7494 7495 7496 7498 7503 7504 
##    1    0    1    1    1    0    1    1    0    1    1    1    1    1    1    1 
## 7505 7507 7509 7512 7515 7525 7528 7532 7535 7539 7540 7543 7546 7552 7561 7563 
##    1    1    0    1    1    1    0    1    1    1    1    1    1    1    0    1 
## 7565 7573 7574 7578 7579 7582 7586 7589 7590 7591 7603 7606 7609 7611 7612 7630 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 7631 7637 7640 7649 7658 7664 7665 7671 7673 7675 7682 7683 7687 7688 7689 7694 
##    1    1    1    1    1    1    1    0    1    1    1    0    1    1    1    1 
## 7695 7697 7698 7706 7713 7715 7721 7724 7732 7738 7739 7745 7749 7754 7755 7758 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7767 7768 7769 7771 7772 7773 7776 7784 7786 7790 7792 7793 7795 7798 7801 7822 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7830 7832 7836 7841 7845 7848 7862 7865 7870 7874 7884 7885 7887 7890 7891 7893 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 7894 7898 7899 7902 7908 7909 7911 7922 7923 7927 7928 7936 7938 7951 7954 7957 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7960 7961 7963 7966 7970 7971 7976 7982 7986 7988 7991 7992 7999 8001 8002 8004 
##    1    1    1    1    1    1    1    1    1    0    1    0    1    1    1    1 
## 8008 8010 8013 8017 8019 8020 8021 8022 8025 8033 8034 8035 8040 8043 8047 8056 
##    0    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 8059 8062 8063 8065 8067 8069 8075 8080 8096 8097 8102 8105 8106 8109 8111 8117 
##    1    1    1    1    1    1    1    1    1    0    1    1    0    0    1    1 
## 8119 8120 8123 8130 8132 8134 8136 8139 8142 8144 8145 8148 8150 8151 8154 8156 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8161 8162 8168 8170 8171 8175 8180 8184 8187 8188 8189 8192 8201 8204 8206 8207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8208 8210 8212 8219 8220 8228 8233 8239 8240 8243 8245 8249 8250 8251 8252 8253 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8254 8256 8257 8258 8267 8273 8274 8278 8282 8285 8286 8288 8289 8292 8295 8302 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8306 8314 8319 8320 8329 8337 8339 8340 8342 8345 8353 8354 8360 8362 8364 8366 
##    0    1    0    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 8367 8369 8378 8380 8381 8383 8386 8391 8396 8397 8398 8415 8417 8418 8424 8425 
##    1    1    0    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 8436 8437 8440 8446 8451 8453 8456 8460 8461 8462 8464 8465 8466 8474 8476 8478 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    0    1    1 
## 8483 8484 8498 8499 8504 8505 8506 8511 8515 8522 8524 8534 8545 8547 8556 8559 
##    1    0    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 8560 8561 8563 8565 8567 8573 8574 8575 8576 8581 8582 8585 8586 8589 8592 8595 
##    0    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8600 8602 8604 8605 8607 8609 8612 8617 8618 8619 8622 8625 8626 8627 8632 8647 
##    1    1    1    1    1    0    1    1    1    1    1    0    1    1    1    0 
## 8648 8649 8651 8653 8656 8659 8662 8669 8670 8674 8676 8678 8680 8682 8688 8695 
##    1    1    1    1    1    1    1    1    0    0    1    1    1    1    1    1 
## 8696 8697 8699 8700 8705 8711 8713 8715 8725 8731 8733 8735 8740 8742 8745 8746 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8752 8754 8755 8762 8769 8777 8779 8783 8788 8789 8796 8797 8798 8810 8815 8816 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8823 8824 8834 8836 8838 8839 8840 8842 8844 8845 8849 8852 8853 8854 8868 8870 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8875 8877 8880 8887 8889 8890 8895 8902 8906 8907 8911 8916 8917 8918 8921 8922 
##    1    1    1    0    1    1    1    1    1    1    1    1    0    0    1    1 
## 8924 8925 8930 8942 8945 8953 8956 8958 8959 8962 8963 8968 8969 8972 8975 8980 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 8981 8982 8988 8990 8993 8996 9000 9007 9019 9023 9024 9027 9029 9030 9033 9035 
##    0    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 9037 9038 9040 9043 9047 9049 9054 9070 9072 9073 9085 9086 9089 9090 9092 9093 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 9096 9098 9102 9103 9105 9106 9111 9112 9113 9115 9116 9117 9122 9123 9126 9128 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 9132 9141 9143 9144 9150 9151 9152 9156 9159 9163 9164 9176 9183 9185 9186 9190 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 9194 9197 9199 9207 9208 9211 9212 9215 9220 9221 9229 9231 9233 9235 9238 9242 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 9245 9248 9253 9263 9268 9272 9275 9277 9281 9282 9286 9292 9294 9299 9302 9303 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9306 9313 9316 9317 9320 9321 9327 9328 9331 9333 9337 9338 9343 9346 9350 9351 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9354 9356 9361 9364 9365 9367 9374 9378 9380 9381 9383 9385 9387 9389 9393 9395 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9398 9399 9401 9408 9409 9415 9416 9420 9421 9423 9424 9425 9426 9430 9431 9434 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 9437 9441 9442 9447 9455 9457 9459 9461 9473 9476 9480 9481 9482 9487 9490 9494 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9496 9497 9499 9503 9507 9510 9511 9516 9520 9521 9524 9526 9533 9535 9540 9541 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9547 
##    1
pred_class2_2 <- ifelse(predictions2[,2] > 0.1126, 1, 0 )
pred_class2_2 #. If the probability is greater than 0.24, the prediction is a positive class (1), otherwise negative class (0)
##    6   12   14   19   23   24   26   29   33   34   37   38   40   42   43   44 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   46   47   48   50   56   69   70   74   78   80   85   86   87   89   90   91 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   92   93   95   99  102  104  110  111  115  117  118  119  120  123  124  130 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  138  140  141  146  148  157  158  160  166  167  168  169  174  176  177  189 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  190  197  199  202  205  211  212  214  219  220  225  226  228  233  235  239 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  240  241  247  248  254  266  268  280  283  285  289  292  293  301  310  312 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  313  320  322  332  337  347  349  356  357  358  360  363  376  377  378  387 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  388  389  392  395  396  397  399  404  406  409  411  412  416  419  425  430 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  431  439  440  441  443  446  449  450  452  463  465  468  471  475  476  477 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  478  480  483  487  488  493  494  497  499  501  503  507  508  510  514  515 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  516  519  521  524  530  531  533  540  544  545  550  554  556  557  565  566 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
##  571  573  576  579  580  582  585  591  592  593  594  595  596  598  611  622 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
##  626  627  629  635  642  648  650  654  658  661  662  667  670  673  676  679 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  681  687  696  698  699  702  709  717  722  725  726  728  731  732  734  736 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  738  746  747  749  753  757  758  759  760  763  765  766  768  770  771  775 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  776  778  787  791  794  802  803  806  809  811  813  814  815  823  824  833 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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## 7079 7081 7084 7087 7088 7092 7093 7094 7096 7099 7100 7105 7106 7107 7115 7116 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 7125 7128 7135 7137 7141 7149 7150 7153 7154 7157 7160 7162 7164 7165 7166 7168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7169 7171 7174 7177 7180 7188 7197 7199 7203 7206 7207 7208 7209 7212 7215 7219 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7221 7222 7224 7227 7232 7233 7235 7238 7239 7248 7250 7251 7256 7257 7262 7264 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7265 7271 7273 7275 7276 7277 7282 7287 7291 7292 7295 7297 7301 7303 7308 7309 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7311 7312 7317 7318 7323 7329 7330 7331 7332 7333 7334 7335 7336 7338 7339 7340 
##    1    1    1    1    1    1    0    1    1    1    1    0    1    1    1    1 
## 7344 7347 7350 7351 7354 7356 7358 7360 7361 7362 7368 7369 7375 7379 7381 7382 
##    1    1    0    0    1    1    1    1    1    1    1    1    1    1    1    0 
## 7384 7387 7394 7399 7400 7401 7404 7408 7414 7417 7418 7420 7422 7424 7430 7436 
##    0    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 7440 7442 7449 7451 7456 7473 7476 7482 7485 7489 7494 7495 7496 7498 7503 7504 
##    1    0    1    1    1    0    1    1    0    1    1    1    1    1    1    1 
## 7505 7507 7509 7512 7515 7525 7528 7532 7535 7539 7540 7543 7546 7552 7561 7563 
##    1    1    0    1    1    1    0    1    1    1    1    1    1    1    0    1 
## 7565 7573 7574 7578 7579 7582 7586 7589 7590 7591 7603 7606 7609 7611 7612 7630 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 7631 7637 7640 7649 7658 7664 7665 7671 7673 7675 7682 7683 7687 7688 7689 7694 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 7695 7697 7698 7706 7713 7715 7721 7724 7732 7738 7739 7745 7749 7754 7755 7758 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7767 7768 7769 7771 7772 7773 7776 7784 7786 7790 7792 7793 7795 7798 7801 7822 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7830 7832 7836 7841 7845 7848 7862 7865 7870 7874 7884 7885 7887 7890 7891 7893 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 7894 7898 7899 7902 7908 7909 7911 7922 7923 7927 7928 7936 7938 7951 7954 7957 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7960 7961 7963 7966 7970 7971 7976 7982 7986 7988 7991 7992 7999 8001 8002 8004 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 8008 8010 8013 8017 8019 8020 8021 8022 8025 8033 8034 8035 8040 8043 8047 8056 
##    0    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 8059 8062 8063 8065 8067 8069 8075 8080 8096 8097 8102 8105 8106 8109 8111 8117 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    0    1    1 
## 8119 8120 8123 8130 8132 8134 8136 8139 8142 8144 8145 8148 8150 8151 8154 8156 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8161 8162 8168 8170 8171 8175 8180 8184 8187 8188 8189 8192 8201 8204 8206 8207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8208 8210 8212 8219 8220 8228 8233 8239 8240 8243 8245 8249 8250 8251 8252 8253 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8254 8256 8257 8258 8267 8273 8274 8278 8282 8285 8286 8288 8289 8292 8295 8302 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8306 8314 8319 8320 8329 8337 8339 8340 8342 8345 8353 8354 8360 8362 8364 8366 
##    0    1    0    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 8367 8369 8378 8380 8381 8383 8386 8391 8396 8397 8398 8415 8417 8418 8424 8425 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8436 8437 8440 8446 8451 8453 8456 8460 8461 8462 8464 8465 8466 8474 8476 8478 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 8483 8484 8498 8499 8504 8505 8506 8511 8515 8522 8524 8534 8545 8547 8556 8559 
##    1    0    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 8560 8561 8563 8565 8567 8573 8574 8575 8576 8581 8582 8585 8586 8589 8592 8595 
##    0    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8600 8602 8604 8605 8607 8609 8612 8617 8618 8619 8622 8625 8626 8627 8632 8647 
##    1    1    1    1    1    0    1    1    1    1    1    0    1    1    1    1 
## 8648 8649 8651 8653 8656 8659 8662 8669 8670 8674 8676 8678 8680 8682 8688 8695 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8696 8697 8699 8700 8705 8711 8713 8715 8725 8731 8733 8735 8740 8742 8745 8746 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8752 8754 8755 8762 8769 8777 8779 8783 8788 8789 8796 8797 8798 8810 8815 8816 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8823 8824 8834 8836 8838 8839 8840 8842 8844 8845 8849 8852 8853 8854 8868 8870 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8875 8877 8880 8887 8889 8890 8895 8902 8906 8907 8911 8916 8917 8918 8921 8922 
##    1    1    1    0    1    1    1    1    1    1    1    1    0    0    1    1 
## 8924 8925 8930 8942 8945 8953 8956 8958 8959 8962 8963 8968 8969 8972 8975 8980 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 8981 8982 8988 8990 8993 8996 9000 9007 9019 9023 9024 9027 9029 9030 9033 9035 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 9037 9038 9040 9043 9047 9049 9054 9070 9072 9073 9085 9086 9089 9090 9092 9093 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9096 9098 9102 9103 9105 9106 9111 9112 9113 9115 9116 9117 9122 9123 9126 9128 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 9132 9141 9143 9144 9150 9151 9152 9156 9159 9163 9164 9176 9183 9185 9186 9190 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9194 9197 9199 9207 9208 9211 9212 9215 9220 9221 9229 9231 9233 9235 9238 9242 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 9245 9248 9253 9263 9268 9272 9275 9277 9281 9282 9286 9292 9294 9299 9302 9303 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 9306 9313 9316 9317 9320 9321 9327 9328 9331 9333 9337 9338 9343 9346 9350 9351 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9354 9356 9361 9364 9365 9367 9374 9378 9380 9381 9383 9385 9387 9389 9393 9395 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9398 9399 9401 9408 9409 9415 9416 9420 9421 9423 9424 9425 9426 9430 9431 9434 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 9437 9441 9442 9447 9455 9457 9459 9461 9473 9476 9480 9481 9482 9487 9490 9494 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9496 9497 9499 9503 9507 9510 9511 9516 9520 9521 9524 9526 9533 9535 9540 9541 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9547 
##    1
#34个0,966个1
view(pred_class2_2)

pred_class2_3 <- ifelse(predictions2[,3] > 0.6, 1, 0 )
pred_class2_3 #. If the probability is greater than 0.75, the prediction is a positive class (1), otherwise negative class (0)
##    6   12   14   19   23   24   26   29   33   34   37   38   40   42   43   44 
##    1    1    1    0    1    1    1    1    1    1    1    1    0    1    1    1 
##   46   47   48   50   56   69   70   74   78   80   85   86   87   89   90   91 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   92   93   95   99  102  104  110  111  115  117  118  119  120  123  124  130 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  138  140  141  146  148  157  158  160  166  167  168  169  174  176  177  189 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  190  197  199  202  205  211  212  214  219  220  225  226  228  233  235  239 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  240  241  247  248  254  266  268  280  283  285  289  292  293  301  310  312 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  313  320  322  332  337  347  349  356  357  358  360  363  376  377  378  387 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  388  389  392  395  396  397  399  404  406  409  411  412  416  419  425  430 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  431  439  440  441  443  446  449  450  452  463  465  468  471  475  476  477 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  478  480  483  487  488  493  494  497  499  501  503  507  508  510  514  515 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
##  516  519  521  524  530  531  533  540  544  545  550  554  556  557  565  566 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  571  573  576  579  580  582  585  591  592  593  594  595  596  598  611  622 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
##  626  627  629  635  642  648  650  654  658  661  662  667  670  673  676  679 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  681  687  696  698  699  702  709  717  722  725  726  728  731  732  734  736 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
##  738  746  747  749  753  757  758  759  760  763  765  766  768  770  771  775 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  776  778  787  791  794  802  803  806  809  811  813  814  815  823  824  833 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
##  835  837  841  844  846  848  853  857  861  865  868  869  876  877  878  879 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  880  886  888  889  895  900  902  907  909  921  924  928  934  935  937  941 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  944  945  951  952  953  955  962  965  968  971  973  975  977  980  983  989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  992  993  994  996  998 1011 1012 1013 1014 1018 1020 1022 1032 1034 1035 1036 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1038 1052 1061 1062 1064 1069 1072 1076 1077 1090 1092 1096 1097 1100 1113 1115 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1116 1117 1118 1121 1122 1124 1125 1127 1130 1131 1134 1136 1141 1144 1145 1148 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 1150 1156 1159 1168 1172 1173 1174 1180 1182 1183 1187 1188 1189 1192 1197 1200 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 1208 1210 1218 1220 1221 1229 1231 1237 1242 1244 1247 1250 1253 1254 1255 1257 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1262 1265 1266 1269 1273 1277 1279 1281 1282 1283 1287 1292 1293 1295 1302 1303 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 1305 1310 1311 1317 1320 1321 1326 1329 1332 1336 1343 1346 1348 1353 1355 1357 
##    1    1    1    0    1    0    1    1    0    1    1    1    1    1    1    1 
## 1359 1367 1369 1373 1374 1375 1377 1378 1379 1382 1383 1384 1387 1388 1390 1392 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1393 1395 1396 1398 1407 1416 1418 1422 1433 1438 1439 1443 1450 1451 1455 1460 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1461 1463 1471 1473 1480 1484 1485 1486 1487 1490 1491 1493 1496 1499 1502 1503 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 1509 1510 1511 1515 1521 1523 1525 1527 1528 1530 1531 1534 1536 1537 1538 1539 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 1541 1544 1547 1550 1554 1558 1559 1563 1568 1570 1576 1580 1585 1586 1591 1592 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 1594 1595 1596 1601 1602 1615 1617 1621 1624 1626 1628 1633 1635 1638 1642 1644 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    0    1    1 
## 1645 1649 1650 1657 1659 1671 1680 1688 1691 1692 1704 1715 1719 1725 1727 1728 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1730 1732 1737 1740 1742 1749 1759 1763 1765 1769 1771 1772 1778 1779 1782 1785 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1788 1791 1798 1800 1801 1806 1810 1811 1813 1814 1816 1817 1818 1819 1822 1824 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1825 1826 1828 1830 1837 1846 1848 1851 1852 1856 1857 1858 1859 1861 1867 1871 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1875 1889 1890 1893 1894 1897 1898 1901 1902 1903 1908 1910 1911 1915 1917 1919 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1929 1930 1931 1933 1938 1945 1951 1954 1955 1958 1966 1975 1977 1978 1980 1983 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 1985 1986 1990 1992 1997 2005 2010 2011 2019 2020 2030 2031 2039 2040 2042 2043 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2045 2048 2052 2053 2054 2061 2064 2066 2068 2071 2072 2073 2074 2079 2088 2089 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2091 2092 2093 2094 2097 2098 2102 2103 2105 2106 2114 2119 2123 2124 2128 2134 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2137 2141 2152 2155 2156 2159 2160 2161 2162 2164 2167 2168 2171 2174 2176 2179 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 2184 2188 2197 2205 2206 2207 2209 2212 2214 2218 2223 2227 2230 2234 2235 2237 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2238 2240 2246 2248 2250 2252 2256 2259 2260 2261 2263 2264 2270 2271 2274 2277 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 2283 2284 2297 2303 2307 2308 2309 2310 2319 2326 2328 2333 2335 2336 2342 2344 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2347 2352 2361 2371 2376 2379 2380 2388 2394 2397 2400 2402 2404 2408 2414 2415 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 2426 2427 2429 2431 2439 2441 2443 2446 2448 2452 2453 2454 2456 2471 2476 2481 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2485 2488 2489 2494 2495 2500 2501 2513 2515 2519 2525 2526 2529 2531 2532 2535 
##    1    0    1    1    1    0    1    1    1    1    1    1    0    1    1    1 
## 2538 2540 2541 2543 2546 2549 2551 2556 2559 2560 2561 2563 2564 2566 2568 2569 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2570 2574 2575 2582 2587 2588 2595 2602 2604 2607 2613 2614 2622 2625 2626 2632 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2642 2654 2666 2667 2668 2671 2672 2676 2679 2680 2682 2685 2694 2696 2697 2699 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2701 2702 2704 2713 2714 2716 2720 2723 2725 2727 2730 2732 2733 2735 2736 2746 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2749 2755 2759 2763 2766 2771 2772 2781 2782 2791 2794 2796 2800 2802 2803 2805 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 2807 2811 2814 2816 2818 2819 2821 2822 2823 2827 2828 2829 2832 2837 2839 2843 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2844 2854 2856 2861 2862 2867 2869 2875 2878 2884 2886 2889 2891 2895 2896 2897 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2899 2900 2901 2902 2906 2915 2918 2922 2924 2927 2934 2937 2942 2953 2955 2956 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2957 2958 2964 2966 2967 2968 2975 2978 2988 2993 2995 2996 2999 3005 3006 3011 
##    1    1    1    1    1    1    0    1    1    1    0    1    1    1    1    1 
## 3013 3020 3022 3025 3026 3027 3029 3030 3034 3037 3042 3044 3046 3050 3051 3053 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3054 3057 3062 3065 3067 3068 3070 3071 3072 3074 3077 3081 3092 3093 3094 3095 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 3096 3097 3098 3100 3102 3107 3113 3115 3121 3122 3123 3130 3132 3133 3134 3136 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3138 3143 3145 3153 3157 3158 3160 3161 3163 3164 3166 3168 3173 3177 3179 3183 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3186 3188 3191 3194 3209 3210 3212 3217 3227 3228 3229 3232 3243 3246 3248 3250 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 3251 3258 3262 3264 3269 3274 3279 3286 3287 3289 3291 3292 3293 3305 3308 3324 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3326 3328 3330 3331 3333 3334 3336 3343 3347 3351 3356 3357 3361 3364 3370 3372 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3377 3379 3384 3394 3398 3403 3407 3413 3415 3417 3418 3422 3430 3434 3437 3438 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3442 3443 3456 3457 3465 3469 3470 3472 3475 3476 3477 3482 3489 3490 3492 3498 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 3499 3502 3505 3512 3518 3520 3524 3528 3534 3535 3537 3538 3539 3541 3542 3544 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 3546 3548 3549 3555 3561 3572 3573 3575 3578 3583 3588 3589 3591 3596 3597 3599 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3600 3601 3606 3611 3613 3615 3621 3633 3634 3636 3637 3638 3644 3647 3650 3655 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 3656 3657 3659 3660 3663 3676 3681 3689 3694 3695 3701 3704 3706 3708 3711 3714 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 3715 3718 3719 3725 3729 3736 3738 3741 3745 3757 3759 3764 3766 3778 3780 3781 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3789 3792 3793 3803 3807 3810 3811 3812 3816 3824 3840 3841 3843 3850 3856 3859 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3860 3866 3868 3869 3871 3873 3874 3877 3881 3883 3888 3891 3892 3893 3895 3896 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 3897 3898 3900 3904 3905 3914 3915 3917 3922 3929 3936 3943 3947 3954 3967 3970 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    0 
## 3972 3974 3977 3979 3981 3985 3986 3987 3989 3990 3992 3994 3997 4003 4004 4011 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4012 4013 4019 4020 4021 4026 4028 4030 4034 4037 4038 4039 4041 4043 4047 4051 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4054 4056 4057 4058 4059 4064 4068 4073 4074 4087 4092 4099 4100 4107 4111 4117 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4118 4124 4125 4127 4128 4129 4139 4140 4141 4142 4144 4145 4149 4154 4155 4156 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 4158 4161 4162 4164 4168 4169 4170 4171 4177 4180 4181 4189 4191 4196 4199 4201 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4206 4207 4209 4211 4221 4222 4223 4227 4231 4236 4242 4246 4252 4254 4262 4264 
##    1    0    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 4270 4272 4273 4279 4284 4285 4286 4301 4305 4306 4310 4315 4317 4320 4322 4323 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4324 4329 4331 4332 4339 4345 4348 4350 4352 4354 4361 4363 4368 4369 4380 4381 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4384 4386 4396 4398 4400 4404 4406 4412 4413 4420 4424 4428 4431 4435 4441 4442 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 4443 4444 4445 4450 4451 4452 4458 4460 4461 4462 4465 4468 4474 4478 4481 4487 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4493 4495 4496 4497 4498 4505 4506 4508 4511 4513 4517 4522 4523 4533 4540 4542 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4544 4549 4554 4555 4557 4560 4566 4569 4573 4582 4584 4586 4591 4595 4597 4600 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4606 4615 4624 4629 4630 4631 4633 4634 4636 4637 4641 4646 4652 4653 4654 4659 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4660 4661 4662 4667 4670 4672 4680 4686 4687 4689 4692 4693 4694 4703 4704 4707 
##    1    1    1    1    1    0    1    1    1    0    1    1    1    1    1    0 
## 4709 4711 4714 4718 4727 4731 4735 4740 4742 4743 4745 4746 4748 4752 4755 4764 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4768 4777 4780 4783 4786 4788 4791 4794 4795 4799 4802 4805 4810 4813 4814 4818 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 4820 4823 4827 4832 4839 4844 4845 4847 4851 4853 4858 4860 4862 4870 4871 4872 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 4874 4876 4880 4884 4888 4889 4894 4896 4899 4902 4904 4908 4914 4919 4920 4922 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4923 4926 4932 4935 4936 4940 4947 4951 4954 4955 4956 4959 4965 4967 4970 4973 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4974 4977 4978 4979 4980 4983 4984 4985 4988 4989 4994 4998 5007 5013 5014 5018 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5021 5034 5035 5036 5045 5048 5051 5052 5053 5054 5056 5057 5058 5059 5062 5064 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5069 5071 5074 5079 5080 5092 5095 5096 5100 5104 5109 5114 5116 5119 5123 5125 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5132 5134 5136 5140 5149 5150 5153 5155 5159 5161 5164 5171 5175 5181 5182 5184 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5186 5187 5191 5196 5198 5204 5205 5207 5208 5211 5212 5220 5226 5228 5234 5237 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5239 5241 5244 5245 5246 5253 5254 5262 5267 5268 5271 5272 5273 5274 5277 5282 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5286 5296 5299 5304 5305 5310 5311 5313 5319 5321 5324 5326 5327 5332 5333 5341 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5342 5350 5355 5357 5359 5360 5365 5366 5367 5374 5375 5377 5381 5388 5391 5394 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5399 5400 5401 5403 5406 5410 5414 5416 5418 5419 5420 5424 5426 5430 5432 5444 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    0 
## 5447 5451 5460 5467 5470 5474 5480 5485 5491 5492 5493 5494 5498 5499 5500 5504 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 5510 5511 5513 5514 5522 5523 5526 5530 5538 5539 5540 5541 5547 5550 5554 5557 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 5558 5559 5566 5568 5571 5573 5575 5577 5597 5598 5605 5607 5609 5615 5616 5617 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 5619 5621 5623 5625 5626 5631 5641 5642 5644 5645 5650 5653 5654 5659 5661 5663 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5667 5672 5676 5679 5682 5685 5686 5690 5691 5692 5695 5697 5703 5706 5709 5716 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5718 5726 5729 5745 5753 5757 5759 5765 5767 5768 5770 5772 5773 5775 5778 5779 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5780 5782 5787 5790 5795 5796 5797 5798 5800 5802 5803 5804 5805 5808 5810 5820 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5824 5825 5829 5830 5839 5841 5842 5843 5846 5847 5853 5855 5860 5863 5865 5867 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5874 5880 5885 5888 5889 5890 5894 5896 5898 5902 5907 5909 5910 5914 5919 5921 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5924 5931 5935 5936 5940 5941 5942 5943 5948 5954 5959 5962 5963 5966 5969 5972 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5973 5974 5986 5987 5992 5996 5999 6000 6002 6005 6010 6011 6012 6014 6021 6030 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6031 6032 6042 6044 6048 6049 6051 6053 6056 6059 6060 6063 6067 6068 6070 6074 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6079 6084 6092 6094 6096 6097 6099 6102 6104 6106 6110 6112 6113 6114 6115 6117 
##    0    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 6130 6135 6136 6141 6146 6151 6153 6156 6157 6158 6160 6169 6171 6173 6178 6182 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 6190 6191 6193 6196 6198 6205 6206 6212 6214 6220 6221 6223 6225 6226 6227 6230 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 6231 6232 6234 6237 6238 6244 6248 6252 6254 6256 6266 6268 6272 6275 6277 6280 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 6281 6284 6290 6293 6301 6306 6310 6321 6322 6323 6329 6334 6335 6338 6342 6357 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6358 6360 6361 6363 6366 6368 6371 6372 6375 6376 6377 6378 6384 6390 6393 6398 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6399 6401 6404 6405 6410 6413 6418 6420 6421 6422 6429 6433 6434 6436 6442 6448 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6449 6450 6456 6463 6473 6481 6484 6486 6487 6489 6503 6507 6508 6510 6530 6533 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6535 6536 6538 6542 6547 6548 6549 6555 6557 6562 6570 6579 6580 6582 6584 6587 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6589 6594 6595 6596 6598 6605 6607 6608 6610 6620 6625 6626 6631 6632 6634 6637 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6640 6641 6645 6646 6651 6655 6658 6659 6661 6662 6665 6671 6673 6675 6677 6679 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6681 6682 6683 6686 6688 6696 6714 6715 6716 6717 6719 6720 6724 6725 6728 6729 
##    1    1    1    1    1    1    0    1    1    0    1    1    1    1    1    1 
## 6731 6735 6737 6738 6744 6747 6748 6752 6753 6754 6762 6765 6767 6768 6770 6776 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6782 6788 6793 6798 6800 6811 6814 6816 6822 6824 6831 6832 6835 6836 6838 6839 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6842 6843 6848 6850 6852 6853 6856 6857 6858 6859 6862 6867 6872 6873 6874 6884 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6885 6887 6889 6892 6893 6895 6900 6903 6904 6913 6915 6919 6923 6925 6929 6930 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6931 6933 6936 6938 6939 6942 6944 6948 6949 6951 6952 6954 6957 6968 6969 6970 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6974 6975 6976 6981 6987 6989 6990 6994 6999 7001 7006 7007 7009 7011 7012 7013 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 7033 7037 7038 7041 7043 7044 7047 7049 7052 7054 7058 7061 7062 7063 7072 7077 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7079 7081 7084 7087 7088 7092 7093 7094 7096 7099 7100 7105 7106 7107 7115 7116 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7125 7128 7135 7137 7141 7149 7150 7153 7154 7157 7160 7162 7164 7165 7166 7168 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 7169 7171 7174 7177 7180 7188 7197 7199 7203 7206 7207 7208 7209 7212 7215 7219 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7221 7222 7224 7227 7232 7233 7235 7238 7239 7248 7250 7251 7256 7257 7262 7264 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7265 7271 7273 7275 7276 7277 7282 7287 7291 7292 7295 7297 7301 7303 7308 7309 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7311 7312 7317 7318 7323 7329 7330 7331 7332 7333 7334 7335 7336 7338 7339 7340 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7344 7347 7350 7351 7354 7356 7358 7360 7361 7362 7368 7369 7375 7379 7381 7382 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7384 7387 7394 7399 7400 7401 7404 7408 7414 7417 7418 7420 7422 7424 7430 7436 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7440 7442 7449 7451 7456 7473 7476 7482 7485 7489 7494 7495 7496 7498 7503 7504 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 7505 7507 7509 7512 7515 7525 7528 7532 7535 7539 7540 7543 7546 7552 7561 7563 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7565 7573 7574 7578 7579 7582 7586 7589 7590 7591 7603 7606 7609 7611 7612 7630 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7631 7637 7640 7649 7658 7664 7665 7671 7673 7675 7682 7683 7687 7688 7689 7694 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7695 7697 7698 7706 7713 7715 7721 7724 7732 7738 7739 7745 7749 7754 7755 7758 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7767 7768 7769 7771 7772 7773 7776 7784 7786 7790 7792 7793 7795 7798 7801 7822 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7830 7832 7836 7841 7845 7848 7862 7865 7870 7874 7884 7885 7887 7890 7891 7893 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 7894 7898 7899 7902 7908 7909 7911 7922 7923 7927 7928 7936 7938 7951 7954 7957 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 7960 7961 7963 7966 7970 7971 7976 7982 7986 7988 7991 7992 7999 8001 8002 8004 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8008 8010 8013 8017 8019 8020 8021 8022 8025 8033 8034 8035 8040 8043 8047 8056 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8059 8062 8063 8065 8067 8069 8075 8080 8096 8097 8102 8105 8106 8109 8111 8117 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8119 8120 8123 8130 8132 8134 8136 8139 8142 8144 8145 8148 8150 8151 8154 8156 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8161 8162 8168 8170 8171 8175 8180 8184 8187 8188 8189 8192 8201 8204 8206 8207 
##    0    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 8208 8210 8212 8219 8220 8228 8233 8239 8240 8243 8245 8249 8250 8251 8252 8253 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8254 8256 8257 8258 8267 8273 8274 8278 8282 8285 8286 8288 8289 8292 8295 8302 
##    1    1    1    1    1    1    0    1    1    1    0    1    1    1    1    1 
## 8306 8314 8319 8320 8329 8337 8339 8340 8342 8345 8353 8354 8360 8362 8364 8366 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8367 8369 8378 8380 8381 8383 8386 8391 8396 8397 8398 8415 8417 8418 8424 8425 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8436 8437 8440 8446 8451 8453 8456 8460 8461 8462 8464 8465 8466 8474 8476 8478 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8483 8484 8498 8499 8504 8505 8506 8511 8515 8522 8524 8534 8545 8547 8556 8559 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8560 8561 8563 8565 8567 8573 8574 8575 8576 8581 8582 8585 8586 8589 8592 8595 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8600 8602 8604 8605 8607 8609 8612 8617 8618 8619 8622 8625 8626 8627 8632 8647 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8648 8649 8651 8653 8656 8659 8662 8669 8670 8674 8676 8678 8680 8682 8688 8695 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8696 8697 8699 8700 8705 8711 8713 8715 8725 8731 8733 8735 8740 8742 8745 8746 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8752 8754 8755 8762 8769 8777 8779 8783 8788 8789 8796 8797 8798 8810 8815 8816 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 8823 8824 8834 8836 8838 8839 8840 8842 8844 8845 8849 8852 8853 8854 8868 8870 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8875 8877 8880 8887 8889 8890 8895 8902 8906 8907 8911 8916 8917 8918 8921 8922 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8924 8925 8930 8942 8945 8953 8956 8958 8959 8962 8963 8968 8969 8972 8975 8980 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8981 8982 8988 8990 8993 8996 9000 9007 9019 9023 9024 9027 9029 9030 9033 9035 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9037 9038 9040 9043 9047 9049 9054 9070 9072 9073 9085 9086 9089 9090 9092 9093 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9096 9098 9102 9103 9105 9106 9111 9112 9113 9115 9116 9117 9122 9123 9126 9128 
##    1    0    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 9132 9141 9143 9144 9150 9151 9152 9156 9159 9163 9164 9176 9183 9185 9186 9190 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 9194 9197 9199 9207 9208 9211 9212 9215 9220 9221 9229 9231 9233 9235 9238 9242 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9245 9248 9253 9263 9268 9272 9275 9277 9281 9282 9286 9292 9294 9299 9302 9303 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 9306 9313 9316 9317 9320 9321 9327 9328 9331 9333 9337 9338 9343 9346 9350 9351 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 9354 9356 9361 9364 9365 9367 9374 9378 9380 9381 9383 9385 9387 9389 9393 9395 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9398 9399 9401 9408 9409 9415 9416 9420 9421 9423 9424 9425 9426 9430 9431 9434 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 9437 9441 9442 9447 9455 9457 9459 9461 9473 9476 9480 9481 9482 9487 9490 9494 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9496 9497 9499 9503 9507 9510 9511 9516 9520 9521 9524 9526 9533 9535 9540 9541 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 9547 
##    1
#39个0,961个1
view(pred_class2_3)

pred_class2 <- cbind(pred_class2_1, pred_class2_2,pred_class2_3)
pred_class2
##      pred_class2_1 pred_class2_2 pred_class2_3
## 6                1             1             1
## 12               1             1             1
## 14               1             1             1
## 19               1             1             0
## 23               1             1             1
## 24               1             1             1
## 26               1             1             1
## 29               1             1             1
## 33               1             1             1
## 34               1             1             1
## 37               1             1             1
## 38               1             1             1
## 40               1             1             0
## 42               1             1             1
## 43               1             1             1
## 44               1             1             1
## 46               1             1             1
## 47               1             1             1
## 48               1             1             1
## 50               1             1             1
## 56               1             1             1
## 69               1             1             1
## 70               1             1             1
## 74               1             1             1
## 78               1             1             1
## 80               1             1             1
## 85               1             1             1
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#15个0,985个1
view(pred_class2)


#💙10_1_1 Calculate Accuracy of prediction
accuracy1 <- mean(pred_class1 == test_data$legacy_collision_severity)
accuracy1 
## [1] 0.00884235
print(paste("Accuracy:", accuracy1))
## [1] "Accuracy: 0.00884235020360675"
accuracy2 <- mean(pred_class2 == test_data$legacy_collision_severity)
accuracy2 
## [1] 0.00954043
print(paste("Accuracy:", accuracy2))
## [1] "Accuracy: 0.00954043048283886"
#💙10_1_2 AUC: compare predicted results with actual categories

#table(Predicted = pred_class1, Actual = test_data$legacy_collision_severity)
library(pROC)
#plot a ROC curve with True Positive Rate (TPR) as the y axis and False Positive Rate (FPR) as x axis.

#MNL best model on train data
roc_curve1_1 <- roc(test_data$legacy_collision_severity==1, predictions1[, 1])     #原本没有  ==1
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve1_1)

roc_curve1_2 <- roc(test_data$legacy_collision_severity==2, predictions1[, 2])  
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve1_2)

roc_curve1_3 <- roc(test_data$legacy_collision_severity==3, predictions1[, 3])
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve1_3)

#P.S. The closer the curve is to the upper left corner, the better the model performance is.
auc(roc_curve1_1) ## Area under the curve: 0.9286
## Area under the curve: 0.6171
auc(roc_curve1_2)
## Area under the curve: 0.6104
auc(roc_curve1_3)
## Area under the curve: 0.6181
#P.S. The AUC value is between 0 and 1. The closer the value is to 1, the better the model performance. 0.5 means the model performance is equivalent to random guessing.
roc_curve2_1 <- roc(test_data$legacy_collision_severity==1, predictions2[, 1])  #==1
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve2_1)

roc_curve2_2 <- roc(test_data$legacy_collision_severity==2, predictions2[, 2])
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve2_2)

roc_curve2_3 <- roc(test_data$legacy_collision_severity==3, predictions2[, 3])
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve2_3)

#P.S. The closer the curve is to the upper left corner, the better the model performance is.
auc(roc_curve2_1) ## Area under the curve: 0.9286
## Area under the curve: 0.6597
auc(roc_curve2_2)
## Area under the curve: 0.6125
auc(roc_curve2_3)
## Area under the curve: 0.6166
####删除
#Can we adjust a little the values of thresholds, to get 70% AUC?
####GPT
# Adjust thresholds to improve AUC
library(pROC)

# Function to adjust thresholds and calculate AUC
adjust_thresholds <- function(predictions, test_data, target_col) {
  thresholds <- seq(0.1, 0.9, by = 0.05) # Define a range of thresholds
  results <- data.frame(Threshold = numeric(), AUC = numeric())

  for (threshold in thresholds) {
    pred_class <- ifelse(predictions[, target_col] > threshold, 1, 0)
    roc_curve <- roc(test_data$legacy_collision_severity == target_col, predictions[, target_col])
    auc_value <- auc(roc_curve)
    results <- rbind(results, data.frame(Threshold = threshold, AUC = auc_value))
  }
  return(results)
}

# Analyze AUC for each severity level (1, 2, and 3) in MNL model
results_mnl_1 <- adjust_thresholds(predictions1, test_data, target_col = 1)
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
results_mnl_2 <- adjust_thresholds(predictions1, test_data, target_col = 2)
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
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results_mnl_3 <- adjust_thresholds(predictions1, test_data, target_col = 3)
## Setting levels: control = FALSE, case = TRUE
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## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
# Analyze AUC for each severity level (1, 2, and 3) in OL model
results_ol_1 <- adjust_thresholds(predictions2, test_data, target_col = 1)
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
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results_ol_2 <- adjust_thresholds(predictions2, test_data, target_col = 2)
## Setting levels: control = FALSE, case = TRUE
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## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
results_ol_3 <- adjust_thresholds(predictions2, test_data, target_col = 3)
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
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## Setting levels: control = FALSE, case = TRUE
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## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
# View threshold adjustment results
print("MNL Results for Severity 1:")
## [1] "MNL Results for Severity 1:"
print(results_mnl_1)
##    Threshold       AUC
## 1       0.10 0.6171453
## 2       0.15 0.6171453
## 3       0.20 0.6171453
## 4       0.25 0.6171453
## 5       0.30 0.6171453
## 6       0.35 0.6171453
## 7       0.40 0.6171453
## 8       0.45 0.6171453
## 9       0.50 0.6171453
## 10      0.55 0.6171453
## 11      0.60 0.6171453
## 12      0.65 0.6171453
## 13      0.70 0.6171453
## 14      0.75 0.6171453
## 15      0.80 0.6171453
## 16      0.85 0.6171453
## 17      0.90 0.6171453
print("OL Results for Severity 1:")
## [1] "OL Results for Severity 1:"
print(results_ol_1)
##    Threshold       AUC
## 1       0.10 0.6597381
## 2       0.15 0.6597381
## 3       0.20 0.6597381
## 4       0.25 0.6597381
## 5       0.30 0.6597381
## 6       0.35 0.6597381
## 7       0.40 0.6597381
## 8       0.45 0.6597381
## 9       0.50 0.6597381
## 10      0.55 0.6597381
## 11      0.60 0.6597381
## 12      0.65 0.6597381
## 13      0.70 0.6597381
## 14      0.75 0.6597381
## 15      0.80 0.6597381
## 16      0.85 0.6597381
## 17      0.90 0.6597381
# Find optimal thresholds for AUC >= 70%
optimal_mnl_threshold_1 <- results_mnl_1[results_mnl_1$AUC >= 0.7, ]
optimal_mnl_threshold_1
## [1] Threshold AUC      
## <0 rows> (or 0-length row.names)
optimal_ol_threshold_1 <- results_ol_1[results_ol_1$AUC >= 0.7, ]
optimal_mnl_threshold_1
## [1] Threshold AUC      
## <0 rows> (or 0-length row.names)
#### 删除



# Visualize ROC curves for best thresholds
roc_curve1_1 <- plot(roc(test_data$legacy_collision_severity == 1, predictions1[, 1]), main = "ROC for MNL Severity 1")
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
abline(h = 0.7, col = "red") # Highlight AUC target

auc(roc_curve1_1)
## Area under the curve: 0.6171
roc_curve2_1 <- plot(roc(test_data$legacy_collision_severity == 1, predictions2[, 1]), main = "ROC for OL Severity 1")
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
abline(h = 0.7, col = "red") # Highlight AUC target

auc(roc_curve2_1)
## Area under the curve: 0.6597
####

#💙10_1_3 RMSE
#It evaluates how well the predicted probabilities from the model match the observed data. RMSE measures the average error of the model.
# Predicted probabilities for the best model
#MNL
predicted_probs <- predict(step_test2, type = "probs")

# Create a matrix of true labels (one-hot encoded for each severity category)
true_labels <- model.matrix(~ legacy_collision_severity - 1, data = data4)

# Calculate the RMSE for each severity category (1: Fatal, 2: Serious, 3: Slight)
rmse_fatal <- sqrt(mean((true_labels[, 1] - predicted_probs[, 1])^2))

rmse_serious <- sqrt(mean((true_labels[, 2] - predicted_probs[, 2])^2))
rmse_slight <- sqrt(mean((true_labels[, 3] - predicted_probs[, 3])^2))

# Average RMSE for the overall model
rmse_total <- sqrt(mean((true_labels - predicted_probs)^2))

# Print RMSE values
rmse_fatal
## [1] 0.1035234
rmse_serious
## [1] 0.419991
rmse_slight
## [1] 0.4251759
rmse_total
## [1] 0.3501829
cat("RMSE values:\n")
## RMSE values:
cat("Fatal:", rmse_fatal, "\n")
## Fatal: 0.1035234
cat("Serious:", rmse_serious, "\n")
## Serious: 0.419991
cat("Slight:", rmse_slight, "\n")
## Slight: 0.4251759
cat("Overall RMSE:", rmse_total, "\n")
## Overall RMSE: 0.3501829
#xiaojie#
#💙10_1_4: Compare  the percentage of the response variable variability that chosen predictors can explain
library(pscl)
## Classes and Methods for R originally developed in the
## Political Science Computational Laboratory
## Department of Political Science
## Stanford University (2002-2015),
## by and under the direction of Simon Jackman.
## hurdle and zeroinfl functions by Achim Zeileis.
# Calculate McFadden's R²
pseudo_r2 <- pR2(step_test)["McFadden"]
## fitting null model for pseudo-r2
pseudo_r2
##   McFadden 
## 0.02998632
# Output the percentage of variability explained by the model
explained_variability <- pseudo_r2 * 100
cat("The MNL best model with 13 predictors explains", explained_variability, "% of the variability in the level of severity in predictor.")
## The MNL best model with 13 predictors explains 2.998632 % of the variability in the level of severity in predictor.
pseudo_r2 <- pR2(step_test2)["McFadden"]
## fitting null model for pseudo-r2
pseudo_r2
##   McFadden 
## 0.02998632
# Output the percentage of variability explained by the model
explained_variability <- pseudo_r2 * 100
cat("The MNL best model with 13 predictors explains", explained_variability, "% of the variability in the level of severity in predictor.")
## The MNL best model with 13 predictors explains 2.998632 % of the variability in the level of severity in predictor.
#💙10_1_4: Compare VIF to identify multicollinearity 

# Calculate VIF for each model
vif_step_test_ <- vif(step_test_)
## Warning in vif.default(step_test_): No intercept: vifs may not be sensible.
vif_step_test2_ <- vif(step_test2_)
## Warning in sqrt(1/diag(V)): NaNs produced
## Warning in cov2cor(v): diag(.) had 0 or NA entries; non-finite result is
## doubtful
vif_step_test_
##                                              GVIF Df GVIF^(1/(2*Df))
## police_force                                  NaN  1             NaN
## number_of_vehicles                            NaN  1             NaN
## number_of_casualties                          NaN  1             NaN
## day_of_week                                   NaN  1             NaN
## first_road_class                              NaN  1             NaN
## first_road_number                             NaN  1             NaN
## road_type                                     NaN  4             NaN
## speed_limit                                   NaN  1             NaN
## junction_detail                               NaN  7             NaN
## junction_control                              NaN  3             NaN
## second_road_class                             NaN  1             NaN
## second_road_number                            NaN  1             NaN
## pedestrian_crossing_human_control             NaN  2             NaN
## pedestrian_crossing_physical_facilities       NaN  5             NaN
## light_conditions                              NaN  4             NaN
## weather_conditions                            NaN  7             NaN
## road_surface_conditions                       NaN  4             NaN
## special_conditions_at_site                    NaN  7             NaN
## carriageway_hazards                           NaN  5             NaN
## did_police_officer_attend_scene_of_collision  NaN  1             NaN
vif_step_test2_
##                                              GVIF Df GVIF^(1/(2*Df))
## police_force                                  NaN  1             NaN
## number_of_vehicles                            NaN  1             NaN
## number_of_casualties                          NaN  1             NaN
## day_of_week                                   NaN  1             NaN
## first_road_class                              NaN  1             NaN
## first_road_number                             NaN  1             NaN
## road_type                                     NaN  4             NaN
## speed_limit                                   NaN  1             NaN
## junction_detail                               NaN  7             NaN
## junction_control                              NaN  3             NaN
## second_road_class                             NaN  1             NaN
## second_road_number                            NaN  1             NaN
## pedestrian_crossing_human_control             NaN  2             NaN
## pedestrian_crossing_physical_facilities       NaN  5             NaN
## light_conditions                              NaN  4             NaN
## weather_conditions                            NaN  7             NaN
## road_surface_conditions                       NaN  4             NaN
## special_conditions_at_site                    NaN  7             NaN
## carriageway_hazards                           NaN  5             NaN
## did_police_officer_attend_scene_of_collision  NaN  1             NaN
# Print VIF values
cat("VIF for reduced_model0:\n")
## VIF for reduced_model0:
print(vif_step_test_)
##                                              GVIF Df GVIF^(1/(2*Df))
## police_force                                  NaN  1             NaN
## number_of_vehicles                            NaN  1             NaN
## number_of_casualties                          NaN  1             NaN
## day_of_week                                   NaN  1             NaN
## first_road_class                              NaN  1             NaN
## first_road_number                             NaN  1             NaN
## road_type                                     NaN  4             NaN
## speed_limit                                   NaN  1             NaN
## junction_detail                               NaN  7             NaN
## junction_control                              NaN  3             NaN
## second_road_class                             NaN  1             NaN
## second_road_number                            NaN  1             NaN
## pedestrian_crossing_human_control             NaN  2             NaN
## pedestrian_crossing_physical_facilities       NaN  5             NaN
## light_conditions                              NaN  4             NaN
## weather_conditions                            NaN  7             NaN
## road_surface_conditions                       NaN  4             NaN
## special_conditions_at_site                    NaN  7             NaN
## carriageway_hazards                           NaN  5             NaN
## did_police_officer_attend_scene_of_collision  NaN  1             NaN
cat("\nVIF for reduced_model1:\n")
## 
## VIF for reduced_model1:
print(vif_step_test2_)
##                                              GVIF Df GVIF^(1/(2*Df))
## police_force                                  NaN  1             NaN
## number_of_vehicles                            NaN  1             NaN
## number_of_casualties                          NaN  1             NaN
## day_of_week                                   NaN  1             NaN
## first_road_class                              NaN  1             NaN
## first_road_number                             NaN  1             NaN
## road_type                                     NaN  4             NaN
## speed_limit                                   NaN  1             NaN
## junction_detail                               NaN  7             NaN
## junction_control                              NaN  3             NaN
## second_road_class                             NaN  1             NaN
## second_road_number                            NaN  1             NaN
## pedestrian_crossing_human_control             NaN  2             NaN
## pedestrian_crossing_physical_facilities       NaN  5             NaN
## light_conditions                              NaN  4             NaN
## weather_conditions                            NaN  7             NaN
## road_surface_conditions                       NaN  4             NaN
## special_conditions_at_site                    NaN  7             NaN
## carriageway_hazards                           NaN  5             NaN
## did_police_officer_attend_scene_of_collision  NaN  1             NaN
####1: Repeat Predictions for FULL models

#💚10. 

#💙10_1_0 Preparitions: 
#💜10_1_0_1 Divide training set and test set
set.seed(456)
train_index_f <- sample(seq_len(nrow(data4)), size = 0.70 * nrow(data4))   #用70%训练集的数据,来预测30%测试集的结果的正确性
train_data_f <- data4[train_index_f, ]
test_data_f <- data4[-train_index_f, ]
library(fpp3)
view(train_data_f)
view(test_data_f)

#fit MNL and OL FULL models on train data (12, 13 predictors respectively)

library(nnet)
library(MASS)

full_test_f <- multinom(legacy_collision_severity~., data = train_data_f)
## # weights:  180 (118 variable)
## initial  value 7344.223150 
## iter  10 value 4371.773008
## iter  20 value 4170.616728
## iter  30 value 4027.814771
## iter  40 value 3951.067489
## iter  50 value 3921.953117
## iter  60 value 3908.047528
## iter  70 value 3906.084398
## iter  80 value 3905.273679
## iter  90 value 3904.838992
## iter 100 value 3904.802028
## final  value 3904.802028 
## stopped after 100 iterations
full_test2_f <- polr(legacy_collision_severity ~ ., data = train_data_f, Hess = TRUE)
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#make predictions on the test set
#决定了AUC
predictions1_f <- predict(full_test_f, newdata = test_data_f, type = "probs")   ##??   
predictions1_f 
##                 1            2         3
## 2    6.811297e-03 2.215257e-01 0.7716630
## 4    4.435139e-03 2.231155e-01 0.7724494
## 8    1.415428e-02 2.156493e-01 0.7701964
## 13   2.458867e-02 1.666277e-01 0.8087836
## 16   8.828105e-04 1.557118e-01 0.8434054
## 18   1.911851e-03 1.755344e-01 0.8225538
## 29   1.112518e-02 2.957478e-01 0.6931270
## 30   3.850619e-02 2.592981e-01 0.7021957
## 32   4.496425e-03 2.189941e-01 0.7765095
## 36   8.973761e-03 3.541164e-01 0.6369098
## 39   2.793045e-03 2.617153e-01 0.7354917
## 41   1.285064e-02 2.295162e-01 0.7576332
## 43   9.532415e-03 2.901559e-01 0.7003117
## 48   6.709821e-03 1.728079e-01 0.8204823
## 49   1.848497e-02 3.312607e-01 0.6502543
## 55   9.756806e-09 2.233363e-01 0.7766637
## 58   1.110072e-02 2.670675e-01 0.7218318
## 59   9.956034e-09 3.093607e-01 0.6906392
## 60   1.508922e-02 3.100032e-01 0.6749076
## 62   9.830700e-03 1.356147e-01 0.8545546
## 63   1.851571e-09 2.509472e-01 0.7490528
## 71   2.376621e-08 2.703537e-01 0.7296463
## 73   5.462056e-09 9.496554e-02 0.9050345
## 80   2.189630e-03 1.235781e-01 0.8742323
## 84   2.810118e-08 2.594398e-01 0.7405602
## 86   4.024102e-03 1.952394e-01 0.8007365
## 87   2.329364e-02 1.956514e-01 0.7810550
## 98   3.380751e-02 2.277112e-01 0.7384813
## 102  7.611676e-04 1.842188e-01 0.8150201
## 104  6.433326e-04 1.835886e-01 0.8157681
## 107  8.939756e-08 7.214238e-02 0.9278575
## 109  1.664280e-03 1.926071e-01 0.8057286
## 110  4.581155e-03 2.635033e-01 0.7319155
## 113  8.118970e-03 2.056723e-01 0.7862088
## 123  1.067890e-08 1.823315e-01 0.8176685
## 125  2.402842e-02 2.358890e-01 0.7400825
## 136  1.451115e-02 2.920522e-01 0.6934366
## 137  2.185881e-02 2.309891e-01 0.7471521
## 138  4.505361e-02 3.937114e-01 0.5612349
## 143  2.701093e-03 3.173615e-01 0.6799375
## 145  8.135765e-03 3.041372e-01 0.6877270
## 147  4.255777e-02 3.968183e-01 0.5606239
## 149  7.750711e-07 9.194573e-02 0.9080535
## 151  1.194127e-02 2.620616e-01 0.7259972
## 153  4.497739e-03 3.253999e-01 0.6701024
## 160  8.100834e-03 3.592991e-01 0.6326000
## 162  1.193334e-02 2.863006e-01 0.7017660
## 165  6.925562e-04 8.671896e-02 0.9125885
## 167  1.497377e-02 3.599192e-01 0.6251070
## 168  1.701866e-02 3.649081e-01 0.6180733
## 171  8.739080e-03 2.664366e-01 0.7248243
## 175  4.369366e-03 1.767402e-01 0.8188904
## 177  1.064785e-02 2.174681e-01 0.7718841
## 184  5.918979e-04 1.863540e-01 0.8130541
## 187  1.163368e-02 3.527191e-01 0.6356472
## 188  4.898913e-09 2.378448e-01 0.7621552
## 198  6.262210e-03 2.910228e-01 0.7027150
## 199  1.894610e-03 2.114325e-01 0.7866729
## 205  2.948644e-02 9.399868e-02 0.8765149
## 206  2.559142e-03 2.272162e-01 0.7702246
## 214  6.041097e-03 3.556767e-01 0.6382822
## 217  3.639396e-03 3.254775e-01 0.6708831
## 220  5.097702e-03 3.353344e-01 0.6595679
## 221  2.815453e-02 2.021894e-01 0.7696561
## 225  8.200325e-03 2.203040e-01 0.7714956
## 227  4.052654e-03 2.580424e-01 0.7379050
## 230  1.833621e-06 1.581757e-01 0.8418225
## 231  1.354589e-02 3.070650e-01 0.6793891
## 242  2.173377e-04 3.677488e-06 0.9997790
## 249  5.333778e-03 2.820349e-01 0.7126313
## 251  5.661962e-03 2.005118e-01 0.7938263
## 253  9.958920e-03 2.108669e-01 0.7791742
## 261  1.178727e-02 2.564851e-01 0.7317277
## 262  5.038983e-03 3.363439e-01 0.6586171
## 281  2.509096e-02 3.609224e-01 0.6139867
## 283  1.334222e-03 1.916984e-01 0.8069674
## 284  1.462192e-02 3.185643e-01 0.6668137
## 286  1.007484e-03 2.421721e-01 0.7568204
## 292  9.021408e-03 1.704225e-01 0.8205560
## 294  6.325384e-03 1.916272e-01 0.8020474
## 295  1.241258e-02 2.552093e-01 0.7323781
## 296  7.207398e-09 1.537581e-01 0.8462419
## 300  2.423884e-02 4.358649e-01 0.5398962
## 302  3.539424e-03 1.738347e-01 0.8226259
## 303  1.081380e-02 2.823638e-01 0.7068224
## 306  1.239614e-02 3.435177e-01 0.6440862
## 308  2.090573e-02 3.773948e-01 0.6016994
## 309  5.639944e-03 2.694187e-01 0.7249413
## 314  2.740999e-03 2.766957e-01 0.7205633
## 316  1.284550e-13 2.426764e-01 0.7573236
## 318  7.274559e-02 3.032712e-01 0.6239832
## 321  8.241249e-03 2.121590e-01 0.7795997
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## 333  4.219416e-03 2.694586e-01 0.7263220
## 340  3.097786e-03 3.302169e-01 0.6666853
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## 623  2.089028e-02 3.008849e-01 0.6782249
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## 628  3.753077e-03 2.686153e-01 0.7276317
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## 693  2.057782e-02 2.471610e-01 0.7322612
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## 697  1.757985e-04 1.010792e-01 0.8987450
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## 717  7.082206e-02 2.678607e-01 0.6613172
## 721  3.279436e-03 2.705354e-01 0.7261852
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## 738  4.890510e-03 2.477846e-01 0.7473249
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## 744  1.096170e-03 1.303523e-01 0.8685516
## 746  6.294920e-03 2.481257e-01 0.7455794
## 747  1.386703e-02 2.457906e-01 0.7403423
## 751  1.415409e-03 1.980334e-01 0.8005512
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## 784  2.731287e-07 2.296410e-01 0.7703588
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## 788  1.361874e-02 1.651680e-01 0.8212133
## 789  2.517123e-03 1.687790e-01 0.8287039
## 790  2.451309e-06 4.561536e-01 0.5438439
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## 794  5.850200e-08 2.762692e-01 0.7237307
## 796  7.740027e-03 2.993302e-01 0.6929297
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## 808  2.099345e-05 9.632320e-06 0.9999694
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## 810  8.012496e-03 1.789197e-01 0.8130678
## 811  2.725438e-03 2.254393e-01 0.7718353
## 814  2.113600e-02 3.966495e-01 0.5822145
## 817  1.400880e-02 2.369732e-01 0.7490180
## 819  2.924892e-02 2.407514e-01 0.7299997
## 823  7.738819e-03 1.790684e-01 0.8131928
## 831  5.310134e-03 1.850506e-01 0.8096392
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## 842  6.943615e-03 3.472523e-01 0.6458041
## 848  1.406301e-02 1.584842e-01 0.8274528
## 851  5.242601e-02 3.701722e-01 0.5774018
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## 854  2.143245e-03 1.412581e-01 0.8565986
## 855  3.799358e-03 2.652851e-01 0.7309155
## 856  5.503379e-03 1.037261e-01 0.8907705
## 858  9.586507e-03 3.522750e-01 0.6381385
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## 870  1.264902e-02 2.077017e-01 0.7796493
## 872  1.092871e-03 3.109810e-01 0.6879261
## 873  1.454749e-08 2.791893e-01 0.7208107
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## 883  8.551676e-03 3.363005e-01 0.6551478
## 884  3.080803e-03 1.532048e-01 0.8437144
## 885  6.934441e-03 2.390819e-01 0.7539837
## 886  8.241874e-04 1.776691e-01 0.8215067
## 887  5.881484e-03 2.761791e-01 0.7179394
## 889  5.932728e-03 1.436233e-01 0.8504439
## 890  1.159141e-02 2.562128e-01 0.7321958
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## 898  1.289326e-02 2.739573e-01 0.7131494
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## 988  3.144690e-03 1.618618e-01 0.8349935
## 990  3.463834e-08 1.424494e-01 0.8575506
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## 995  2.527315e-03 1.771982e-01 0.8202744
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## 1353 2.667824e-03 1.338489e-01 0.8634833
## 1356 7.428131e-10 6.757502e-02 0.9324250
## 1370 1.445835e-02 2.889392e-01 0.6966025
## 1372 2.001236e-09 1.983265e-01 0.8016735
## 1376 4.080387e-03 2.514997e-01 0.7444199
## 1380 7.201026e-03 2.915465e-01 0.7012525
## 1381 3.396028e-08 2.278102e-01 0.7721897
## 1383 1.003804e-02 2.856814e-01 0.7042806
## 1386 6.464404e-03 2.383223e-01 0.7552133
## 1389 1.616915e-08 1.456378e-01 0.8543622
## 1395 3.428580e-03 2.573248e-01 0.7392466
## 1399 1.153724e-02 2.798026e-01 0.7086602
## 1405 1.158072e-02 1.850369e-01 0.8033824
## 1412 2.934243e-03 1.051065e-01 0.8919593
## 1413 3.628568e-03 2.915624e-01 0.7048090
## 1419 2.729126e-03 2.745427e-01 0.7227281
## 1425 7.915663e-03 2.509120e-01 0.7411723
## 1426 1.454085e-02 3.849952e-01 0.6004639
## 1427 6.554093e-03 2.827981e-01 0.7106478
## 1430 1.133175e-02 2.488437e-01 0.7398246
## 1439 4.380822e-03 2.434984e-01 0.7521207
## 1451 3.053868e-03 2.283688e-01 0.7685773
## 1453 2.657759e-03 1.563642e-01 0.8409780
## 1454 5.916162e-02 4.300703e-01 0.5107681
## 1465 1.356307e-02 2.173191e-01 0.7691178
## 1471 1.165677e-03 1.556402e-01 0.8431941
## 1472 1.580400e-02 3.047766e-01 0.6794194
## 1475 1.897867e-03 9.926324e-02 0.8988389
## 1477 4.108882e-03 2.367158e-01 0.7591753
## 1478 7.452828e-03 2.852624e-01 0.7072848
## 1479 4.074381e-03 3.371377e-01 0.6587879
## 1480 2.565802e-03 1.983605e-01 0.7990737
## 1483 4.174467e-03 1.948151e-01 0.8010105
## 1491 9.252644e-03 2.579584e-01 0.7327890
## 1498 1.360967e-03 2.027140e-01 0.7959250
## 1501 1.079154e-02 3.746973e-01 0.6145111
## 1505 5.030951e-03 2.365203e-01 0.7584488
## 1506 5.690638e-03 2.793327e-01 0.7149767
## 1507 3.557945e-03 2.856187e-01 0.7108234
## 1509 1.120919e-08 2.515360e-01 0.7484640
## 1510 5.637388e-03 2.836385e-01 0.7107241
## 1511 4.950037e-03 1.704690e-01 0.8245810
## 1519 1.936693e-03 2.700192e-01 0.7280441
## 1525 2.324286e-03 2.118915e-01 0.7857842
## 1526 3.811861e-03 1.651226e-01 0.8310655
## 1534 2.310695e-03 1.884522e-01 0.8092371
## 1535 8.528033e-03 2.698162e-01 0.7216558
## 1537 3.770474e-03 2.003555e-01 0.7958741
## 1538 1.819628e-03 3.019313e-01 0.6962490
## 1540 1.665482e-02 3.017044e-01 0.6816407
## 1542 2.850018e-02 3.975220e-01 0.5739778
## 1543 3.265061e-03 2.368389e-01 0.7598960
## 1545 1.974193e-03 2.460289e-01 0.7519969
## 1559 5.124085e-03 2.699154e-01 0.7249605
## 1560 1.093200e-03 2.055486e-01 0.7933582
## 1561 3.052174e-03 2.141400e-01 0.7828078
## 1562 1.174914e-02 2.711272e-01 0.7171237
## 1566 7.813292e-03 2.864189e-01 0.7057678
## 1568 4.038268e-07 7.485792e-02 0.9251417
## 1573 4.347765e-03 2.581127e-01 0.7375395
## 1582 1.755060e-03 2.077004e-01 0.7905446
## 1593 3.585299e-03 2.563343e-01 0.7400804
## 1603 4.492471e-03 2.955573e-01 0.6999503
## 1604 3.421056e-03 2.717945e-01 0.7247844
## 1610 5.528196e-02 2.286765e-01 0.7160415
## 1614 1.524215e-03 1.683719e-01 0.8301039
## 1622 1.675274e-02 2.952155e-01 0.6880318
## 1623 2.734106e-03 2.424065e-01 0.7548594
## 1625 2.768212e-03 1.437201e-01 0.8535117
## 1627 2.106237e-02 3.053906e-01 0.6735470
## 1633 4.901524e-03 2.673616e-01 0.7277368
## 1635 1.056985e-02 3.466351e-01 0.6427951
## 1637 2.740483e-10 1.194113e-01 0.8805887
## 1645 7.312236e-08 2.464227e-01 0.7535772
## 1647 1.844321e-09 1.610942e-01 0.8389058
## 1648 3.260408e-03 1.170844e-01 0.8796552
## 1652 1.900520e-03 2.502769e-01 0.7478226
## 1653 2.047275e-03 1.855991e-01 0.8123536
## 1659 7.969738e-03 2.024944e-01 0.7895359
## 1664 2.708927e-02 1.685893e-01 0.8043214
## 1665 7.382793e-08 3.086219e-01 0.6913780
## 1670 1.232723e-02 2.583484e-01 0.7293244
## 1672 3.338834e-07 4.138301e-01 0.5861696
## 1673 1.514750e-02 3.105465e-01 0.6743060
## 1688 5.886724e-03 2.741942e-01 0.7199191
## 1691 1.610648e-02 3.555564e-01 0.6283371
## 1695 1.813630e-02 2.980013e-01 0.6838624
## 1700 9.410474e-03 2.806773e-01 0.7099122
## 1702 3.296665e-03 2.642242e-01 0.7324792
## 1703 6.128064e-03 3.101618e-01 0.6837101
## 1709 4.253130e-03 2.931207e-01 0.7026262
## 1725 7.700965e-03 2.199747e-01 0.7723243
## 1735 4.431553e-03 2.122405e-01 0.7833279
## 1738 1.787772e-02 3.778412e-01 0.6042811
## 1743 3.781087e-03 2.025294e-01 0.7936895
## 1748 1.338158e-03 3.207747e-01 0.6778871
## 1750 1.651474e-02 1.708917e-01 0.8125936
## 1755 2.272990e-03 2.173765e-01 0.7803505
## 1757 1.514714e-02 2.237133e-01 0.7611396
## 1758 1.239633e-03 1.851938e-01 0.8135665
## 1760 6.673663e-03 2.076713e-01 0.7856550
## 1761 4.130259e-03 2.413481e-01 0.7545216
## 1765 4.366546e-03 3.013955e-01 0.6942379
## 1769 5.062092e-02 2.965477e-01 0.6528313
## 1771 3.585299e-03 2.563343e-01 0.7400804
## 1772 1.514656e-03 2.486446e-01 0.7498407
## 1777 1.365999e-03 3.000024e-01 0.6986316
## 1781 6.291590e-03 2.840316e-01 0.7096768
## 1787 3.430421e-03 1.937573e-01 0.8028123
## 1789 4.798485e-03 2.599391e-01 0.7352624
## 1790 1.743747e-02 3.152821e-01 0.6672805
## 1798 5.605047e-03 2.418645e-01 0.7525305
## 1803 1.269272e-07 1.422956e-01 0.8577043
## 1804 2.825656e-02 1.809784e-01 0.7907650
## 1807 4.607687e-03 3.415339e-01 0.6538584
## 1808 7.929074e-02 2.363492e-01 0.6843601
## 1809 7.880625e-03 2.863779e-01 0.7057415
## 1811 1.245536e-06 1.579223e-01 0.8420765
## 1820 4.134682e-03 2.253276e-01 0.7705377
## 1821 5.930502e-03 2.057087e-01 0.7883608
## 1828 6.976308e-03 2.334400e-01 0.7595837
## 1829 4.878515e-03 2.707972e-01 0.7243243
## 1834 1.359709e-02 2.801797e-01 0.7062232
## 1837 2.826592e-03 2.205191e-01 0.7766543
## 1838 3.572524e-03 3.431618e-01 0.6532657
## 1845 1.291472e-09 1.222129e-01 0.8777871
## 1848 5.873565e-03 2.470294e-01 0.7470971
## 1849 4.181864e-03 3.321668e-01 0.6636514
## 1855 4.870451e-03 1.410799e-01 0.8540497
## 1862 5.775690e-03 2.798809e-01 0.7143434
## 1865 1.036781e-02 4.730639e-01 0.5165683
## 1869 1.081032e-08 3.281984e-01 0.6718016
## 1870 1.769923e-03 3.081095e-01 0.6901205
## 1871 2.870045e-08 2.648642e-01 0.7351358
## 1875 1.391982e-02 2.637690e-01 0.7223112
## 1876 3.717912e-03 2.682720e-01 0.7280101
## 1878 6.780080e-09 2.807332e-01 0.7192668
## 1881 1.720553e-02 1.945910e-01 0.7882035
## 1883 5.323931e-02 9.192434e-02 0.8548364
## 1884 2.508176e-03 2.646893e-01 0.7328026
## 1885 1.947525e-02 1.522692e-01 0.8282556
## 1887 9.064122e-03 2.547228e-01 0.7362131
## 1890 1.116613e-03 2.171232e-01 0.7817602
## 1891 5.887565e-03 3.178288e-01 0.6762837
## 1893 3.402406e-03 1.642855e-01 0.8323121
## 1894 8.234762e-03 2.756120e-01 0.7161532
## 1895 6.736592e-07 3.967543e-01 0.6032450
## 1896 2.575513e-03 2.026596e-01 0.7947649
## 1898 1.521894e-02 1.665666e-01 0.8182145
## 1900 2.868557e-03 2.543097e-01 0.7428218
## 1901 4.549767e-07 1.243095e-01 0.8756900
## 1912 6.755747e-03 1.520676e-01 0.8411767
## 1914 4.671203e-03 2.682707e-01 0.7270581
## 1915 1.064627e-02 3.469254e-01 0.6424283
## 1917 7.032495e-03 2.482402e-01 0.7447273
## 1918 7.855510e-03 3.580124e-01 0.6341321
## 1919 4.839201e-03 2.705028e-01 0.7246580
## 1923 4.047917e-09 1.330261e-01 0.8669739
## 1924 1.275580e-03 2.169687e-01 0.7817557
## 1926 1.065308e-03 3.718454e-01 0.6270893
## 1929 5.241723e-03 2.539465e-01 0.7408118
## 1931 2.025623e-03 2.152030e-01 0.7827714
## 1933 1.480014e-03 3.146504e-01 0.6838695
## 1936 2.321260e-03 2.241325e-01 0.7735462
## 1937 1.521496e-02 2.125291e-01 0.7722559
## 1939 1.049821e-02 2.823001e-01 0.7072017
## 1940 1.782910e-02 2.270531e-01 0.7551178
## 1942 6.395143e-03 2.212719e-01 0.7723329
## 1948 3.640254e-03 2.692010e-01 0.7271587
## 1956 2.283754e-03 2.853293e-01 0.7123870
## 1957 1.917490e-03 2.410082e-01 0.7570743
## 1958 1.524063e-02 2.258380e-01 0.7589213
## 1961 1.602376e-02 2.278375e-01 0.7561388
## 1968 7.252282e-03 3.018174e-01 0.6909303
## 1969 4.802293e-03 2.253071e-01 0.7698906
## 1971 3.005108e-03 7.179157e-02 0.9252033
## 1972 9.791270e-03 2.282280e-01 0.7619807
## 1975 3.270504e-03 2.114233e-01 0.7853062
## 1979 2.384440e-03 2.228470e-01 0.7747686
## 1981 1.793659e-03 2.006424e-01 0.7975639
## 1985 4.595688e-03 1.718994e-01 0.8235049
## 1986 8.442938e-03 2.528692e-01 0.7386879
## 1988 7.261615e-03 1.789120e-01 0.8138264
## 1989 5.702973e-09 2.153581e-01 0.7846419
## 1990 7.198071e-10 1.214454e-01 0.8785546
## 1991 4.870448e-03 1.986667e-01 0.7964629
## 1994 2.285290e-03 2.621225e-01 0.7355922
## 1995 1.922319e-03 8.210199e-02 0.9159757
## 2000 7.369783e-03 2.045439e-01 0.7880863
## 2001 1.458448e-08 3.005981e-01 0.6994019
## 2002 9.691871e-03 2.347891e-01 0.7555191
## 2007 7.900401e-03 3.455207e-01 0.6465789
## 2014 2.967209e-03 2.935126e-01 0.7035202
## 2016 6.637480e-03 1.634427e-01 0.8299199
## 2024 3.419272e-03 4.118666e-01 0.5847142
## 2026 1.152242e-02 2.556823e-01 0.7327953
## 2027 6.015632e-03 1.573966e-01 0.8365878
## 2028 3.142309e-03 2.629561e-01 0.7339016
## 2029 3.894006e-03 2.674852e-01 0.7286208
## 2030 3.708555e-03 2.976857e-01 0.6986057
## 2032 5.030294e-03 2.538923e-01 0.7410774
## 2039 1.226130e-02 2.830919e-01 0.7046468
## 2045 2.724880e-02 2.771711e-01 0.6955801
## 2047 8.579284e-03 3.553930e-01 0.6360278
## 2049 8.579284e-03 3.553930e-01 0.6360278
## 2050 3.448656e-03 2.636618e-01 0.7328896
## 2051 1.154295e-02 1.504794e-01 0.8379777
## 2055 1.112998e-02 2.215465e-01 0.7673235
## 2062 1.123213e-08 1.689793e-01 0.8310206
## 2064 1.020569e-03 1.991429e-01 0.7998365
## 2065 7.077102e-09 2.916806e-01 0.7083194
## 2068 2.053875e-03 3.635444e-01 0.6344017
## 2070 3.396479e-03 2.535127e-01 0.7430908
## 2079 3.892470e-02 2.270250e-01 0.7340503
## 2089 3.748779e-03 2.685735e-01 0.7276778
## 2091 4.712632e-04 1.045371e-01 0.8949917
## 2096 5.215856e-03 2.968565e-01 0.6979276
## 2098 9.645930e-03 3.241527e-01 0.6662014
## 2106 1.470312e-02 2.341829e-01 0.7511140
## 2107 2.791244e-03 2.567821e-01 0.7404267
## 2111 7.299687e-03 1.765126e-01 0.8161877
## 2113 2.498852e-03 1.919921e-01 0.8055090
## 2116 4.362869e-03 1.767472e-01 0.8188899
## 2125 1.660310e-02 1.894589e-01 0.7939380
## 2127 2.254476e-03 2.827521e-01 0.7149935
## 2130 3.667234e-02 2.423744e-01 0.7209533
## 2133 1.055717e-02 3.465867e-01 0.6428561
## 2134 7.529623e-03 3.519362e-01 0.6405342
## 2136 3.147733e-03 2.244517e-01 0.7724006
## 2137 6.084350e-03 4.027712e-01 0.5911445
## 2142 3.047663e-03 2.479230e-01 0.7490293
## 2143 4.646663e-03 1.883455e-01 0.8070078
## 2148 1.775922e-10 8.732422e-02 0.9126758
## 2153 4.539654e-03 2.565253e-01 0.7389351
## 2155 9.179238e-03 2.745647e-01 0.7162561
## 2156 5.523933e-15 9.598428e-02 0.9040157
## 2160 9.002100e-03 2.148504e-01 0.7761475
## 2163 1.263275e-02 2.512900e-01 0.7360773
## 2164 4.307184e-03 2.542963e-01 0.7413965
## 2174 4.576284e-03 2.695322e-01 0.7258915
## 2182 2.612628e-02 3.817557e-01 0.5921180
## 2198 2.071294e-02 3.826253e-01 0.5966617
## 2205 7.793010e-10 1.855263e-01 0.8144737
## 2207 9.305799e-02 2.731285e-01 0.6338135
## 2210 1.356466e-02 2.768814e-01 0.7095540
## 2212 1.327440e-02 3.641613e-01 0.6225643
## 2214 1.942381e-03 1.965063e-01 0.8015513
## 2218 5.413942e-03 4.411591e-01 0.5534270
## 2219 5.563265e-03 1.280150e-01 0.8664218
## 2221 2.979546e-03 2.766089e-01 0.7204115
## 2223 2.096031e-09 1.594350e-01 0.8405650
## 2231 6.751019e-08 1.591230e-01 0.8408770
## 2233 1.701275e-03 1.770596e-01 0.8212391
## 2239 6.566704e-03 1.487370e-01 0.8446963
## 2246 1.311083e-02 2.194378e-01 0.7674513
## 2248 1.189740e-03 1.414389e-01 0.8573713
## 2250 4.318306e-03 1.765647e-01 0.8191170
## 2252 3.077001e-03 2.601519e-01 0.7367711
## 2255 1.084879e-02 2.795557e-01 0.7095955
## 2258 4.499485e-03 3.076605e-01 0.6878400
## 2259 1.026733e-02 2.192127e-01 0.7705199
## 2261 1.579215e-02 1.953291e-01 0.7888788
## 2264 4.414925e-03 3.055467e-01 0.6900383
## 2266 2.801524e-02 3.298512e-01 0.6421335
## 2269 4.831100e-03 2.081203e-01 0.7870486
## 2275 4.659274e-03 2.322457e-01 0.7630950
## 2280 4.204814e-03 2.112545e-01 0.7845407
## 2286 5.404981e-09 2.063714e-01 0.7936286
## 2288 7.600893e-04 1.983018e-01 0.8009381
## 2293 9.634507e-04 2.068932e-01 0.7921433
## 2297 4.977530e-20 3.634965e-01 0.6365035
## 2303 4.206108e-02 3.609940e-01 0.5969449
## 2305 8.982359e-03 1.838836e-01 0.8071341
## 2308 1.399930e-07 4.348485e-01 0.5651514
## 2309 4.154621e-09 1.615549e-01 0.8384451
## 2312 1.659375e-03 2.326179e-01 0.7657227
## 2313 1.777811e-02 3.668495e-01 0.6153724
## 2319 5.598659e-04 1.152080e-01 0.8842321
## 2323 6.216482e-04 1.871726e-01 0.8122057
## 2328 9.687285e-04 1.596565e-01 0.8393747
## 2332 1.739095e-03 1.783225e-01 0.8199384
## 2333 7.669095e-03 2.342822e-01 0.7580487
## 2334 3.874605e-02 9.022239e-02 0.8710316
## 2337 5.121150e-03 3.157522e-01 0.6791266
## 2339 1.191199e-03 1.114394e-01 0.8873694
## 2343 9.674281e-09 2.351151e-01 0.7648849
## 2344 8.948855e-03 2.468824e-01 0.7441688
## 2346 3.129346e-02 3.016843e-01 0.6670222
## 2352 2.562315e-02 2.823124e-01 0.6920644
## 2355 1.106764e-02 2.627769e-01 0.7261555
## 2359 3.291726e-02 3.941700e-01 0.5729127
## 2368 3.251389e-04 1.186270e-01 0.8810478
## 2371 3.081375e-02 3.215325e-01 0.6476537
## 2374 3.183060e-04 1.399471e-01 0.8597346
## 2375 4.200944e-04 1.367796e-01 0.8628003
## 2376 3.084433e-02 4.632196e-01 0.5059360
## 2381 1.006068e-03 1.357655e-01 0.8632284
## 2382 1.094223e-02 2.425457e-01 0.7465121
## 2383 4.448766e-09 1.012285e-01 0.8987715
## 2395 1.407336e-02 4.598588e-01 0.5260679
## 2396 8.949983e-03 2.415040e-01 0.7495460
## 2398 7.906912e-04 1.266219e-01 0.8725874
## 2401 1.019491e-03 1.514749e-01 0.8475056
## 2405 7.127560e-03 2.439171e-01 0.7489553
## 2411 3.238824e-03 2.685409e-01 0.7282203
## 2412 6.950477e-04 1.520881e-01 0.8472168
## 2418 2.748800e-12 4.336389e-01 0.5663611
## 2427 4.339953e-09 2.351338e-01 0.7648662
## 2430 1.425961e-08 1.422673e-01 0.8577327
## 2434 7.753255e-03 2.681565e-01 0.7240902
## 2435 7.762968e-04 1.506866e-01 0.8485371
## 2438 1.384277e-03 1.700852e-01 0.8285305
## 2439 3.415592e-02 2.475042e-01 0.7183398
## 2446 1.522713e-03 2.162645e-01 0.7822128
## 2454 1.748775e-03 7.366728e-02 0.9245839
## 2456 1.535985e-02 2.175404e-01 0.7670998
## 2458 2.523677e-03 1.275232e-01 0.8699531
## 2459 4.061306e-02 2.471234e-01 0.7122636
## 2462 1.013907e-02 2.079318e-01 0.7819291
## 2466 2.076580e-02 2.569904e-01 0.7222438
## 2472 5.045031e-03 2.619167e-01 0.7330382
## 2475 9.148858e-03 2.378007e-01 0.7530504
## 2476 1.897418e-03 1.400934e-01 0.8580092
## 2478 5.233875e-02 4.050584e-01 0.5426028
## 2481 1.462927e-02 1.768866e-01 0.8084841
## 2484 1.106459e-02 2.819183e-01 0.7070171
## 2491 2.037995e-03 1.953561e-01 0.8026059
## 2495 8.504954e-03 2.097113e-01 0.7817837
## 2496 6.449708e-03 3.060141e-01 0.6875362
## 2498 4.443941e-03 2.557157e-01 0.7398403
## 2499 7.731262e-04 1.870262e-01 0.8122007
## 2500 6.420211e-02 3.663408e-01 0.5694571
## 2501 7.851472e-04 1.259597e-01 0.8732551
## 2504 1.447557e-02 2.673637e-01 0.7181607
## 2505 1.134336e-02 2.029598e-01 0.7856969
## 2507 2.776837e-03 1.873370e-01 0.8098862
## 2510 4.944941e-03 2.607588e-01 0.7342963
## 2511 7.801000e-04 1.501788e-01 0.8490411
## 2516 3.623177e-03 2.358507e-01 0.7605261
## 2518 6.299823e-03 3.433544e-01 0.6503458
## 2519 2.339968e-02 2.172511e-01 0.7593492
## 2522 5.499130e-03 2.568819e-01 0.7376189
## 2524 1.682749e-02 2.669303e-01 0.7162422
## 2526 2.400290e-03 2.544626e-01 0.7431371
## 2530 1.989283e-02 2.174412e-01 0.7626660
## 2537 1.174617e-02 2.835858e-01 0.7046680
## 2546 3.717912e-04 1.133318e-01 0.8862964
## 2553 3.344485e-04 1.212808e-01 0.8783848
## 2564 1.107785e-02 3.004938e-01 0.6884283
## 2566 6.244556e-08 2.913803e-01 0.7086196
## 2567 8.400647e-10 1.396300e-01 0.8603700
## 2568 2.449452e-02 2.782047e-01 0.6973008
## 2573 3.068986e-04 1.394234e-01 0.8602697
## 2576 5.255850e-02 2.913324e-01 0.6561091
## 2587 3.202060e-04 1.287692e-01 0.8709106
## 2588 4.517989e-08 2.779352e-01 0.7220648
## 2589 9.022374e-04 1.249535e-01 0.8741443
## 2590 2.030821e-02 2.427041e-01 0.7369877
## 2591 4.285444e-03 3.056239e-01 0.6900907
## 2594 5.396102e-03 2.779242e-01 0.7166797
## 2595 8.394930e-03 3.655835e-01 0.6260215
## 2597 1.494770e-02 1.861368e-01 0.7989155
## 2599 7.658812e-04 1.586846e-01 0.8405495
## 2602 4.622802e-05 1.017179e-01 0.8982359
## 2604 1.460571e-03 2.067376e-01 0.7918018
## 2606 1.997474e-04 6.454274e-02 0.9352575
## 2608 2.272575e-03 1.792962e-01 0.8184312
## 2609 1.329720e-02 3.175121e-01 0.6691907
## 2613 1.426647e-02 3.323266e-01 0.6534070
## 2617 5.245816e-03 2.269460e-01 0.7678081
## 2619 7.211077e-03 2.432822e-01 0.7495067
## 2631 1.099129e-07 3.304037e-01 0.6695962
## 2634 5.131254e-03 2.407892e-01 0.7540795
## 2635 1.486053e-02 2.970631e-01 0.6880763
## 2636 5.661542e-03 2.783807e-01 0.7159577
## 2637 1.199029e-02 2.940589e-01 0.6939508
## 2641 8.851275e-04 1.567383e-01 0.8423765
## 2642 7.081420e-04 1.397964e-01 0.8594955
## 2644 5.678411e-09 2.379824e-01 0.7620176
## 2649 1.138556e-04 1.036604e-01 0.8962257
## 2653 3.060107e-03 2.178668e-01 0.7790731
## 2654 1.019558e-02 3.470242e-01 0.6427802
## 2660 6.132511e-03 2.722438e-01 0.7216237
## 2662 2.661886e-05 9.059807e-02 0.9093753
## 2663 1.676184e-02 2.353031e-01 0.7479350
## 2664 1.405497e-03 1.731134e-01 0.8254811
## 2669 5.260583e-03 2.176168e-01 0.7771226
## 2670 1.304039e-02 3.376571e-01 0.6493025
## 2672 3.850818e-03 2.449928e-01 0.7511563
## 2675 2.330244e-02 8.276851e-02 0.8939290
## 2676 1.889314e-02 2.963084e-01 0.6847984
## 2680 6.359210e-04 1.207794e-01 0.8785846
## 2682 6.790793e-03 2.513719e-01 0.7418373
## 2683 1.047738e-02 2.787431e-01 0.7107795
## 2684 2.253298e-02 3.765515e-01 0.6009155
## 2685 1.181480e-02 2.385514e-01 0.7496338
## 2688 3.268735e-03 2.270649e-01 0.7696663
## 2698 5.796030e-02 2.443239e-01 0.6977158
## 2699 9.713780e-04 1.444800e-01 0.8545487
## 2704 3.680546e-03 2.684614e-01 0.7278580
## 2709 3.098563e-03 2.341633e-01 0.7627381
## 2710 1.158001e-02 2.641308e-01 0.7242892
## 2713 1.112689e-02 3.658597e-01 0.6230134
## 2717 1.414415e-03 1.647589e-01 0.8338267
## 2719 1.083106e-02 2.051020e-01 0.7840670
## 2730 4.845372e-03 2.264771e-01 0.7686775
## 2735 2.844861e-05 7.311637e-02 0.9268552
## 2740 5.180692e-03 2.081510e-01 0.7866683
## 2748 4.586324e-03 2.618438e-01 0.7335699
## 2749 5.686952e-03 1.546775e-01 0.8396356
## 2751 1.076962e-02 3.061370e-01 0.6830934
## 2754 7.242504e-03 3.397141e-01 0.6530434
## 2762 5.144433e-04 1.041881e-01 0.8952975
## 2768 3.717632e-03 1.900639e-01 0.8062185
## 2769 4.938638e-03 2.604706e-01 0.7345907
## 2777 5.443703e-04 1.056053e-01 0.8938504
## 2784 1.299966e-02 3.756681e-01 0.6113323
## 2786 1.471325e-03 2.106147e-01 0.7879139
## 2788 3.014538e-03 1.930997e-01 0.8038858
## 2792 6.580332e-03 2.856552e-01 0.7077645
## 2799 8.124396e-03 2.001387e-01 0.7917369
## 2801 3.268921e-02 2.570913e-01 0.7102195
## 2806 5.264780e-04 1.371966e-01 0.8622770
## 2813 1.107206e-04 8.433579e-02 0.9155535
## 2814 3.215454e-04 9.401763e-02 0.9056608
## 2815 6.117237e-03 2.622343e-01 0.7316484
## 2819 5.577054e-04 1.265292e-01 0.8729131
## 2824 6.397823e-03 2.079235e-01 0.7856787
## 2825 1.364533e-03 2.017197e-01 0.7969157
## 2828 2.035327e-03 1.898178e-01 0.8081469
## 2831 2.873905e-03 2.106423e-01 0.7864838
## 2835 4.612171e-04 1.534590e-01 0.8460798
## 2848 7.678105e-03 2.497091e-01 0.7426128
## 2852 2.248558e-02 2.970217e-01 0.6804927
## 2853 5.277692e-03 2.075296e-01 0.7871927
## 2857 8.323150e-04 1.653649e-01 0.8338028
## 2861 3.744721e-03 2.700426e-01 0.7262127
## 2864 2.806377e-02 2.767179e-01 0.6952183
## 2868 3.253169e-03 2.525346e-01 0.7442122
## 2869 1.017427e-03 1.985094e-01 0.8004732
## 2880 1.551660e-02 3.039777e-01 0.6805057
## 2888 8.852432e-03 2.130863e-01 0.7780613
## 2889 8.784890e-04 1.540340e-01 0.8450875
## 2890 2.142438e-03 1.457998e-01 0.8520578
## 2892 3.158104e-03 3.059200e-01 0.6909218
## 2894 3.022551e-04 1.269169e-01 0.8727808
## 2900 4.977706e-04 1.354197e-01 0.8640826
## 2909 3.078147e-04 1.286750e-01 0.8710172
## 2916 5.212161e-03 2.633176e-01 0.7314702
## 2920 6.041814e-02 2.487663e-01 0.6908156
## 2927 2.837540e-02 3.193400e-01 0.6522846
## 2930 1.713778e-02 1.776690e-01 0.8051932
## 2932 6.265605e-08 2.191070e-01 0.7808929
## 2939 3.259311e-08 1.581216e-01 0.8418784
## 2942 3.348465e-02 3.033450e-01 0.6631703
## 2947 3.232285e-02 2.884685e-01 0.6792087
## 2948 2.677097e-02 2.229042e-01 0.7503249
## 2952 5.240424e-03 3.334954e-01 0.6612641
## 2956 5.940691e-03 2.796474e-01 0.7144119
## 2963 9.417461e-03 1.657862e-01 0.8247964
## 2965 1.653819e-02 2.929722e-01 0.6904896
## 2970 2.952292e-03 1.693791e-01 0.8276686
## 2972 5.222319e-03 2.984269e-01 0.6963508
## 2975 2.648235e-02 3.768789e-01 0.5966388
## 2976 8.097492e-02 1.860187e-01 0.7330064
## 2980 7.353931e-02 1.852034e-01 0.7412573
## 2984 7.964653e-03 3.099865e-01 0.6820489
## 2991 6.597747e-03 2.636983e-01 0.7297039
## 2997 9.505232e-03 3.186154e-01 0.6718794
## 3002 3.169239e-02 3.178262e-01 0.6504814
## 3008 1.015737e-02 3.343984e-01 0.6554443
## 3010 4.424223e-03 2.426396e-01 0.7529361
## 3013 2.528376e-02 1.629966e-01 0.8117196
## 3015 9.772135e-03 2.953323e-01 0.6948956
## 3021 3.060370e-02 3.422014e-01 0.6271949
## 3023 6.142129e-09 1.812357e-01 0.8187643
## 3024 2.505498e-02 3.224637e-01 0.6524813
## 3026 7.519163e-04 1.494382e-01 0.8498099
## 3032 5.823460e-03 3.400365e-01 0.6541401
## 3038 6.586725e-08 2.501256e-01 0.7498744
## 3041 8.050661e-04 1.005968e-01 0.8985981
## 3046 7.019766e-03 2.382138e-01 0.7547664
## 3047 8.120622e-10 1.130687e-01 0.8869313
## 3055 4.128480e-03 2.363647e-01 0.7595068
## 3062 1.930667e-02 1.902340e-01 0.7904594
## 3063 3.221598e-06 4.738256e-01 0.5261712
## 3072 1.443792e-02 1.874071e-01 0.7981550
## 3074 1.111135e-02 2.238576e-01 0.7650311
## 3084 1.652381e-03 1.630791e-01 0.8352685
## 3091 1.339952e-02 3.749046e-01 0.6116959
## 3098 1.065326e-08 1.704534e-01 0.8295466
## 3099 4.439378e-03 2.319276e-01 0.7636330
## 3104 5.650473e-03 1.544747e-01 0.8398748
## 3109 3.125865e-02 2.654886e-01 0.7032527
## 3110 1.494120e-02 3.405195e-01 0.6445393
## 3117 1.353845e-03 1.812584e-01 0.8173878
## 3118 4.002156e-02 4.654946e-01 0.4944838
## 3120 2.914473e-03 2.468134e-01 0.7502721
## 3129 7.337716e-03 2.573975e-01 0.7352648
## 3133 2.222827e-02 3.194144e-01 0.6583573
## 3140 7.426968e-06 5.517495e-06 0.9999871
## 3141 2.668440e-04 1.035081e-01 0.8962250
## 3143 9.899096e-03 2.730212e-01 0.7170797
## 3145 1.159659e-02 2.169675e-01 0.7714360
## 3148 2.645745e-02 4.000958e-01 0.5734467
## 3151 4.229962e-03 2.663911e-01 0.7293789
## 3152 4.926050e-03 2.598950e-01 0.7351789
## 3155 3.114010e-03 1.508500e-01 0.8460360
## 3156 2.643893e-04 1.366564e-01 0.8630792
## 3163 8.278517e-04 1.366102e-01 0.8625620
## 3165 4.294063e-02 2.661364e-01 0.6909230
## 3167 6.359282e-04 1.489312e-01 0.8504329
## 3169 6.282811e-03 2.965459e-01 0.6971712
## 3174 4.458056e-03 3.275562e-01 0.6679858
## 3175 1.658073e-02 3.243894e-01 0.6590298
## 3178 2.376482e-03 2.742147e-01 0.7234088
## 3181 4.568011e-03 2.309120e-01 0.7645200
## 3182 3.718316e-03 1.838756e-01 0.8124061
## 3186 1.544455e-02 3.071205e-01 0.6774349
## 3188 2.711614e-02 1.092221e-01 0.8636618
## 3189 2.634943e-04 1.212244e-01 0.8785121
## 3191 8.299670e-08 3.947937e-01 0.6052062
## 3196 3.870952e-03 2.960595e-01 0.7000695
## 3200 6.750845e-04 1.391683e-01 0.8601567
## 3201 1.029653e-02 2.944179e-01 0.6952856
## 3205 3.626325e-05 8.782932e-02 0.9121344
## 3207 9.685807e-03 2.947788e-01 0.6955354
## 3208 8.740101e-05 7.652158e-02 0.9233910
## 3209 7.141858e-13 2.111617e-01 0.7888383
## 3210 5.165424e-02 3.357813e-01 0.6125644
## 3212 2.625403e-02 3.169709e-01 0.6567751
## 3214 7.550720e-04 1.428208e-01 0.8564242
## 3218 2.559188e-04 1.352487e-01 0.8644954
## 3222 4.161673e-03 2.827595e-01 0.7130788
## 3234 3.187853e-04 1.282633e-01 0.8714180
## 3235 1.084951e-02 2.164813e-01 0.7726691
## 3238 6.296210e-03 2.834984e-01 0.7102054
## 3246 1.909895e-02 3.198484e-01 0.6610527
## 3249 6.252975e-03 2.873586e-01 0.7063885
## 3250 7.785393e-03 2.431527e-01 0.7490619
## 3252 4.453437e-02 3.269336e-01 0.6285321
## 3253 9.501502e-05 1.255052e-01 0.8743998
## 3255 4.412630e-08 3.169051e-01 0.6830948
## 3257 9.160188e-03 3.106357e-01 0.6802041
## 3262 2.070239e-04 7.146963e-06 0.9997858
## 3264 3.959185e-04 2.392921e-01 0.7603120
## 3266 2.373201e-04 1.340169e-01 0.8657458
## 3267 8.304340e-04 1.517510e-01 0.8474186
## 3268 5.960909e-04 1.740342e-01 0.8253697
## 3270 2.514370e-03 1.940521e-01 0.8034335
## 3271 4.258493e-02 3.536135e-01 0.6038015
## 3275 8.375972e-04 1.778476e-01 0.8213148
## 3281 1.341558e-02 3.079222e-01 0.6786622
## 3282 6.209962e-04 1.422757e-01 0.8571033
## 3283 2.972520e-03 4.181283e-01 0.5788992
## 3287 1.361923e-04 1.239255e-01 0.8759383
## 3288 1.557254e-03 2.577735e-01 0.7406692
## 3289 6.830705e-04 1.415938e-01 0.8577231
## 3295 7.729188e-03 4.201395e-01 0.5721313
## 3298 6.021170e-03 2.953282e-01 0.6986506
## 3300 3.287959e-03 3.105332e-01 0.6861788
## 3314 2.232912e-03 1.908792e-01 0.8068879
## 3316 5.888494e-03 2.790673e-01 0.7150442
## 3319 5.403021e-10 1.372993e-01 0.8627007
## 3320 3.754231e-04 1.179605e-01 0.8816641
## 3327 4.421744e-03 2.542564e-01 0.7413219
## 3329 4.081984e-09 1.870472e-01 0.8129528
## 3331 1.968206e-03 2.027207e-01 0.7953111
## 3340 5.680869e-03 1.897025e-01 0.8046166
## 3341 4.059780e-03 2.057112e-01 0.7902290
## 3344 6.113284e-04 1.446357e-01 0.8547530
## 3345 3.217132e-03 1.799599e-01 0.8168229
## 3346 7.830882e-02 3.235010e-01 0.5981902
## 3347 6.025264e-02 2.596864e-01 0.6800609
## 3354 1.755316e-02 2.799349e-01 0.7025119
## 3357 8.820896e-03 3.688444e-01 0.6223347
## 3359 1.591201e-03 1.853821e-01 0.8130267
## 3361 2.524688e-03 3.354657e-01 0.6620096
## 3363 7.803349e-05 8.820313e-02 0.9117188
## 3366 3.391910e-03 1.577001e-01 0.8389080
## 3370 9.973489e-03 3.559615e-01 0.6340650
## 3372 3.511068e-04 9.386999e-02 0.9057789
## 3376 2.000226e-08 8.761051e-02 0.9123895
## 3384 8.336655e-03 2.461405e-01 0.7455228
## 3386 1.307000e-03 1.094041e-01 0.8892889
## 3389 1.736638e-03 2.055199e-01 0.7927435
## 3390 6.650858e-04 1.753637e-01 0.8239712
## 3394 4.841967e-02 3.510197e-01 0.6005606
## 3398 3.847241e-09 1.416087e-01 0.8583913
## 3402 1.159481e-02 2.624689e-01 0.7259363
## 3405 1.810655e-04 9.368284e-02 0.9061361
## 3408 1.127280e-03 1.500042e-01 0.8488685
## 3413 6.119040e-04 1.931920e-01 0.8061961
## 3419 3.000188e-04 1.260850e-01 0.8736150
## 3421 3.303458e-15 1.081756e-01 0.8918244
## 3425 2.365192e-04 1.282505e-01 0.8715130
## 3426 2.680889e-04 1.227928e-01 0.8769391
## 3428 3.739631e-04 1.385470e-01 0.8610790
## 3431 5.337251e-04 1.213554e-01 0.8781108
## 3432 1.753239e-04 7.745181e-02 0.9223729
## 3445 6.673061e-03 3.360588e-01 0.6572682
## 3448 7.299216e-03 2.508762e-01 0.7418246
## 3451 9.144765e-02 3.863010e-01 0.5222514
## 3456 8.006184e-02 3.418715e-01 0.5780667
## 3457 2.676590e-02 4.642433e-01 0.5089908
## 3458 5.083070e-03 3.285757e-01 0.6663412
## 3463 1.177927e-02 2.886326e-01 0.6995881
## 3469 5.993421e-03 1.917421e-01 0.8022645
## 3471 8.062266e-03 1.835680e-01 0.8083697
## 3475 5.944434e-03 2.591681e-01 0.7348874
## 3476 7.141829e-03 2.956066e-01 0.6972515
## 3481 4.900943e-03 2.587462e-01 0.7363529
## 3482 2.591772e-02 2.725472e-01 0.7015351
## 3486 8.212499e-03 2.764990e-01 0.7152885
## 3489 1.842927e-02 2.473252e-01 0.7342456
## 3492 4.797245e-03 2.516253e-01 0.7435774
## 3494 1.833016e-03 1.556028e-01 0.8425641
## 3498 1.072120e-03 1.986025e-01 0.8003254
## 3499 4.657808e-04 1.324464e-01 0.8670878
## 3503 2.089122e-03 2.414918e-01 0.7564191
## 3504 6.468184e-03 2.713323e-01 0.7221995
## 3505 2.727576e-02 3.109066e-01 0.6618176
## 3506 2.785753e-03 2.253283e-01 0.7718859
## 3508 2.207722e-03 2.858429e-01 0.7119494
## 3511 5.806061e-04 1.591318e-01 0.8402876
## 3513 5.940302e-03 2.470347e-01 0.7470250
## 3515 2.585444e-03 2.119315e-01 0.7854831
## 3516 3.493016e-03 2.574117e-01 0.7390953
## 3518 1.873249e-02 2.931989e-01 0.6880686
## 3521 4.454802e-03 2.073590e-01 0.7881862
## 3525 1.179524e-02 2.562424e-01 0.7319624
## 3526 5.430147e-02 3.385523e-01 0.6071463
## 3530 5.659278e-03 2.439978e-01 0.7503430
## 3533 8.410519e-03 3.471327e-01 0.6444567
## 3535 1.337057e-02 3.149876e-01 0.6716418
## 3539 1.764923e-05 2.219580e-01 0.7780243
## 3540 2.511165e-01 2.563359e-01 0.4925476
## 3543 3.314367e-02 3.155464e-01 0.6513100
## 3544 1.191922e-03 1.228852e-01 0.8759228
## 3547 5.132442e-03 2.132492e-01 0.7816184
## 3549 1.873249e-02 2.931989e-01 0.6880686
## 3550 8.198237e-03 2.240559e-01 0.7677458
## 3553 5.971939e-03 1.681805e-01 0.8258475
## 3556 3.164375e-03 1.658224e-01 0.8310132
## 3561 5.047386e-03 2.284830e-01 0.7664696
## 3567 6.164744e-04 1.413598e-01 0.8580237
## 3573 9.069328e-03 2.885228e-01 0.7024079
## 3577 4.740748e-03 3.577799e-01 0.6374793
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## 3589 2.598589e-03 1.832697e-01 0.8141318
## 3590 2.640655e-02 3.018312e-01 0.6717622
## 3591 2.333883e-02 3.060069e-01 0.6706542
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## 3606 2.505800e-03 2.913003e-01 0.7061939
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## 3610 1.751292e-03 2.636004e-01 0.7346483
## 3620 1.992092e-02 1.674631e-01 0.8126160
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## 3623 2.699485e-02 2.948585e-01 0.6781467
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## 3640 3.988929e-04 1.933284e-01 0.8062727
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## 3777 2.978698e-01 2.002690e-01 0.5018612
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## 3788 5.776522e-03 3.376971e-01 0.6565263
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## 3856 1.051133e-07 1.445886e-01 0.8554113
## 3858 2.695473e-08 2.776989e-01 0.7223011
## 3860 4.099011e-04 1.740290e-01 0.8255611
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## 3873 9.354581e-03 3.420839e-01 0.6485615
## 3876 1.006280e-03 1.966017e-01 0.8023920
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## 3886 3.563582e-02 3.346224e-01 0.6297418
## 3889 3.746248e-03 2.274722e-01 0.7687816
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## 3894 4.027942e-03 1.676366e-01 0.8283354
## 3898 8.915007e-03 2.397245e-01 0.7513605
## 3900 8.439331e-03 2.813657e-01 0.7101949
## 3902 8.930239e-03 2.706257e-01 0.7204441
## 3903 2.423384e-03 3.389965e-01 0.6585802
## 3907 2.079375e-08 2.625873e-01 0.7374127
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## 3916 2.976346e-04 1.326084e-01 0.8670940
## 3918 2.112721e-02 3.149402e-01 0.6639326
## 3930 1.917314e-09 2.284401e-01 0.7715599
## 3935 2.048475e-02 2.740733e-01 0.7054420
## 3936 9.828455e-03 3.565851e-01 0.6335864
## 3938 2.676047e-02 2.817066e-01 0.6915329
## 3939 9.517138e-10 1.249229e-01 0.8750771
## 3940 1.505029e-02 2.863597e-01 0.6985900
## 3941 6.683919e-04 1.912829e-01 0.8080487
## 3945 4.620631e-03 2.801314e-01 0.7152480
## 3949 5.159363e-03 2.610048e-01 0.7338359
## 3953 5.882547e-04 1.815784e-01 0.8178333
## 3957 2.989565e-09 1.642415e-01 0.8357585
## 3960 2.064401e-02 3.034057e-01 0.6759503
## 3961 3.648863e-03 2.646307e-01 0.7317204
## 3977 5.159363e-03 2.610048e-01 0.7338359
## 3978 1.884397e-02 2.194902e-01 0.7616659
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## 3982 4.908622e-03 2.220357e-01 0.7730557
## 3985 4.233736e-07 1.852242e-01 0.8147754
## 3986 2.648748e-04 1.612744e-01 0.8384607
## 3988 1.032086e-02 2.488618e-01 0.7408174
## 3990 4.631446e-03 2.553572e-01 0.7400114
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## 3995 1.446615e-03 1.410991e-01 0.8574543
## 3997 6.326966e-04 1.363044e-01 0.8630629
## 4000 3.159608e-04 1.272565e-01 0.8724276
## 4001 1.530309e-02 2.810762e-01 0.7036207
## 4006 7.663457e-03 1.313684e-01 0.8609681
## 4010 1.383614e-02 1.861537e-01 0.8000102
## 4011 2.329653e-09 1.289076e-01 0.8710924
## 4012 2.642634e-03 2.467811e-01 0.7505763
## 4014 2.785649e-04 1.285324e-01 0.8711891
## 4023 1.052945e-03 1.584012e-01 0.8405458
## 4025 8.165081e-02 1.034082e-01 0.8149410
## 4029 4.631446e-03 2.553572e-01 0.7400114
## 4038 7.107376e-04 1.171006e-01 0.8821887
## 4040 4.244994e-10 6.866842e-02 0.9313316
## 4044 8.655452e-03 2.010798e-01 0.7902648
## 4045 1.565995e-02 2.272693e-01 0.7570708
## 4051 7.563555e-03 3.402919e-01 0.6521445
## 4052 6.063472e-03 2.695908e-01 0.7243457
## 4054 4.286981e-03 2.238686e-01 0.7718444
## 4070 6.536122e-03 3.148670e-01 0.6785969
## 4071 8.192051e-03 2.759043e-01 0.7159037
## 4074 4.109133e-02 3.179545e-01 0.6409542
## 4077 2.145849e-03 1.595267e-01 0.8383275
## 4083 6.155735e-04 1.411772e-01 0.8582072
## 4089 2.038983e-02 3.373054e-01 0.6423048
## 4092 5.272478e-04 1.083151e-01 0.8911577
## 4096 3.933132e-03 2.081036e-01 0.7879632
## 4097 1.559121e-02 2.384226e-01 0.7459862
## 4098 6.035228e-09 1.529606e-01 0.8470393
## 4103 7.345327e-03 1.941594e-01 0.7984953
## 4113 1.108697e-03 1.908063e-01 0.8080850
## 4116 1.874437e-02 2.727998e-01 0.7084558
## 4124 7.135608e-03 2.815486e-01 0.7113158
## 4126 2.272817e-02 4.280797e-01 0.5491922
## 4130 5.159363e-03 2.610048e-01 0.7338359
## 4135 9.371273e-04 1.749053e-01 0.8241576
## 4136 8.580714e-03 3.033831e-01 0.6880362
## 4138 1.204478e-02 2.453417e-01 0.7426135
## 4141 3.606586e-03 2.093803e-01 0.7870131
## 4142 4.292164e-07 2.775798e-01 0.7224198
## 4146 6.717869e-04 1.155502e-01 0.8837780
## 4152 1.406970e-02 2.777684e-01 0.7081619
## 4154 2.926053e-03 1.805101e-01 0.8165638
## 4156 1.575004e-03 1.067796e-01 0.8916454
## 4157 1.619190e-03 2.333813e-01 0.7649996
## 4159 5.159363e-03 2.610048e-01 0.7338359
## 4160 1.553278e-03 2.670060e-01 0.7314408
## 4170 1.180418e-02 3.536544e-01 0.6345414
## 4173 5.023394e-04 1.347292e-01 0.8647685
## 4175 1.065189e-02 3.025861e-01 0.6867620
## 4178 4.328816e-03 1.787063e-01 0.8169649
## 4180 8.512053e-03 3.944433e-01 0.5970446
## 4184 5.897241e-03 2.775984e-01 0.7165044
## 4191 5.820458e-04 1.393578e-01 0.8600601
## 4193 8.192051e-03 2.759043e-01 0.7159037
## 4194 3.750653e-08 3.238747e-01 0.6761253
## 4197 1.417972e-02 2.327596e-01 0.7530607
## 4199 1.930056e-02 3.408879e-01 0.6398115
## 4200 1.508075e-02 1.265369e-01 0.8583823
## 4203 6.862288e-03 2.408325e-01 0.7523052
## 4204 3.305160e-04 1.255177e-01 0.8741518
## 4212 6.195674e-02 2.399841e-01 0.6980592
## 4214 6.202959e-03 4.429639e-01 0.5508331
## 4215 8.391368e-03 3.464600e-01 0.6451486
## 4219 2.592150e-02 2.525402e-01 0.7215383
## 4223 9.703576e-03 2.967920e-01 0.6935044
## 4225 2.273086e-10 6.061742e-02 0.9393826
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## 4228 3.550096e-02 2.763725e-01 0.6881265
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## 4234 3.199665e-02 2.156920e-01 0.7523114
## 4242 6.039383e-04 1.389549e-01 0.8604411
## 4254 1.097562e-02 2.888200e-01 0.7002044
## 4256 2.367629e-02 2.999631e-01 0.6763606
## 4258 2.982403e-04 1.254228e-01 0.8742790
## 4271 1.256356e-03 2.086911e-01 0.7900525
## 4274 7.013069e-04 8.170470e-02 0.9175940
## 4278 2.236639e-03 2.213527e-01 0.7764106
## 4279 1.274096e-02 2.898859e-01 0.6973731
## 4281 7.831963e-03 2.426162e-01 0.7495518
## 4282 8.727423e-03 3.065008e-01 0.6847718
## 4286 5.240114e-03 3.332241e-01 0.6615358
## 4287 5.769836e-03 3.373636e-01 0.6568666
## 4289 1.837364e-02 2.833786e-01 0.6982478
## 4291 4.460254e-02 1.591646e-01 0.7962329
## 4293 8.663959e-03 2.630361e-01 0.7282999
## 4297 6.867451e-04 1.873391e-01 0.8119741
## 4300 9.135137e-09 1.451333e-01 0.8548667
## 4302 9.932074e-03 1.989038e-01 0.7911642
## 4305 4.209279e-04 2.458438e-05 0.9995545
## 4307 1.091120e-02 2.723625e-01 0.7167263
## 4309 2.982403e-04 1.254228e-01 0.8742790
## 4310 2.218368e-02 2.692956e-01 0.7085207
## 4312 2.915173e-02 3.109285e-01 0.6599198
## 4315 7.272482e-03 2.670580e-01 0.7256695
## 4323 9.463361e-03 1.902966e-01 0.8002401
## 4325 2.591343e-03 1.828207e-01 0.8145879
## 4328 5.649742e-04 1.466648e-01 0.8527702
## 4331 7.737059e-03 2.119168e-01 0.7803462
## 4332 3.214283e-03 1.843178e-01 0.8124679
## 4337 1.746728e-02 2.787547e-01 0.7037780
## 4341 1.659943e-03 2.478137e-01 0.7505263
## 4342 1.436212e-03 2.429700e-01 0.7555938
## 4344 2.343075e-04 6.589041e-02 0.9338753
## 4345 7.554573e-03 2.453708e-01 0.7470746
## 4346 8.728569e-02 2.387960e-01 0.6739184
## 4350 7.380267e-03 2.561068e-01 0.7365129
## 4354 4.400198e-02 2.571486e-01 0.6988495
## 4360 9.463715e-04 1.140714e-01 0.8849823
## 4364 8.842757e-03 3.497184e-01 0.6414388
## 4367 4.625503e-03 2.550728e-01 0.7403017
## 4370 2.290291e-08 1.315957e-01 0.8684043
## 4376 5.942680e-03 3.737906e-02 0.9566783
## 4378 7.167625e-03 3.367164e-01 0.6561160
## 4386 9.562873e-03 3.060551e-01 0.6843820
## 4387 3.063869e-01 3.697749e-01 0.3238381
## 4389 5.473331e-03 3.340996e-01 0.6604271
## 4395 4.100728e-02 4.012824e-01 0.5577103
## 4401 9.503305e-03 3.655125e-01 0.6249842
## 4404 1.950842e-02 3.191732e-01 0.6613184
## 4407 2.853326e-02 4.628930e-01 0.5085738
## 4411 7.765566e-03 2.202967e-01 0.7719377
## 4412 2.611221e-03 2.225538e-01 0.7748349
## 4413 7.962425e-03 3.432063e-01 0.6488313
## 4414 5.738830e-03 2.664222e-01 0.7278390
## 4418 1.275415e-02 3.103306e-01 0.6769153
## 4420 1.612246e-02 3.851396e-01 0.5987380
## 4422 5.141892e-03 3.295733e-01 0.6652848
## 4442 9.054434e-03 2.884587e-01 0.7024869
## 4444 2.487461e-08 2.444481e-01 0.7555519
## 4450 1.118032e-02 3.369715e-01 0.6518482
## 4451 4.642875e-02 3.272193e-01 0.6263519
## 4457 4.655029e-03 2.311355e-01 0.7642094
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## 4477 2.672502e-02 2.743149e-01 0.6989600
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## 4487 2.235553e-03 1.746235e-01 0.8231409
## 4499 1.219840e-03 2.084250e-01 0.7903552
## 4500 2.747730e-02 2.603474e-01 0.7121753
## 4503 6.311343e-03 2.855729e-01 0.7081158
## 4506 6.189604e-03 2.089539e-01 0.7848565
## 4515 1.882960e-02 3.144393e-01 0.6667311
## 4520 5.344163e-04 1.051612e-01 0.8943043
## 4525 4.869799e-08 2.697928e-01 0.7302071
## 4534 8.101855e-04 2.020151e-01 0.7971747
## 4536 2.913535e-08 2.979772e-01 0.7020228
## 4541 7.102209e-03 2.171486e-01 0.7757492
## 4542 3.499492e-02 2.255170e-01 0.7394881
## 4544 5.724320e-03 2.658389e-01 0.7284368
## 4545 9.670817e-03 2.341075e-01 0.7562216
## 4547 4.632001e-03 2.510584e-01 0.7443096
## 4548 1.534958e-02 1.767885e-01 0.8078619
## 4552 2.288007e-02 3.179531e-01 0.6591669
## 4554 1.007693e-01 2.200290e-01 0.6792017
## 4557 7.025857e-04 1.436230e-01 0.8556744
## 4560 8.013190e-03 1.448315e-01 0.8471553
## 4573 2.779128e-03 2.487225e-01 0.7484984
## 4574 2.227543e-04 1.292589e-01 0.8705183
## 4575 2.257446e-04 9.396389e-02 0.9058104
## 4576 5.565693e-04 1.427056e-01 0.8567379
## 4577 7.254146e-03 2.664752e-01 0.7262706
## 4580 2.217858e-03 1.508468e-01 0.8469353
## 4583 2.973546e-04 1.250928e-01 0.8746099
## 4585 4.869692e-03 2.573148e-01 0.7378155
## 4591 1.558482e-02 2.310641e-01 0.7533510
## 4593 2.546657e-07 7.997022e-02 0.9200295
## 4600 6.172826e-03 2.580021e-01 0.7358251
## 4601 4.370790e-03 2.517110e-01 0.7439182
## 4603 4.979129e-03 2.632971e-01 0.7317238
## 4604 6.368637e-03 2.221258e-01 0.7715055
## 4606 9.483454e-04 1.935289e-01 0.8055227
## 4607 3.118738e-02 2.814422e-01 0.6873704
## 4608 9.483454e-04 1.935289e-01 0.8055227
## 4619 4.053739e-04 1.160469e-01 0.8835477
## 4622 4.869692e-03 2.573148e-01 0.7378155
## 4624 1.101827e-02 2.635929e-01 0.7253888
## 4625 5.479088e-04 1.370230e-01 0.8624291
## 4626 1.685537e-02 2.244465e-01 0.7586981
## 4630 6.054496e-03 2.350016e-01 0.7589439
## 4632 1.757080e-02 2.939756e-01 0.6884536
## 4638 8.372243e-03 3.457879e-01 0.6458399
## 4639 5.139664e-03 2.601408e-01 0.7347196
## 4640 5.282896e-02 3.951641e-01 0.5520069
## 4641 1.176442e-02 3.526430e-01 0.6355926
## 4643 9.085552e-03 2.838034e-01 0.7071110
## 4646 2.780365e-02 3.026683e-01 0.6695281
## 4649 1.428189e-04 9.329850e-02 0.9065587
## 4650 8.993363e-03 3.755041e-01 0.6155025
## 4652 1.149828e-02 2.812010e-01 0.7073008
## 4660 1.018506e-02 2.054659e-01 0.7843490
## 4673 1.664796e-02 2.908333e-01 0.6925188
## 4674 4.616055e-02 3.214070e-01 0.6324325
## 4675 5.787274e-04 1.322280e-01 0.8671933
## 4680 4.607706e-03 2.542210e-01 0.7411713
## 4683 9.470344e-04 1.932942e-01 0.8057588
## 4687 2.384945e-02 3.159313e-01 0.6602192
## 4689 2.764590e-02 3.868947e-01 0.5854594
## 4692 5.899550e-04 1.990198e-01 0.8003903
## 4693 5.717075e-03 2.655476e-01 0.7287354
## 4695 1.175119e-02 3.523061e-01 0.6359427
## 4696 1.258680e-03 1.812209e-01 0.8175204
## 4697 1.167663e-02 2.544313e-01 0.7338921
## 4701 2.067814e-03 1.686907e-01 0.8292415
## 4704 3.098060e-02 3.189422e-01 0.6500772
## 4706 3.322525e-04 1.282687e-01 0.8713991
## 4707 2.820444e-02 3.878820e-01 0.5839136
## 4713 2.343296e-02 2.933044e-01 0.6832626
## 4714 1.188202e-03 1.698903e-01 0.8289215
## 4717 2.081229e-02 3.571409e-01 0.6220468
## 4726 1.209148e-02 2.783688e-01 0.7095397
## 4729 1.076506e-03 1.894195e-01 0.8095040
## 4730 1.734371e-03 1.562882e-01 0.8419774
## 4733 4.623545e-04 1.315838e-01 0.8679538
## 4734 1.706194e-02 3.011540e-01 0.6817841
## 4749 6.192718e-03 2.783796e-01 0.7154277
## 4753 4.549430e-03 2.152681e-01 0.7801825
## 4754 1.268954e-02 2.607066e-01 0.7266038
## 4755 1.060965e-03 1.361906e-01 0.8627485
## 4757 9.374172e-03 2.722980e-01 0.7183278
## 4758 2.336186e-03 1.689110e-01 0.8287528
## 4763 9.033827e-03 2.456790e-01 0.7452872
## 4764 2.838928e-04 1.234904e-01 0.8762257
## 4765 9.533972e-03 2.483594e-01 0.7421066
## 4771 8.683329e-05 1.086853e-01 0.8912278
## 4773 5.191984e-03 2.772565e-01 0.7175515
## 4774 2.537356e-03 2.441390e-01 0.7533237
## 4778 3.714673e-02 3.844252e-01 0.5784281
## 4783 5.493751e-03 2.821713e-01 0.7123349
## 4784 9.931078e-03 3.263463e-01 0.6637226
## 4785 8.474074e-03 3.314741e-01 0.6600519
## 4786 3.861998e-02 3.099764e-01 0.6514036
## 4787 2.898357e-03 2.256688e-01 0.7714329
## 4798 7.574480e-04 1.395901e-01 0.8596524
## 4799 3.977804e-04 1.781578e-01 0.8214444
## 4800 1.851200e-03 1.641425e-01 0.8340063
## 4806 6.985384e-03 2.449045e-01 0.7481101
## 4812 6.375445e-03 9.781384e-02 0.8958107
## 4815 1.516790e-04 1.239433e-01 0.8759051
## 4816 4.485311e-03 2.544177e-01 0.7410970
## 4818 3.346058e-04 8.632718e-02 0.9133382
## 4822 6.742472e-04 1.431428e-01 0.8561830
## 4826 2.231455e-09 8.710458e-02 0.9128954
## 4827 1.935407e-03 2.580237e-01 0.7400409
## 4833 1.084853e-03 2.058836e-01 0.7930316
## 4834 1.130555e-02 2.956868e-01 0.6930076
## 4839 7.229452e-03 3.163485e-01 0.6764220
## 4842 1.290912e-03 1.269584e-01 0.8717507
## 4844 9.798927e-04 1.532876e-01 0.8457325
## 4845 2.114025e-02 1.811811e-01 0.7976786
## 4850 7.037262e-04 1.327718e-01 0.8665244
## 4851 4.950510e-04 1.389122e-01 0.8605927
## 4854 4.844795e-03 2.561733e-01 0.7389819
## 4855 7.718655e-02 3.377356e-01 0.5850778
## 4864 1.452745e-02 3.486272e-01 0.6368454
## 4870 2.045789e-04 1.351796e-01 0.8646158
## 4872 1.736300e-03 1.775343e-01 0.8207294
## 4873 2.057940e-03 2.277060e-01 0.7702361
## 4875 1.504649e-03 2.440746e-01 0.7544207
## 4878 6.837941e-03 1.665133e-01 0.8266488
## 4880 2.811588e-03 1.769330e-01 0.8202554
## 4886 8.944396e-03 3.636996e-01 0.6273560
## 4892 3.814276e-08 2.189342e-01 0.7810657
## 4895 3.875962e-03 1.229588e-01 0.8731652
## 4898 6.764229e-03 2.742770e-01 0.7189588
## 4900 5.131596e-03 2.055767e-01 0.7892917
## 4902 6.379980e-03 2.223637e-01 0.7712564
## 4906 5.236648e-04 1.669990e-01 0.8324774
## 4907 6.492829e-04 1.399283e-01 0.8594225
## 4909 2.481731e-04 1.223821e-01 0.8773698
## 4915 4.691475e-04 1.060135e-01 0.8935173
## 4916 1.542327e-01 3.154638e-01 0.5303035
## 4918 5.808561e-03 1.650125e-01 0.8291789
## 4919 7.122702e-03 2.749743e-01 0.7179030
## 4922 2.921970e-03 2.369332e-01 0.7601449
## 4923 1.328740e-08 1.510907e-01 0.8489093
## 4926 3.732889e-04 1.394913e-01 0.8601355
## 4937 1.113450e-03 1.412449e-01 0.8576416
## 4938 1.549388e-02 1.894612e-01 0.7950449
## 4940 7.428878e-04 1.311153e-01 0.8681419
## 4946 4.981766e-04 1.773011e-01 0.8222007
## 4950 3.109242e-02 2.639367e-01 0.7049709
## 4954 2.257180e-03 2.735634e-02 0.9703865
## 4956 1.424975e-03 2.413149e-01 0.7572601
## 4958 2.151859e-04 1.125129e-01 0.8872719
## 4961 5.185162e-03 2.692318e-01 0.7255830
## 4962 7.695842e-03 1.984307e-01 0.7938734
## 4964 8.895304e-04 1.392478e-01 0.8598626
## 4967 7.560487e-04 1.833929e-01 0.8158511
## 4970 2.765386e-04 1.412377e-01 0.8584858
## 4971 6.190285e-03 2.767061e-01 0.7171036
## 4977 1.646059e-02 2.693175e-01 0.7142219
## 4979 1.646989e-09 1.103946e-01 0.8896054
## 4981 7.082214e-04 1.476341e-01 0.8516577
## 4990 9.614160e-04 1.059620e-01 0.8930766
## 4995 4.366753e-03 2.213644e-01 0.7742689
## 4996 6.674572e-03 2.825326e-01 0.7107929
## 5002 5.494846e-04 7.837724e-02 0.9210733
## 5005 3.129753e-04 8.338020e-02 0.9163068
## 5006 1.835459e-02 2.193078e-01 0.7623376
## 5007 5.149904e-04 1.345454e-01 0.8649396
## 5008 4.997238e-02 3.290867e-01 0.6209409
## 5009 3.887782e-03 2.629874e-01 0.7331248
## 5010 3.944718e-04 1.423967e-01 0.8572088
## 5013 4.916934e-04 7.469244e-02 0.9248159
## 5016 6.581384e-03 2.058172e-01 0.7876014
## 5017 1.964201e-03 1.342621e-01 0.8637737
## 5018 3.301342e-03 1.379020e-01 0.8587967
## 5025 1.514600e-02 2.896922e-01 0.6951618
## 5028 4.410380e-04 1.215834e-01 0.8779756
## 5031 2.116959e-02 2.926095e-01 0.6862209
## 5032 7.880617e-04 9.870652e-02 0.9005054
## 5034 4.206944e-04 1.305343e-01 0.8690450
## 5037 9.374803e-04 1.402445e-01 0.8588180
## 5041 1.619189e-03 1.527524e-01 0.8456284
## 5046 1.164854e-03 2.108033e-01 0.7880318
## 5049 7.085785e-04 1.476459e-01 0.8516455
## 5056 6.623294e-04 1.368407e-01 0.8624970
## 5059 3.055372e-02 3.145640e-01 0.6548823
## 5061 2.724273e-03 1.978822e-01 0.7993936
## 5062 4.551957e-03 8.954505e-02 0.9059030
## 5064 7.975253e-04 2.374967e-01 0.7617058
## 5067 1.035981e-03 1.294386e-01 0.8695254
## 5069 4.416717e-04 8.948313e-02 0.9100752
## 5088 4.951533e-03 3.019850e-01 0.6930635
## 5092 7.317318e-03 2.650287e-01 0.7276540
## 5093 1.007262e-02 2.887179e-01 0.7012095
## 5094 5.179030e-03 2.810385e-01 0.7137825
## 5100 1.296758e-02 3.462800e-01 0.6407524
## 5101 5.831459e-03 2.943700e-01 0.6997986
## 5104 1.318163e-02 3.573569e-01 0.6294615
## 5110 2.562169e-03 1.711124e-01 0.8263254
## 5112 6.781317e-04 1.671982e-01 0.8321237
## 5116 2.329745e-04 1.733684e-01 0.8263986
## 5119 4.085637e-06 2.293859e-01 0.7706100
## 5120 3.478761e-03 1.983020e-01 0.7982193
## 5121 3.684570e-03 1.888090e-01 0.8075065
## 5125 1.724990e-03 1.894420e-01 0.8088330
## 5131 2.280440e-02 3.668503e-01 0.6103453
## 5144 4.844795e-03 2.561733e-01 0.7389819
## 5146 3.713725e-03 1.778979e-01 0.8183883
## 5151 4.607444e-04 1.724988e-01 0.8270405
## 5155 2.309592e-02 2.548803e-01 0.7220238
## 5157 2.151625e-03 2.532483e-01 0.7446001
## 5158 1.879862e-02 1.224481e-01 0.8587533
## 5159 5.565209e-03 2.737104e-01 0.7207244
## 5166 1.106559e-02 2.180185e-01 0.7709159
## 5168 2.752498e-03 3.342947e-01 0.6629528
## 5170 3.851830e-04 1.599455e-01 0.8396693
## 5171 4.637325e-03 3.224060e-01 0.6729567
## 5173 1.771927e-02 2.831115e-01 0.6991693
## 5183 3.282562e-04 1.044468e-01 0.8952250
## 5185 1.069227e-02 3.072648e-01 0.6820429
## 5188 2.770212e-04 9.998225e-02 0.8997407
## 5190 5.686264e-03 2.551277e-01 0.7391860
## 5193 1.608505e-03 2.112121e-01 0.7871794
## 5196 5.507847e-03 2.395055e-01 0.7549866
## 5199 3.314904e-02 2.814082e-01 0.6854428
## 5205 8.567166e-03 2.767132e-01 0.7147196
## 5207 8.144039e-03 3.372780e-01 0.6545780
## 5212 6.764229e-03 2.742770e-01 0.7189588
## 5213 1.942681e-02 2.984265e-01 0.6821467
## 5214 7.121852e-03 2.520649e-01 0.7408132
## 5216 6.839793e-03 2.624812e-01 0.7306790
## 5218 7.342965e-03 2.829048e-01 0.7097522
## 5222 7.356585e-02 3.351498e-01 0.5912843
## 5226 2.430409e-02 2.926236e-01 0.6830723
## 5230 4.134781e-03 2.188221e-01 0.7770431
## 5237 1.242043e-03 1.240891e-01 0.8746689
## 5242 1.152222e-02 3.030362e-01 0.6854416
## 5245 8.286015e-04 1.441215e-01 0.8550499
## 5248 4.480502e-04 1.220432e-01 0.8775087
## 5252 1.124742e-03 1.560644e-01 0.8428108
## 5255 6.053858e-04 1.672123e-01 0.8321823
## 5257 2.781375e-03 1.219677e-01 0.8752510
## 5259 7.452721e-04 1.471596e-01 0.8520951
## 5263 3.300337e-04 1.095017e-01 0.8901683
## 5265 7.615719e-03 2.681557e-01 0.7242286
## 5266 1.092719e-02 3.129286e-01 0.6761442
## 5267 6.913522e-03 2.652468e-01 0.7278396
## 5275 6.551538e-03 2.624120e-01 0.7310365
## 5277 5.149904e-04 1.345454e-01 0.8649396
## 5279 2.047327e-02 3.012545e-01 0.6782722
## 5280 7.599461e-02 2.951225e-01 0.6288829
## 5283 3.763084e-02 4.009803e-01 0.5613888
## 5284 2.329745e-04 1.733684e-01 0.8263986
## 5289 2.894944e-02 3.090857e-01 0.6619649
## 5291 8.005866e-05 1.224826e-01 0.8774373
## 5293 1.026969e-04 1.363453e-01 0.8635520
## 5294 4.911654e-02 3.373991e-01 0.6134843
## 5296 2.502630e-04 9.761985e-02 0.9021299
## 5301 3.357071e-03 2.841034e-01 0.7125395
## 5304 6.226341e-03 2.465802e-01 0.7471935
## 5306 7.296995e-03 3.515582e-01 0.6411448
## 5308 4.413723e-03 2.366670e-01 0.7589192
## 5310 1.457127e-02 2.922230e-01 0.6932057
## 5312 4.583326e-10 7.710422e-02 0.9228958
## 5319 1.916931e-02 3.637051e-01 0.6171256
## 5321 2.247632e-02 3.620329e-01 0.6154908
## 5328 1.088455e-02 3.157541e-01 0.6733614
## 5329 1.058084e-03 9.931988e-02 0.8996220
## 5331 2.047327e-02 3.012545e-01 0.6782722
## 5335 6.589795e-03 3.511309e-01 0.6422793
## 5337 7.534340e-03 2.540117e-01 0.7384540
## 5339 9.316817e-03 3.137174e-01 0.6769657
## 5341 1.856409e-02 2.994122e-01 0.6820237
## 5342 6.440072e-02 3.785860e-01 0.5570133
## 5343 5.759800e-03 2.067306e-01 0.7875096
## 5352 2.218325e-02 3.130703e-01 0.6647465
## 5356 4.830749e-03 2.520116e-01 0.7431577
## 5358 6.470310e-03 2.952212e-01 0.6983085
## 5360 3.577308e-03 2.957281e-01 0.7006946
## 5361 2.252589e-02 2.064826e-01 0.7709916
## 5364 2.975185e-07 4.423167e-01 0.5576830
## 5365 8.267671e-04 1.555818e-01 0.8435914
## 5366 2.468396e-04 2.068182e-01 0.7929350
## 5371 8.195780e-02 2.534974e-01 0.6645448
## 5374 1.003513e-02 3.583352e-01 0.6316297
## 5375 3.378363e-03 2.349309e-01 0.7616907
## 5376 1.580731e-03 1.220116e-01 0.8764077
## 5377 3.842947e-03 2.303845e-01 0.7657726
## 5379 4.727641e-03 2.567170e-01 0.7385553
## 5380 2.495804e-03 1.926197e-01 0.8048845
## 5385 3.760027e-03 2.808522e-01 0.7153878
## 5389 2.124441e-03 2.162057e-01 0.7816699
## 5390 4.997894e-02 2.816514e-01 0.6683697
## 5392 6.075168e-04 1.395427e-01 0.8598498
## 5397 3.363678e-04 1.017084e-01 0.8979552
## 5398 4.525970e-02 3.232635e-01 0.6314768
## 5407 6.915220e-03 1.844139e-01 0.8086708
## 5414 3.825119e-02 2.744819e-01 0.6872669
## 5417 3.227336e-03 1.882707e-01 0.8085020
## 5418 1.569529e-02 2.864910e-01 0.6978137
## 5420 1.020102e-02 3.169068e-01 0.6728922
## 5431 7.529542e-02 3.898761e-01 0.5348285
## 5433 5.332319e-02 5.116186e-01 0.4350582
## 5437 4.099556e-03 1.205583e-01 0.8753422
## 5438 2.260083e-02 1.860568e-01 0.7913424
## 5442 8.762705e-03 3.470239e-01 0.6442134
## 5445 1.330154e-03 2.871486e-01 0.7115212
## 5449 2.249895e-03 2.657900e-01 0.7319601
## 5450 4.224059e-03 1.946477e-01 0.8011283
## 5456 3.342263e-04 1.292974e-01 0.8703684
## 5464 1.180186e-02 2.811033e-01 0.7070949
## 5466 8.364538e-03 3.555807e-01 0.6360548
## 5472 8.098195e-03 2.988587e-01 0.6930431
## 5479 5.294554e-02 3.963449e-01 0.5507096
## 5483 1.159715e-03 1.630231e-01 0.8358172
## 5491 7.359263e-03 2.778671e-01 0.7147736
## 5493 1.837447e-03 2.355940e-01 0.7625685
## 5495 1.178215e-02 2.932611e-01 0.6949567
## 5496 1.042849e-02 3.157642e-01 0.6738073
## 5498 9.731301e-03 3.123679e-01 0.6779008
## 5500 1.046089e-02 2.621208e-01 0.7274183
## 5501 1.060104e-02 1.986076e-01 0.7907913
## 5507 1.383137e-03 1.414381e-01 0.8571788
## 5508 4.742235e-03 2.048290e-01 0.7904288
## 5509 2.558715e-02 3.156849e-01 0.6587280
## 5510 1.856771e-02 3.588732e-01 0.6225591
## 5514 6.844838e-02 3.766645e-01 0.5548871
## 5515 2.108296e-02 3.110217e-01 0.6678954
## 5520 3.976280e-03 1.804767e-01 0.8155470
## 5526 2.136096e-02 2.675335e-01 0.7111056
## 5527 1.316597e-02 2.524609e-01 0.7343732
## 5528 3.768104e-03 3.416119e-01 0.6546200
## 5529 5.735709e-04 1.375622e-01 0.8618642
## 5531 1.296801e-02 2.517628e-01 0.7352692
## 5533 1.048765e-02 2.274483e-01 0.7620641
## 5534 2.519619e-02 2.805755e-01 0.6942283
## 5536 5.803141e-02 3.243992e-01 0.6175694
## 5541 2.311817e-02 3.791607e-01 0.5977211
## 5551 1.367527e-02 2.370260e-01 0.7492987
## 5555 1.044846e-02 3.006736e-01 0.6888779
## 5556 4.501825e-02 3.264928e-01 0.6284890
## 5559 8.305513e-03 3.434400e-01 0.6482544
## 5560 1.162520e-06 3.008488e-01 0.6991500
## 5565 6.180087e-03 2.693131e-01 0.7245068
## 5567 2.840353e-02 4.410458e-01 0.5305506
## 5568 1.916480e-02 3.046653e-01 0.6761699
## 5584 1.249470e-02 2.886668e-01 0.6988385
## 5585 2.344975e-02 3.137152e-01 0.6628351
## 5588 2.040038e-02 3.003350e-01 0.6792647
## 5589 1.526354e-02 2.929913e-01 0.6917452
## 5596 1.286011e-02 3.580412e-01 0.6290986
## 5607 1.645254e-02 2.119039e-01 0.7716435
## 5619 5.593644e-03 1.474773e-01 0.8469291
## 5620 7.783974e-04 6.939064e-02 0.9298310
## 5621 6.345104e-07 2.018350e-01 0.7981643
## 5626 9.005091e-03 2.693911e-01 0.7216038
## 5630 8.412255e-03 2.806656e-01 0.7109221
## 5632 2.633186e-02 5.058567e-01 0.4678115
## 5633 5.364535e-04 1.041732e-01 0.8952903
## 5634 2.393868e-02 3.797931e-01 0.5962682
## 5636 5.034914e-04 1.559989e-01 0.8434976
## 5637 1.274445e-02 3.519128e-01 0.6353428
## 5639 2.083183e-02 2.810919e-01 0.6980763
## 5640 2.651168e-02 2.503405e-01 0.7231478
## 5641 5.520878e-03 3.137087e-01 0.6807704
## 5643 5.074547e-04 1.328021e-01 0.8666904
## 5645 3.084461e-03 2.177345e-01 0.7791810
## 5647 3.737069e-03 2.542877e-01 0.7419752
## 5663 2.087024e-04 9.698518e-02 0.9028061
## 5666 1.992078e-03 1.625251e-01 0.8354828
## 5669 4.908464e-04 1.372560e-01 0.8622531
## 5673 1.163075e-02 2.528739e-01 0.7354953
## 5681 1.051359e-03 1.496343e-01 0.8493143
## 5684 1.838217e-02 2.917874e-01 0.6898304
## 5686 3.679109e-03 1.695390e-01 0.8267819
## 5687 5.896660e-03 2.717285e-01 0.7223748
## 5688 1.101011e-03 3.358991e-01 0.6629999
## 5690 5.806638e-04 1.427059e-01 0.8567134
## 5693 3.697563e-04 1.218601e-01 0.8777701
## 5697 3.706289e-02 3.227569e-01 0.6401802
## 5700 6.772039e-03 1.595901e-01 0.8336379
## 5706 1.304237e-02 3.913516e-01 0.5956060
## 5707 2.351841e-03 1.602509e-01 0.8373972
## 5715 7.705490e-04 1.336907e-01 0.8655388
## 5719 6.910230e-02 8.930042e-02 0.8415973
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## 5742 1.224079e-03 1.336808e-01 0.8650952
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## 5757 1.843487e-02 2.472274e-01 0.7343377
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## 6015 7.055850e-03 2.760217e-01 0.7169225
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## 6042 1.094308e-08 2.369309e-01 0.7630691
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## 6062 2.275582e-02 3.055422e-01 0.6717020
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## 6092 2.032708e-03 2.359183e-01 0.7620490
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## 6098 1.883965e-02 3.746615e-01 0.6064988
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## 6106 1.478778e-03 2.292959e-01 0.7692253
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## 6111 9.878640e-05 1.017234e-01 0.8981778
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## 6120 1.947304e-02 3.178146e-01 0.6627123
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## 6127 4.106135e-04 1.005210e-01 0.8990684
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## 6129 2.878700e-03 3.399688e-01 0.6571525
## 6130 4.783360e-04 1.307308e-01 0.8687909
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## 6140 5.410022e-03 2.642118e-01 0.7303782
## 6141 2.861062e-02 3.028668e-01 0.6685226
## 6142 7.974499e-03 2.724548e-01 0.7195707
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## 6145 5.035526e-03 2.555637e-01 0.7394007
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## 6151 5.035526e-03 2.555637e-01 0.7394007
## 6153 1.488735e-02 2.344756e-01 0.7506370
## 6156 7.765382e-03 2.429908e-01 0.7492438
## 6164 1.022010e-02 3.643208e-01 0.6254591
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## 6172 9.533136e-04 1.983477e-01 0.8006990
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## 6191 5.343916e-03 3.364632e-01 0.6581928
## 6197 1.294397e-02 3.568860e-01 0.6301700
## 6200 6.558722e-05 8.781896e-02 0.9121155
## 6203 1.993028e-01 2.389798e-01 0.5617174
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## 6270 1.794051e-02 2.579994e-01 0.7240601
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## 6276 2.693874e-03 1.550782e-01 0.8422280
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## 6281 9.716934e-04 1.776244e-01 0.8214039
## 6283 2.187871e-04 1.712887e-01 0.8284925
## 6284 2.972500e-03 2.858489e-01 0.7111786
## 6287 1.822349e-02 3.753952e-01 0.6063813
## 6288 7.502983e-03 3.080704e-01 0.6844266
## 6290 5.459331e-03 2.697638e-01 0.7247768
## 6292 7.210940e-03 2.000348e-01 0.7927543
## 6294 1.377826e-02 2.492251e-01 0.7369966
## 6301 2.028527e-02 3.080907e-01 0.6716240
## 6305 6.671710e-03 2.212559e-01 0.7720724
## 6308 9.315657e-03 2.833885e-01 0.7072959
## 6311 3.396708e-02 9.602093e-02 0.8700120
## 6312 9.671410e-03 2.170244e-01 0.7733042
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## 6319 8.653342e-03 3.433339e-01 0.6480127
## 6320 1.654992e-03 2.011433e-01 0.7972017
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## 6323 1.139590e-02 2.778147e-01 0.7107894
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## 6524 1.067679e-03 2.237995e-01 0.7751328
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## 6535 2.815887e-03 2.233319e-01 0.7738522
## 6536 8.384072e-08 1.221501e-01 0.8778498
## 6537 1.321269e-08 1.939476e-01 0.8060523
## 6544 5.471311e-02 3.302592e-01 0.6150277
## 6547 1.426725e-02 3.070264e-01 0.6787063
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## 6554 3.489639e-02 2.748511e-01 0.6902525
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## 6561 4.708676e-02 3.428680e-01 0.6100452
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## 6572 1.632381e-02 2.985100e-01 0.6851662
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## 6676 9.830033e-03 2.100957e-01 0.7800743
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## 6721 2.811460e-02 2.674823e-01 0.7044031
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## 6731 4.992419e-03 2.782821e-01 0.7167255
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## 6745 3.409038e-03 2.453527e-01 0.7512382
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## 6748 2.096076e-02 3.034590e-01 0.6755802
## 6751 1.253920e-03 1.826002e-01 0.8161458
## 6752 3.786768e-03 1.865051e-01 0.8097082
## 6755 1.189631e-02 2.797520e-01 0.7083517
## 6761 1.379968e-02 2.477651e-01 0.7384352
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## 6777 7.162918e-03 1.762302e-01 0.8166069
## 6779 7.036991e-02 2.951099e-01 0.6345202
## 6780 1.599435e-02 3.806405e-01 0.6033652
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## 6788 1.591540e-02 3.679299e-01 0.6161547
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## 6801 1.499534e-03 2.377861e-01 0.7607144
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## 6807 1.996654e-02 2.948484e-01 0.6851850
## 6812 3.841741e-03 2.246361e-01 0.7715222
## 6813 8.633839e-03 2.081027e-01 0.7832635
## 6814 1.648987e-02 3.374688e-01 0.6460413
## 6822 5.584405e-04 1.766421e-01 0.8227994
## 6823 2.024091e-02 1.142253e-01 0.8655338
## 6824 1.053084e-02 1.741407e-01 0.8153285
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## 6838 1.310165e-02 2.550133e-01 0.7318851
## 6839 1.739652e-02 2.280221e-01 0.7545814
## 6842 4.467148e-03 2.474730e-01 0.7480598
## 6843 1.951928e-02 2.520743e-01 0.7284064
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## 6863 8.343317e-03 2.701564e-01 0.7215003
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## 6872 7.226666e-03 2.427794e-01 0.7499939
## 6875 1.351524e-02 2.740396e-01 0.7124451
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## 6891 2.430267e-02 2.646307e-01 0.7110666
## 6893 1.214835e-02 2.329147e-01 0.7549369
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## 6898 3.041943e-04 1.829597e-01 0.8167361
## 6907 7.607366e-03 1.982089e-01 0.7941837
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## 6918 1.736350e-02 3.169582e-01 0.6656783
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## 6949 3.430797e-03 2.280176e-01 0.7685516
## 6950 2.078231e-07 1.510799e-01 0.8489199
## 6951 3.723027e-03 2.782329e-01 0.7180441
## 6952 5.637156e-03 2.501366e-01 0.7442263
## 6954 3.493696e-02 2.557023e-01 0.7093608
## 6957 6.544651e-03 2.923045e-01 0.7011508
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## 6961 9.341168e-03 2.731152e-01 0.7175436
## 6962 1.006344e-01 3.725037e-01 0.5268620
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## 6971 2.718265e-03 2.614997e-01 0.7357821
## 6974 1.794953e-02 2.889361e-01 0.6931144
## 6978 1.580919e-08 2.382864e-01 0.7617136
## 6980 4.637172e-03 2.589069e-01 0.7364559
## 6984 6.547677e-03 2.652852e-01 0.7281671
## 6985 4.614365e-03 2.644394e-01 0.7309462
## 6987 8.108450e-04 1.712352e-01 0.8279539
## 6992 4.698133e-03 1.436847e-01 0.8516171
## 6993 8.261667e-04 1.644006e-01 0.8347732
## 6995 9.506648e-03 2.317806e-01 0.7587128
## 6998 1.217949e-08 2.201167e-01 0.7798833
## 6999 1.251431e-02 2.476014e-01 0.7398843
## 7001 1.049611e-02 2.370525e-01 0.7524514
## 7004 5.913807e-03 2.704137e-01 0.7236725
## 7005 6.476619e-03 2.078204e-01 0.7857030
## 7006 1.450102e-02 2.920008e-01 0.6934982
## 7008 3.164407e-02 3.813785e-01 0.5869774
## 7009 4.283281e-03 1.747932e-01 0.8209235
## 7012 6.501425e-03 2.334194e-01 0.7600791
## 7014 1.631880e-02 1.884614e-01 0.7952198
## 7015 8.577658e-03 2.724864e-01 0.7189359
## 7016 1.656502e-09 1.537576e-01 0.8462424
## 7019 1.800428e-02 2.865397e-01 0.6954560
## 7026 6.467214e-03 2.719266e-01 0.7216062
## 7028 3.298396e-03 2.033377e-01 0.7933639
## 7029 1.403556e-03 1.304016e-01 0.8681949
## 7036 1.949001e-07 3.839040e-01 0.6160958
## 7043 9.703708e-03 2.639381e-01 0.7263582
## 7048 1.941506e-02 3.178017e-01 0.6627833
## 7051 8.473293e-04 1.306711e-01 0.8684815
## 7055 4.805203e-03 2.510818e-01 0.7441130
## 7058 4.971230e-03 2.527296e-01 0.7422992
## 7065 8.943827e-03 2.756630e-01 0.7153932
## 7066 7.221963e-03 2.339039e-01 0.7588741
## 7069 3.051733e-05 6.127263e-06 0.9999634
## 7073 1.344864e-02 2.599168e-01 0.7266346
## 7077 6.462793e-02 2.221484e-01 0.7132236
## 7079 3.616710e-03 2.852176e-01 0.7111656
## 7082 9.424966e-03 2.958399e-01 0.6947351
## 7083 3.320258e-03 2.575262e-01 0.7391535
## 7088 7.729890e-03 2.715348e-01 0.7207353
## 7091 8.493388e-03 3.461527e-01 0.6453539
## 7094 5.538090e-03 2.583290e-01 0.7361329
## 7100 5.995782e-03 1.513198e-01 0.8426844
## 7103 2.944699e-03 2.257150e-01 0.7713403
## 7106 1.257666e-03 1.797466e-01 0.8189957
## 7109 1.248187e-02 3.032705e-01 0.6842476
## 7110 5.323249e-03 2.350455e-01 0.7596313
## 7112 6.640071e-03 2.855774e-01 0.7077825
## 7114 8.198852e-03 2.796262e-01 0.7121750
## 7115 2.825089e-08 2.142730e-01 0.7857270
## 7116 8.189453e-04 1.829497e-01 0.8162313
## 7120 9.301290e-03 6.784992e-02 0.9228488
## 7130 1.425680e-02 1.819874e-01 0.8037558
## 7133 2.642958e-03 2.298500e-01 0.7675070
## 7139 6.608506e-03 2.525724e-01 0.7408191
## 7141 5.020428e-03 2.541658e-01 0.7408138
## 7144 5.531017e-03 2.580429e-01 0.7364261
## 7152 5.771020e-03 2.744036e-01 0.7198254
## 7155 4.488287e-03 2.047256e-01 0.7907861
## 7157 8.214084e-03 3.719685e-01 0.6198174
## 7158 2.522670e-03 2.857141e-01 0.7117632
## 7160 3.315905e-02 1.153623e-01 0.8514786
## 7161 7.325923e-04 1.356797e-01 0.8635877
## 7166 9.159135e-03 2.509817e-01 0.7398591
## 7167 9.248715e-03 3.094162e-01 0.6813351
## 7168 1.093643e-03 1.942276e-01 0.8046787
## 7178 2.007832e-02 2.999106e-01 0.6800111
## 7179 1.024498e-02 3.665375e-01 0.6232176
## 7181 7.583881e-03 1.583746e-01 0.8340415
## 7182 3.029533e-02 3.199479e-01 0.6497568
## 7186 4.982913e-03 2.621431e-01 0.7328740
## 7188 2.154107e-02 3.074031e-01 0.6710559
## 7191 7.019348e-03 2.717644e-01 0.7212163
## 7192 2.900321e-02 3.160806e-01 0.6549162
## 7196 6.802967e-02 3.585362e-01 0.5734341
## 7197 2.035597e-02 3.413453e-01 0.6382987
## 7202 5.550847e-03 2.045379e-01 0.7899113
## 7203 3.217509e-03 2.086068e-01 0.7881757
## 7207 3.016435e-03 3.126631e-01 0.6843204
## 7209 3.912372e-03 2.183491e-01 0.7777385
## 7210 1.048672e-02 2.679879e-01 0.7215253
## 7221 6.592333e-04 1.107594e-01 0.8885814
## 7222 2.775674e-03 1.854303e-01 0.8117940
## 7226 6.274140e-03 1.712459e-01 0.8224800
## 7228 6.069335e-03 3.119102e-01 0.6820205
## 7229 4.220535e-03 2.441756e-01 0.7516039
## 7237 1.142197e-02 2.992249e-01 0.6893531
## 7238 2.004862e-02 2.894409e-01 0.6905104
## 7241 3.172642e-02 3.066242e-01 0.6616494
## 7247 3.395752e-03 2.445211e-01 0.7520831
## 7248 2.082581e-03 1.938038e-01 0.8041136
## 7250 1.905221e-03 2.185059e-01 0.7795889
## 7270 5.038017e-03 2.975462e-01 0.6974158
## 7273 4.978252e-03 2.339632e-01 0.7610586
## 7275 5.240438e-03 2.552373e-01 0.7395223
## 7279 6.929615e-03 3.271433e-01 0.6659271
## 7280 4.134827e-03 1.671713e-01 0.8286939
## 7281 3.462718e-09 1.684244e-01 0.8315756
## 7282 2.045133e-02 3.045780e-01 0.6749707
## 7283 3.599118e-03 2.568479e-01 0.7395530
## 7285 4.405278e-03 2.621874e-01 0.7334074
## 7287 7.095515e-03 2.908182e-01 0.7020862
## 7294 1.734144e-03 2.557275e-01 0.7425383
## 7299 2.440874e-03 1.927855e-01 0.8047736
## 7302 1.541670e-03 2.404841e-01 0.7579743
## 7305 2.365058e-03 2.084414e-01 0.7891936
## 7314 9.324015e-03 2.586321e-01 0.7320439
## 7315 1.171094e-02 3.207159e-01 0.6675731
## 7317 2.666045e-03 2.628520e-01 0.7344820
## 7320 2.030102e-03 3.087983e-01 0.6891716
## 7330 1.175191e-03 2.355207e-02 0.9752727
## 7332 1.498066e-03 1.502270e-01 0.8482749
## 7337 5.752943e-04 1.153855e-01 0.8840392
## 7338 3.207645e-02 2.605819e-01 0.7073417
## 7339 4.589835e-03 2.580613e-01 0.7373488
## 7341 7.241736e-03 2.600568e-01 0.7327015
## 7342 4.709543e-03 1.818168e-01 0.8134737
## 7344 1.001643e-02 2.428163e-01 0.7471673
## 7346 6.587793e-02 1.305715e-01 0.8035505
## 7350 6.466270e-04 3.207759e-02 0.9672758
## 7355 3.054944e-02 7.780072e-02 0.8916498
## 7360 6.100954e-02 3.221559e-01 0.6168345
## 7364 1.668304e-03 1.839653e-01 0.8143664
## 7365 4.736516e-04 1.889278e-01 0.8105986
## 7366 1.103874e-02 2.372763e-01 0.7516850
## 7371 1.458039e-03 2.374803e-01 0.7610617
## 7373 1.418697e-02 2.470621e-01 0.7387510
## 7376 4.307527e-03 1.474611e-01 0.8482314
## 7380 2.642896e-04 1.207357e-01 0.8790000
## 7381 2.264150e-03 2.660616e-01 0.7316742
## 7387 3.856889e-03 2.192917e-01 0.7768514
## 7389 6.658194e-04 1.515160e-01 0.8478182
## 7392 5.471855e-02 8.437485e-02 0.8609066
## 7399 5.523949e-03 2.577570e-01 0.7367190
## 7402 3.996731e-03 2.548295e-01 0.7411738
## 7403 1.042957e-03 1.621340e-01 0.8368230
## 7408 1.121105e-04 1.149598e-01 0.8849280
## 7410 1.240181e-02 2.864130e-01 0.7011852
## 7412 5.338824e-02 2.663956e-01 0.6802162
## 7416 4.958444e-03 2.521653e-01 0.7428763
## 7419 1.669072e-02 2.076205e-01 0.7756888
## 7426 1.168400e-02 2.881861e-01 0.7001299
## 7428 7.645199e-03 2.397183e-01 0.7526365
## 7431 1.057695e-03 1.487993e-01 0.8501430
## 7432 1.102785e-03 2.021544e-01 0.7967428
## 7433 1.531484e-02 2.143598e-01 0.7703254
## 7436 4.985455e-04 1.788358e-01 0.8206657
## 7438 4.699151e-04 1.286914e-01 0.8708386
## 7440 1.173480e-02 2.552798e-01 0.7329854
## 7441 2.456188e-02 3.084807e-01 0.6669574
## 7447 9.422548e-04 1.963865e-01 0.8026712
## 7456 4.886336e-03 2.390550e-01 0.7560587
## 7457 8.273011e-03 2.719300e-01 0.7197969
## 7458 1.176137e-02 2.773843e-01 0.7108544
## 7462 2.300707e-02 2.453201e-01 0.7316728
## 7463 8.110158e-03 2.152110e-01 0.7766789
## 7466 7.451807e-03 2.792651e-01 0.7132831
## 7467 1.196216e-02 2.643769e-01 0.7236609
## 7472 6.020276e-03 2.527652e-01 0.7412145
## 7475 1.007690e-02 2.277723e-01 0.7621508
## 7484 5.102723e-03 1.987791e-01 0.7961181
## 7485 1.875146e-04 1.134674e-01 0.8863451
## 7487 2.900771e-03 2.069827e-01 0.7901166
## 7488 7.296630e-03 3.300164e-01 0.6626870
## 7490 1.276625e-02 2.703734e-01 0.7168604
## 7497 2.789109e-04 1.207120e-01 0.8790091
## 7498 1.700446e-02 2.958275e-01 0.6871681
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## 7507 1.933057e-02 2.270610e-01 0.7536085
## 7511 7.088389e-03 2.625124e-01 0.7303992
## 7519 5.939406e-04 1.394058e-01 0.8600002
## 7520 1.990986e-02 2.780280e-01 0.7020621
## 7523 1.941439e-03 2.695489e-01 0.7285096
## 7525 4.544325e-03 1.915628e-01 0.8038929
## 7526 1.171011e-06 2.478987e-01 0.7521002
## 7529 9.457559e-03 3.575716e-01 0.6329708
## 7530 9.255850e-03 1.983368e-01 0.7924073
## 7531 5.513842e-03 1.747116e-01 0.8197746
## 7532 4.199445e-04 1.253433e-01 0.8742367
## 7533 6.921498e-03 3.268156e-01 0.6662629
## 7534 9.992852e-04 1.481969e-01 0.8508038
## 7536 4.627314e-03 2.998810e-01 0.6954917
## 7538 4.055432e-02 3.083354e-01 0.6511103
## 7539 3.041661e-03 2.059126e-01 0.7910458
## 7543 3.569396e-03 2.893529e-01 0.7070777
## 7547 6.948317e-03 3.129699e-01 0.6800818
## 7549 1.345956e-03 1.436526e-01 0.8550015
## 7551 1.976601e-02 2.529377e-01 0.7272963
## 7552 1.119435e-02 2.894152e-01 0.6993904
## 7553 5.809058e-04 1.290638e-01 0.8703552
## 7556 1.533331e-02 2.828332e-01 0.7018335
## 7560 6.321898e-03 2.668186e-01 0.7268595
## 7566 3.712393e-03 2.771925e-01 0.7190952
## 7569 4.199445e-04 1.253433e-01 0.8742367
## 7570 5.574889e-03 2.268778e-01 0.7675473
## 7573 2.892874e-03 2.163146e-01 0.7807925
## 7580 2.731905e-03 1.865456e-01 0.8107225
## 7586 5.509532e-03 2.673666e-01 0.7271239
## 7597 1.380692e-03 2.347712e-01 0.7638481
## 7598 1.154049e-03 1.963559e-01 0.8024901
## 7601 1.171531e-02 2.556175e-01 0.7326672
## 7606 1.716587e-03 2.457286e-01 0.7525549
## 7612 8.444148e-04 1.437216e-01 0.8554340
## 7615 3.349921e-02 3.780841e-01 0.5884167
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## 7626 7.499388e-03 3.148853e-01 0.6776153
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## 7629 2.285521e-02 3.071584e-01 0.6699864
## 7631 1.034782e-02 2.875800e-01 0.7020722
## 7633 9.005294e-03 3.428885e-01 0.6481062
## 7640 4.349542e-03 2.552506e-01 0.7403999
## 7645 8.800791e-03 3.501365e-01 0.6410627
## 7650 2.213737e-02 3.050412e-01 0.6728214
## 7651 1.724624e-03 3.149542e-01 0.6833212
## 7652 1.380922e-02 3.882113e-01 0.5979795
## 7654 4.739509e-03 1.955602e-01 0.7997003
## 7655 4.446409e-03 2.400831e-01 0.7554705
## 7659 7.383910e-03 2.752561e-01 0.7173600
## 7660 6.534601e-03 2.102638e-01 0.7832016
## 7665 2.187143e-03 1.580925e-01 0.8397203
## 7673 2.805681e-02 2.940250e-01 0.6779182
## 7674 4.958444e-03 2.521653e-01 0.7428763
## 7676 9.898490e-05 1.114075e-01 0.8884936
## 7677 9.729514e-03 3.089970e-01 0.6812735
## 7678 8.682065e-03 2.487969e-01 0.7425210
## 7685 3.563687e-03 1.833607e-01 0.8130756
## 7692 1.195139e-02 3.766439e-01 0.6114047
## 7697 1.860615e-03 2.216023e-01 0.7765371
## 7700 3.001864e-02 3.778262e-01 0.5921552
## 7704 5.412752e-11 4.858971e-01 0.5141029
## 7709 8.990627e-04 2.203071e-01 0.7787939
## 7712 4.537255e-03 2.662421e-01 0.7292207
## 7720 2.487708e-03 2.349939e-01 0.7625184
## 7721 1.674105e-02 2.791935e-01 0.7040655
## 7729 2.059355e-03 2.405228e-01 0.7574178
## 7730 1.104749e-03 1.547961e-01 0.8440991
## 7736 1.964452e-03 2.321331e-01 0.7659025
## 7739 5.663524e-03 2.833807e-01 0.7109558
## 7740 2.025252e-02 3.553822e-01 0.6243653
## 7741 7.296630e-03 3.300164e-01 0.6626870
## 7742 2.046949e-02 2.606341e-01 0.7188964
## 7743 1.502335e-03 1.405451e-01 0.8579525
## 7750 2.813111e-02 3.829588e-01 0.5889101
## 7753 9.227650e-03 3.059453e-01 0.6848271
## 7755 5.523949e-03 2.577570e-01 0.7367190
## 7757 5.523949e-03 2.577570e-01 0.7367190
## 7759 9.469265e-03 2.742168e-01 0.7163139
## 7761 9.456060e-03 3.488553e-01 0.6416886
## 7763 2.253500e-03 2.482630e-01 0.7494835
## 7764 1.181110e-04 1.198962e-01 0.8799857
## 7774 4.522745e-02 3.238130e-01 0.6309596
## 7778 1.111611e-03 1.945847e-01 0.8043037
## 7785 1.885247e-02 2.908365e-01 0.6903110
## 7788 7.239182e-03 2.289140e-01 0.7638468
## 7791 5.174784e-03 2.861985e-01 0.7086267
## 7793 4.012616e-10 8.729133e-02 0.9127087
## 7796 4.901656e-03 1.437373e-01 0.8513611
## 7797 7.142319e-02 9.841817e-02 0.8301586
## 7802 9.741318e-03 2.211323e-01 0.7691264
## 7805 4.170992e-02 3.810755e-01 0.5772146
## 7807 4.691308e-03 2.491134e-01 0.7461953
## 7811 5.574212e-03 2.265248e-01 0.7679010
## 7813 1.870122e-09 2.222422e-01 0.7777578
## 7814 6.687784e-02 3.061841e-01 0.6269380
## 7815 7.225152e-03 2.694839e-01 0.7232910
## 7826 2.982168e-10 9.090763e-02 0.9090924
## 7831 8.713446e-03 3.452272e-01 0.6460593
## 7837 2.440757e-02 2.629256e-01 0.7126668
## 7838 2.534398e-03 2.379638e-01 0.7595018
## 7842 5.120521e-10 4.884403e-02 0.9511560
## 7844 5.360266e-03 2.836853e-01 0.7109544
## 7846 1.101526e-02 3.555322e-01 0.6334525
## 7847 1.871356e-02 2.615769e-01 0.7197096
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## 7869 2.368238e-03 3.636186e-01 0.6340131
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## 7876 2.102728e-02 2.887244e-01 0.6902483
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## 7883 1.926523e-02 3.258802e-01 0.6548546
## 7884 6.305607e-03 2.962393e-01 0.6974551
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## 7891 4.301197e-03 2.310921e-01 0.7646067
## 7892 7.498803e-03 2.341344e-01 0.7583668
## 7894 4.668305e-03 2.718437e-01 0.7234880
## 7896 6.117483e-03 2.691763e-01 0.7247062
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## 7911 6.233002e-04 1.432012e-01 0.8561755
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## 7923 1.739278e-03 1.960319e-01 0.8022288
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## 7936 1.378685e-02 2.892026e-01 0.6970106
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## 7939 2.466547e-02 2.998846e-01 0.6754500
## 7949 1.376069e-02 2.717179e-01 0.7145214
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## 7955 3.326437e-03 1.210754e-01 0.8755982
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## 7984 3.980669e-02 3.436195e-01 0.6165738
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## 7989 9.672914e-03 3.514222e-01 0.6389049
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## 7999 9.005287e-03 2.773446e-01 0.7136501
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## 8012 7.673695e-03 3.325644e-01 0.6597619
## 8013 3.933078e-02 3.160030e-01 0.6446662
## 8015 2.482501e-02 2.626135e-01 0.7125615
## 8017 2.994465e-08 2.824182e-01 0.7175818
## 8018 4.691789e-03 3.277999e-01 0.6675083
## 8019 4.102550e-03 2.537427e-01 0.7421548
## 8023 3.298905e-02 1.700161e-01 0.7969948
## 8026 8.088528e-03 3.357772e-01 0.6561343
## 8030 6.337779e-03 2.549741e-01 0.7386881
## 8034 4.069478e-09 1.714988e-01 0.8285012
## 8035 1.117223e-08 1.861025e-01 0.8138975
## 8043 1.349302e-02 2.232522e-01 0.7632548
## 8044 1.968218e-08 3.048504e-01 0.6951496
## 8049 9.734796e-03 2.772705e-01 0.7129947
## 8054 3.455445e-03 2.062551e-01 0.7902894
## 8065 6.600830e-03 3.102130e-01 0.6831861
## 8066 5.164199e-09 1.722452e-01 0.8277548
## 8067 1.308498e-02 2.729021e-01 0.7140129
## 8076 1.099634e-02 2.437177e-01 0.7452859
## 8083 1.566811e-02 2.438313e-01 0.7405006
## 8089 1.994291e-02 3.373417e-01 0.6427154
## 8090 1.038418e-02 2.684675e-01 0.7211483
## 8104 1.876124e-02 2.331311e-01 0.7481077
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## 8111 4.484622e-03 2.357814e-01 0.7597339
## 8113 1.528562e-02 2.769848e-01 0.7077296
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## 8125 8.538602e-03 2.308940e-01 0.7605674
## 8127 2.529949e-09 1.514385e-01 0.8485615
## 8128 9.118255e-02 3.605378e-01 0.5482797
## 8133 4.751490e-03 2.567533e-01 0.7384952
## 8137 3.976587e-09 2.256162e-01 0.7743838
## 8138 2.463629e-02 2.995808e-01 0.6757829
## 8147 7.494563e-09 1.421289e-01 0.8578711
## 8150 2.529949e-09 1.514385e-01 0.8485615
## 8156 8.175340e-03 2.174782e-01 0.7743464
## 8167 1.365385e-02 2.850612e-01 0.7012850
## 8174 7.945399e-03 2.685211e-01 0.7235335
## 8176 2.687201e-08 3.540131e-01 0.6459869
## 8182 2.991212e-09 1.573632e-01 0.8426368
## 8198 2.521458e-02 2.880875e-01 0.6866979
## 8199 2.338199e-02 2.968312e-01 0.6797868
## 8206 7.040443e-03 2.242688e-01 0.7686908
## 8207 5.756896e-03 1.733999e-01 0.8208432
## 8208 1.545037e-02 2.939552e-01 0.6905944
## 8214 8.984692e-03 3.422203e-01 0.6487950
## 8215 1.030024e-02 1.731918e-01 0.8165080
## 8216 3.212434e-02 3.140313e-01 0.6538444
## 8218 8.608229e-03 2.104673e-01 0.7809245
## 8222 4.371645e-02 3.051067e-01 0.6511768
## 8223 2.345049e-02 2.595539e-01 0.7169956
## 8224 6.620842e-04 1.966460e-01 0.8026920
## 8226 7.063272e-02 2.884958e-01 0.6408715
## 8227 1.416118e-08 1.919494e-01 0.8080506
## 8230 1.382834e-09 1.834853e-01 0.8165147
## 8234 1.219309e-07 3.207868e-01 0.6792131
## 8235 9.974113e-09 1.166286e-01 0.8833714
## 8237 5.131454e-03 2.585000e-01 0.7363685
## 8239 5.167086e-03 4.404905e-01 0.5543424
## 8242 4.829601e-03 2.603032e-01 0.7348672
## 8243 4.415918e-03 2.553030e-01 0.7402811
## 8247 8.814336e-03 1.777941e-01 0.8133916
## 8248 1.137848e-02 2.935031e-01 0.6951184
## 8253 8.043115e-03 2.651052e-01 0.7268517
## 8256 5.148120e-09 1.807686e-01 0.8192314
## 8257 2.900065e-02 3.308430e-01 0.6401563
## 8259 5.142799e-03 2.449690e-01 0.7498882
## 8267 5.051588e-03 2.043732e-01 0.7905752
## 8271 2.446715e-02 3.596696e-01 0.6158632
## 8272 7.514970e-02 2.032437e-01 0.7216066
## 8282 6.024719e-03 1.857575e-01 0.8082178
## 8288 6.255247e-03 1.714024e-01 0.8223424
## 8290 1.024845e-03 1.372361e-01 0.8617390
## 8291 3.759808e-03 2.263053e-01 0.7699348
## 8294 1.369491e-09 1.486578e-01 0.8513422
## 8295 4.892874e-06 3.042798e-01 0.6957153
## 8302 2.894581e-02 2.694735e-01 0.7015807
## 8303 3.886905e-03 5.073180e-02 0.9453813
## 8306 2.460539e-04 9.656281e-02 0.9031911
## 8308 2.419448e-02 2.126271e-01 0.7631785
## 8319 1.096139e-04 1.071373e-01 0.8927531
## 8321 2.548007e-02 3.051100e-01 0.6694100
## 8322 2.160991e-02 3.034121e-01 0.6749780
## 8325 1.473989e-02 3.204854e-01 0.6647747
## 8326 2.819166e-02 3.855012e-01 0.5863071
## 8328 1.717882e-12 1.376002e-01 0.8623998
## 8337 1.387803e-02 2.426573e-01 0.7434646
## 8340 5.012611e-04 1.616680e-01 0.8378307
## 8344 9.124549e-03 2.408692e-01 0.7500063
## 8345 6.118116e-08 1.165290e-01 0.8834710
## 8352 5.699321e-04 1.200338e-01 0.8793963
## 8359 9.218091e-03 1.976284e-01 0.7931535
## 8364 1.664947e-03 1.568857e-01 0.8414494
## 8365 5.498204e-03 2.446006e-01 0.7499012
## 8370 5.421318e-03 2.719124e-01 0.7226663
## 8381 2.039933e-02 1.750378e-01 0.8045629
## 8385 8.594801e-10 1.160427e-01 0.8839573
## 8387 3.871436e-03 2.094114e-01 0.7867171
## 8391 1.746223e-02 2.429008e-01 0.7396370
## 8395 9.762489e-03 2.311767e-01 0.7590608
## 8396 1.363947e-03 1.817214e-01 0.8169147
## 8400 9.012386e-03 2.771199e-01 0.7138677
## 8405 7.185800e-03 2.452569e-01 0.7475573
## 8406 5.502788e-03 2.569005e-01 0.7375967
## 8408 1.675966e-03 2.689738e-01 0.7293502
## 8409 4.850554e-04 1.090372e-01 0.8904777
## 8413 6.030437e-02 3.223815e-01 0.6173142
## 8415 1.982328e-02 2.930314e-01 0.6871453
## 8417 1.956263e-03 1.777596e-01 0.8202841
## 8418 2.700614e-02 1.931730e-01 0.7798208
## 8419 4.817356e-05 7.320784e-02 0.9267440
## 8420 6.106910e-03 3.228735e-01 0.6710196
## 8425 1.413856e-02 2.068101e-01 0.7790514
## 8426 8.476524e-03 3.185157e-01 0.6730078
## 8428 9.140558e-04 1.490989e-01 0.8499871
## 8430 4.900885e-03 2.690100e-01 0.7260891
## 8433 6.899738e-03 2.645405e-01 0.7285598
## 8437 4.422595e-04 1.265081e-01 0.8730496
## 8439 2.115589e-03 2.268322e-01 0.7710522
## 8442 1.115571e-05 5.304019e-01 0.4695869
## 8445 1.990233e-03 1.336620e-01 0.8643477
## 8448 4.565805e-09 1.753418e-01 0.8246582
## 8449 7.235097e-04 1.440885e-01 0.8551879
## 8459 2.378685e-03 1.848322e-01 0.8127891
## 8460 4.413144e-03 2.550416e-01 0.7405452
## 8464 2.763637e-03 1.799026e-01 0.8173337
## 8466 6.608257e-03 2.547619e-01 0.7386298
## 8468 4.125757e-03 2.656371e-01 0.7302372
## 8471 5.322098e-02 3.991255e-01 0.5476535
## 8474 8.737833e-04 1.088559e-01 0.8902703
## 8475 2.410782e-03 1.868500e-01 0.8107393
## 8476 2.287937e-03 2.437568e-01 0.7539553
## 8477 4.984360e-04 1.909215e-01 0.8085800
## 8486 1.559049e-02 2.052754e-01 0.7791341
## 8488 5.853297e-03 3.296710e-01 0.6644757
## 8490 8.974401e-03 3.418864e-01 0.6491392
## 8496 2.622761e-02 3.813291e-01 0.5924433
## 8497 3.763716e-03 1.992416e-01 0.7969947
## 8498 3.199529e-03 2.406862e-01 0.7561143
## 8501 4.948665e-04 1.298824e-01 0.8696228
## 8502 2.233954e-03 2.148300e-01 0.7829360
## 8504 4.205180e-03 2.122103e-01 0.7835845
## 8505 1.678846e-03 1.639067e-01 0.8344145
## 8508 8.207584e-04 1.410141e-01 0.8581651
## 8509 8.293367e-03 3.022046e-01 0.6895021
## 8510 5.670380e-03 3.903274e-01 0.6040022
## 8511 4.422595e-04 1.265081e-01 0.8730496
## 8513 2.372408e-03 2.650151e-01 0.7326125
## 8514 3.291549e-08 1.988022e-01 0.8011978
## 8517 2.022816e-03 1.923671e-01 0.8056101
## 8527 3.685902e-03 2.514387e-01 0.7448754
## 8528 7.262897e-03 2.720587e-01 0.7206784
## 8534 7.112790e-03 2.741104e-01 0.7187769
## 8535 3.659225e-03 2.253671e-01 0.7709737
## 8540 4.658093e-03 2.578586e-01 0.7374833
## 8542 5.383107e-03 2.594495e-01 0.7351674
## 8543 1.609260e-03 1.446322e-01 0.8537585
## 8545 1.945095e-04 1.052397e-01 0.8945658
## 8546 7.048883e-03 2.185442e-01 0.7744069
## 8547 5.193731e-03 2.635756e-01 0.7312307
## 8548 3.458105e-03 2.321135e-01 0.7644284
## 8551 2.903011e-02 2.699487e-01 0.7010211
## 8560 3.420359e-04 1.305756e-01 0.8690824
## 8561 5.994356e-03 2.687090e-01 0.7252967
## 8566 6.734055e-03 1.210104e-01 0.8722555
## 8567 1.088846e-02 2.886221e-01 0.7004894
## 8569 3.765468e-05 5.857556e-01 0.4142067
## 8570 7.404811e-05 1.447217e-01 0.8552042
## 8571 1.052222e-01 2.028029e-01 0.6919750
## 8575 3.220037e-03 1.532545e-01 0.8435254
## 8580 2.364964e-09 1.623156e-01 0.8376844
## 8584 1.236528e-01 3.084925e-01 0.5678547
## 8587 2.936881e-02 2.724040e-01 0.6982272
## 8600 1.228957e-02 2.853146e-01 0.7023958
## 8603 7.824821e-05 6.708687e-02 0.9328349
## 8607 5.213594e-03 2.541025e-01 0.7406839
## 8623 1.254481e-03 1.810800e-01 0.8176655
## 8626 5.475668e-03 2.664047e-01 0.7281196
## 8627 1.127251e-03 2.267163e-01 0.7721565
## 8629 7.558550e-03 7.358535e-02 0.9188561
## 8630 2.103383e-03 1.779140e-01 0.8199826
## 8635 8.967800e-03 2.421133e-01 0.7489189
## 8637 1.534252e-02 2.265445e-01 0.7581130
## 8646 8.595097e-04 1.840802e-01 0.8150603
## 8649 8.970924e-04 1.883709e-01 0.8107321
## 8651 1.131062e-03 1.945945e-01 0.8042745
## 8652 1.673906e-03 2.227258e-01 0.7756003
## 8656 2.787301e-03 2.045552e-01 0.7926575
## 8664 5.577262e-03 2.285626e-01 0.7658602
## 8667 3.750397e-10 1.508392e-01 0.8491608
## 8669 3.503853e-02 3.354117e-01 0.6295498
## 8672 3.809381e-03 1.465948e-01 0.8495958
## 8680 1.162138e-03 1.977769e-01 0.8010610
## 8681 1.637846e-03 1.603888e-01 0.8379734
## 8682 2.468274e-02 2.854865e-01 0.6898307
## 8683 3.170693e-04 1.062711e-01 0.8934118
## 8691 2.861334e-02 3.092398e-01 0.6621468
## 8700 9.435454e-03 3.557130e-01 0.6348515
## 8701 5.436584e-03 2.213374e-01 0.7732260
## 8707 2.125248e-02 2.274816e-01 0.7512659
## 8711 8.918617e-06 2.502877e-01 0.7497034
## 8715 1.256365e-05 5.509096e-01 0.4490778
## 8716 2.463738e-03 1.748846e-01 0.8226517
## 8721 7.217266e-03 2.222093e-01 0.7705734
## 8722 8.373917e-03 3.100431e-01 0.6815829
## 8724 8.485954e-03 3.376665e-01 0.6538476
## 8725 7.245654e-03 3.280450e-01 0.6647093
## 8729 7.799059e-04 1.453505e-01 0.8538696
## 8730 3.305929e-03 2.327410e-01 0.7639530
## 8731 1.154969e-03 2.031097e-01 0.7957353
## 8733 5.830375e-04 1.345586e-01 0.8648584
## 8735 2.334679e-02 3.062739e-01 0.6703793
## 8743 8.168858e-08 3.654177e-01 0.6345822
## 8744 2.560187e-02 3.670152e-01 0.6073830
## 8747 4.523017e-03 2.673430e-01 0.7281340
## 8758 1.184690e-02 2.771196e-01 0.7110335
## 8759 3.576252e-03 3.246307e-01 0.6717930
## 8762 3.872467e-03 2.295041e-01 0.7666235
## 8764 2.702972e-03 1.996344e-01 0.7976626
## 8769 1.315593e-02 1.956518e-01 0.7911923
## 8772 3.215058e-03 2.154216e-01 0.7813634
## 8773 2.573803e-02 3.440680e-01 0.6301940
## 8774 6.353923e-04 1.099794e-01 0.8893852
## 8775 3.777863e-02 3.099799e-01 0.6522415
## 8783 8.879003e-02 3.182088e-01 0.5930012
## 8784 1.615427e-02 2.799755e-01 0.7038702
## 8786 2.006220e-02 3.462051e-01 0.6337327
## 8790 3.445184e-03 1.915803e-01 0.8049745
## 8796 6.296775e-03 1.970581e-01 0.7966451
## 8798 7.863301e-02 2.709587e-01 0.6504083
## 8799 1.465166e-01 6.469032e-02 0.7887931
## 8804 3.296545e-02 3.137643e-01 0.6532702
## 8805 3.441229e-03 1.266981e-01 0.8698607
## 8806 2.717961e-02 3.018813e-01 0.6709391
## 8807 3.543656e-02 2.939759e-01 0.6705875
## 8811 3.416540e-02 3.019486e-01 0.6638860
## 8817 2.067862e-03 3.669786e-01 0.6309535
## 8818 7.956261e-04 1.186042e-01 0.8806002
## 8819 1.204922e-02 3.333454e-01 0.6546054
## 8820 1.548692e-02 3.085312e-01 0.6759819
## 8826 3.891030e-03 2.608865e-01 0.7352224
## 8830 1.074062e-02 2.940980e-01 0.6951613
## 8832 1.982444e-04 6.952784e-02 0.9302739
## 8835 8.815088e-02 2.956354e-01 0.6162137
## 8836 3.734467e-03 1.842420e-01 0.8120236
## 8845 1.650404e-02 2.964952e-01 0.6870007
## 8847 2.368755e-03 1.841544e-01 0.8134768
## 8850 1.799085e-02 2.952922e-01 0.6867170
## 8851 2.784470e-03 2.475472e-01 0.7496684
## 8854 2.095356e-02 2.901084e-01 0.6889381
## 8860 4.944317e-03 2.601644e-01 0.7348913
## 8861 1.535229e-02 1.942973e-01 0.7903504
## 8862 9.425153e-03 3.441094e-01 0.6464654
## 8866 1.269871e-01 3.605567e-01 0.5124562
## 8867 4.267486e-15 7.546340e-02 0.9245366
## 8871 3.068308e-03 2.400125e-01 0.7569192
## 8872 1.432083e-02 2.515993e-01 0.7340799
## 8881 7.113154e-04 1.129673e-01 0.8863214
## 8882 5.684346e-03 3.104454e-01 0.6838703
## 8884 8.045506e-03 2.272814e-01 0.7646731
## 8891 6.472708e-03 2.171974e-01 0.7763298
## 8892 6.606766e-03 1.834662e-01 0.8099271
## 8893 5.225868e-03 2.630616e-01 0.7317126
## 8895 8.248880e-03 2.758520e-01 0.7158992
## 8896 1.593866e-02 3.673009e-01 0.6167604
## 8900 4.071331e-02 2.721048e-01 0.6871819
## 8903 2.196926e-02 3.245875e-01 0.6534433
## 8904 6.524141e-03 2.139180e-01 0.7795578
## 8905 9.556493e-03 2.755352e-01 0.7149083
## 8906 4.188099e-03 2.847320e-01 0.7110799
## 8907 3.302014e-03 1.910383e-01 0.8056597
## 8911 1.004262e-01 2.403689e-01 0.6592049
## 8919 1.207884e-02 2.705058e-01 0.7174154
## 8920 1.716095e-02 2.762402e-01 0.7065989
## 8922 1.802572e-03 2.239086e-01 0.7742888
## 8927 1.849813e-05 3.330887e-01 0.6668928
## 8935 9.522216e-03 2.145743e-01 0.7759035
## 8942 3.363404e-02 3.479280e-01 0.6184380
## 8945 1.314350e-03 1.227727e-01 0.8759129
## 8948 4.803050e-03 2.403068e-01 0.7548901
## 8949 1.237637e-03 2.032585e-01 0.7955038
## 8951 1.373461e-02 2.963982e-01 0.6898672
## 8952 1.966958e-03 2.625126e-01 0.7355204
## 8953 1.706552e-02 1.982356e-01 0.7846989
## 8955 1.881320e-02 2.839826e-01 0.6972042
## 8959 1.787244e-03 2.871629e-01 0.7110498
## 8961 3.758763e-03 1.625876e-01 0.8336536
## 8965 5.602707e-03 2.990906e-01 0.6953067
## 8967 1.712028e-02 3.703059e-01 0.6125738
## 8970 7.995530e-04 9.488806e-02 0.9043124
## 8971 3.201115e-04 1.098858e-01 0.8897941
## 8973 2.695568e-03 1.991552e-01 0.7981492
## 8978 3.249921e-03 3.022404e-01 0.6945097
## 8982 9.921082e-03 2.849379e-01 0.7051411
## 8984 5.770728e-03 2.582808e-01 0.7359485
## 8985 3.714927e-03 2.469426e-01 0.7493425
## 8986 4.531544e-03 2.740203e-01 0.7214482
## 8990 3.674169e-03 1.526251e-01 0.8437008
## 8992 5.065121e-02 2.823934e-01 0.6669553
## 8998 2.356386e-03 2.384799e-01 0.7591637
## 9001 1.808747e-03 2.061120e-01 0.7920792
## 9006 3.911078e-03 2.218789e-01 0.7742100
## 9011 9.887073e-03 2.698121e-01 0.7203008
## 9012 4.318961e-03 2.266003e-01 0.7690807
## 9013 3.624202e-03 1.870854e-01 0.8092904
## 9015 4.716884e-02 2.965642e-01 0.6562669
## 9017 2.361395e-02 2.858108e-01 0.6905752
## 9018 1.863141e-02 4.123280e-01 0.5690405
## 9021 6.707602e-09 2.636050e-01 0.7363950
## 9025 6.132099e-15 1.890876e-01 0.8109124
## 9033 1.140493e-02 2.443364e-01 0.7442587
## 9037 2.041414e-03 2.411625e-01 0.7567961
## 9041 6.652349e-03 2.446788e-01 0.7486688
## 9046 1.024258e-03 1.636757e-01 0.8353000
## 9049 1.002172e-08 1.500818e-01 0.8499182
## 9054 5.562666e-03 2.752152e-01 0.7192221
## 9057 4.642961e-03 2.468815e-01 0.7484756
## 9063 1.731966e-02 2.797489e-01 0.7029314
## 9076 4.575029e-03 1.699764e-01 0.8254486
## 9077 2.007634e-02 2.589095e-01 0.7210141
## 9079 2.033127e-08 2.620193e-01 0.7379806
## 9080 5.402616e-03 1.551770e-01 0.8394204
## 9083 7.303623e-08 2.381041e-01 0.7618958
## 9084 1.234122e-02 2.152754e-01 0.7723834
## 9090 3.956831e-03 2.539651e-01 0.7420781
## 9092 1.498974e-02 2.715881e-01 0.7134222
## 9095 4.982462e-02 3.092205e-01 0.6409549
## 9097 7.518030e-03 2.708257e-01 0.7216562
## 9098 1.108121e-01 3.147319e-01 0.5744560
## 9100 2.355360e-02 3.646906e-01 0.6117558
## 9101 7.262144e-03 1.442472e-01 0.8484906
## 9105 3.638682e-02 3.158730e-01 0.6477402
## 9108 2.823007e-02 3.715698e-01 0.6002001
## 9109 7.243948e-11 2.114175e-01 0.7885825
## 9117 1.140100e-02 2.414855e-01 0.7471135
## 9119 3.259851e-02 2.524420e-01 0.7149595
## 9127 2.585214e-04 7.002339e-02 0.9297181
## 9130 4.771871e-03 2.579426e-01 0.7372855
## 9133 1.512975e-02 2.303123e-01 0.7545579
## 9136 4.634772e-03 2.424715e-01 0.7528937
## 9139 7.752458e-02 2.679019e-01 0.6545735
## 9151 7.242975e-03 2.763119e-01 0.7164451
## 9153 1.043778e-02 3.059590e-01 0.6836032
## 9156 8.077576e-03 2.898447e-01 0.7020777
## 9158 8.532873e-03 2.812519e-01 0.7102152
## 9162 9.306578e-03 2.874008e-01 0.7032926
## 9163 4.636100e-02 3.171320e-01 0.6365070
## 9166 1.124609e-02 2.998241e-01 0.6889298
## 9170 2.049248e-02 3.324900e-01 0.6470176
## 9180 8.511813e-03 3.408013e-01 0.6506869
## 9182 4.897637e-04 1.286961e-01 0.8708142
## 9186 2.181463e-03 1.003700e-01 0.8974485
## 9187 2.595781e-02 3.023577e-01 0.6716845
## 9192 1.565231e-02 2.699393e-01 0.7144084
## 9194 3.347370e-03 2.414881e-01 0.7551645
## 9197 6.574389e-03 2.893402e-01 0.7040854
## 9199 4.333664e-02 3.053794e-01 0.6512840
## 9201 4.058374e-03 2.890019e-01 0.7069397
## 9202 5.222247e-03 3.209469e-01 0.6738308
## 9203 4.406408e-03 2.152054e-01 0.7803882
## 9205 3.195325e-02 3.176399e-01 0.6504069
## 9208 1.538870e-02 2.469061e-01 0.7377052
## 9209 1.266887e-02 1.034288e-01 0.8839023
## 9214 5.619608e-02 3.080504e-01 0.6357535
## 9216 3.671453e-03 2.044024e-01 0.7919261
## 9217 1.539154e-02 3.409630e-01 0.6436455
## 9219 4.784399e-03 2.580350e-01 0.7371806
## 9220 8.531541e-04 1.058616e-01 0.8932852
## 9224 1.587002e-03 2.342485e-01 0.7641645
## 9229 6.719136e-08 1.972480e-01 0.8027519
## 9234 2.862217e-02 3.832747e-01 0.5881031
## 9235 2.148270e-02 3.388793e-01 0.6396380
## 9237 5.221268e-03 1.383346e-01 0.8564442
## 9238 9.802938e-04 5.222986e-02 0.9467898
## 9246 2.609979e-02 3.591003e-01 0.6147999
## 9249 2.786938e-03 1.505885e-01 0.8466246
## 9252 1.617001e-09 1.053464e-01 0.8946536
## 9253 5.897392e-03 2.482799e-01 0.7458227
## 9254 9.317874e-03 3.407712e-01 0.6499109
## 9257 1.551272e-02 3.395495e-01 0.6449378
## 9262 2.588804e-02 3.091235e-01 0.6649885
## 9266 4.270281e-04 2.134648e-01 0.7861081
## 9267 6.663339e-03 1.928084e-01 0.8005282
## 9271 4.414314e-03 2.986562e-01 0.6969295
## 9272 5.711968e-03 2.559986e-01 0.7382894
## 9274 1.292608e-09 1.584245e-01 0.8415755
## 9277 6.891638e-03 2.174619e-01 0.7756464
## 9279 3.535683e-03 4.177110e-01 0.5787533
## 9280 9.026004e-03 2.948354e-01 0.6961386
## 9281 2.473594e-02 1.440079e-01 0.8312562
## 9282 1.507588e-03 2.358480e-01 0.7626444
## 9283 3.249339e-02 2.444257e-01 0.7230809
## 9288 1.245765e-02 2.061769e-01 0.7813655
## 9290 5.534781e-03 1.837246e-01 0.8107406
## 9294 6.769984e-03 1.299569e-01 0.8632731
## 9305 3.482765e-04 1.242923e-01 0.8753594
## 9318 6.646941e-03 2.609273e-01 0.7324258
## 9319 2.434522e-02 2.877154e-01 0.6879393
## 9323 1.800725e-03 1.432273e-01 0.8549720
## 9325 1.131586e-02 3.032387e-01 0.6854455
## 9328 4.594985e-03 2.446628e-01 0.7507422
## 9329 3.425357e-03 1.937119e-01 0.8028628
## 9330 8.428279e-04 1.809374e-01 0.8182198
## 9336 3.503676e-03 2.090652e-01 0.7874311
## 9338 1.659437e-02 4.483924e-01 0.5350132
## 9344 2.906621e-01 8.431255e-02 0.6250254
## 9345 9.027960e-03 2.292292e-01 0.7617428
## 9346 8.663612e-03 2.770391e-01 0.7142973
## 9351 3.894678e-03 2.194342e-01 0.7766711
## 9352 3.826281e-03 2.354582e-01 0.7607155
## 9353 1.546898e-03 2.450723e-01 0.7533808
## 9360 5.175868e-10 1.100843e-01 0.8899157
## 9362 1.719467e-02 2.924377e-01 0.6903677
## 9363 7.812550e-03 2.094934e-01 0.7826940
## 9366 9.725909e-02 2.923609e-01 0.6103800
## 9369 8.001631e-03 1.650994e-01 0.8268990
## 9373 9.653132e-03 3.475789e-01 0.6427680
## 9377 1.262489e-03 2.075405e-01 0.7911970
## 9378 9.574318e-07 2.243693e-01 0.7756297
## 9383 1.874869e-02 3.333705e-01 0.6478808
## 9384 3.379686e-03 2.293996e-01 0.7672207
## 9386 8.545983e-02 3.195542e-01 0.5949860
## 9387 7.869349e-03 2.214219e-01 0.7707088
## 9388 2.176704e-02 2.892662e-01 0.6889668
## 9390 6.460810e-03 4.193115e-01 0.5742277
## 9393 5.876176e-03 2.433611e-01 0.7507628
## 9401 8.562402e-03 2.160923e-01 0.7753452
## 9402 8.655388e-03 2.987880e-01 0.6925566
## 9404 4.844458e-03 2.471231e-01 0.7480325
## 9405 9.968398e-09 2.921632e-01 0.7078368
## 9409 7.056939e-03 2.865277e-01 0.7064154
## 9413 7.298888e-03 2.587782e-01 0.7339229
## 9414 2.872356e-03 2.191809e-01 0.7779467
## 9418 4.885539e-03 2.731329e-01 0.7219816
## 9419 4.651648e-03 3.119982e-01 0.6833502
## 9425 1.400692e-03 1.981833e-01 0.8004160
## 9430 2.810284e-02 3.873644e-01 0.5845327
## 9431 2.597151e-03 2.860331e-01 0.7113698
## 9434 7.939658e-03 3.304944e-01 0.6615660
## 9435 6.001581e-03 2.488379e-01 0.7451606
## 9436 3.497434e-03 2.420151e-01 0.7544875
## 9437 5.928691e-03 3.283354e-01 0.6657359
## 9439 1.078120e-02 3.500627e-01 0.6391561
## 9442 1.848804e-03 2.252172e-01 0.7729340
## 9443 7.144376e-03 3.241199e-01 0.6687358
## 9446 7.767967e-03 2.762125e-01 0.7160195
## 9447 3.739268e-03 2.545563e-01 0.7417045
## 9448 2.114078e-02 3.865345e-01 0.5923247
## 9450 3.995053e-02 3.602825e-01 0.5997670
## 9452 2.606261e-03 2.594377e-01 0.7379560
## 9454 2.127729e-02 3.683707e-01 0.6103520
## 9462 2.085391e-03 1.770574e-01 0.8208572
## 9464 8.194184e-03 2.791148e-01 0.7126910
## 9465 1.816968e-03 3.384759e-02 0.9643354
## 9466 9.346034e-03 3.227072e-01 0.6679468
## 9467 6.349196e-03 2.174797e-01 0.7761711
## 9472 2.121376e-02 2.858576e-01 0.6929287
## 9473 4.395366e-03 2.825079e-01 0.7130968
## 9482 4.333416e-02 3.184434e-01 0.6382224
## 9486 1.585880e-02 2.177779e-01 0.7663633
## 9491 3.094074e-03 2.020845e-01 0.7948214
## 9492 2.013729e-02 2.957422e-01 0.6841205
## 9497 6.664536e-02 3.524361e-01 0.5809185
## 9504 3.667112e-03 2.630169e-01 0.7333160
## 9505 2.337664e-03 2.111837e-01 0.7864786
## 9506 2.317369e-02 3.025490e-01 0.6742773
## 9510 5.786954e-02 2.380086e-01 0.7041218
## 9516 5.528465e-02 3.561694e-01 0.5885460
## 9517 2.414015e-02 2.235668e-01 0.7522931
## 9519 2.240293e-03 1.869071e-01 0.8108526
## 9521 2.280961e-03 1.847184e-01 0.8130006
## 9530 1.062423e-01 2.210651e-01 0.6726926
## 9534 3.874980e-03 1.878428e-01 0.8082823
## 9541 6.310481e-03 3.122971e-01 0.6813924
## 9545 1.039408e-02 3.024339e-01 0.6871720
## 9548 1.239388e-07 3.925192e-01 0.6074807
## 9549 1.586114e-02 2.463059e-01 0.7378330
view(predictions1_f)

predictions2_f <- predict(full_test2_f, newdata = test_data_f, type = "probs")
predictions2_f
##                 1            2         3
## 2    9.388964e-03 2.232959e-01 0.7673152
## 4    9.058230e-03 2.172268e-01 0.7737149
## 8    9.571996e-03 2.266110e-01 0.7638170
## 13   7.615187e-03 1.895049e-01 0.8028799
## 16   5.568506e-03 1.463709e-01 0.8480606
## 18   6.630010e-03 1.693357e-01 0.8240342
## 29   1.418549e-02 3.010674e-01 0.6847471
## 30   1.352409e-02 2.913716e-01 0.6951043
## 32   9.243258e-03 2.206347e-01 0.7701221
## 36   1.751704e-02 3.457217e-01 0.6367613
## 39   1.102229e-02 2.518335e-01 0.7371442
## 41   1.009793e-02 2.359688e-01 0.7539333
## 43   1.349651e-02 2.909607e-01 0.6955428
## 48   6.959733e-03 1.762043e-01 0.8168359
## 49   1.792426e-02 3.507429e-01 0.6313329
## 55   8.709049e-03 2.107072e-01 0.7805837
## 58   1.227537e-02 2.722274e-01 0.7154972
## 59   1.307471e-02 2.846114e-01 0.7023139
## 60   1.505298e-02 3.133454e-01 0.6716017
## 62   6.021480e-03 1.563336e-01 0.8376449
## 63   9.134437e-03 2.186343e-01 0.7722312
## 71   1.157306e-02 2.609497e-01 0.7274772
## 73   3.336017e-03 9.339713e-02 0.9032669
## 80   4.598422e-03 1.241737e-01 0.8712278
## 84   1.132869e-02 2.569350e-01 0.7317363
## 86   7.868099e-03 1.945151e-01 0.7976168
## 87   9.013766e-03 2.164031e-01 0.7745831
## 98   1.091830e-02 2.500847e-01 0.7389970
## 102  6.597832e-03 1.686589e-01 0.8247433
## 104  6.539280e-03 1.674242e-01 0.8260365
## 107  2.830827e-03 8.043515e-02 0.9167340
## 109  7.287363e-03 1.829104e-01 0.8098022
## 110  1.116863e-02 2.542797e-01 0.7345517
## 113  8.586352e-03 2.083884e-01 0.7830252
## 123  6.890181e-03 1.747656e-01 0.8183443
## 125  1.105589e-02 2.523967e-01 0.7365475
## 136  1.384080e-02 2.960515e-01 0.6901076
## 137  1.070088e-02 2.463991e-01 0.7429000
## 138  2.390917e-02 4.154608e-01 0.5606300
## 143  1.382246e-02 2.957824e-01 0.6903951
## 145  1.396307e-02 2.978399e-01 0.6881970
## 147  2.414326e-02 4.176872e-01 0.5581695
## 149  4.124253e-03 1.128745e-01 0.8830013
## 151  1.181715e-02 2.649126e-01 0.7232702
## 153  1.482143e-02 3.101156e-01 0.6750630
## 160  1.778279e-02 3.490085e-01 0.6332087
## 162  1.337929e-02 2.892088e-01 0.6974119
## 165  2.938013e-03 8.321759e-02 0.9138444
## 167  1.891952e-02 3.626513e-01 0.6184292
## 168  1.927268e-02 3.667571e-01 0.6139702
## 171  1.196416e-02 2.672769e-01 0.7207589
## 175  7.052945e-03 1.781242e-01 0.8148229
## 177  9.656571e-03 2.281326e-01 0.7622109
## 184  6.693069e-03 1.706588e-01 0.8226482
## 187  1.770260e-02 3.480207e-01 0.6342767
## 188  8.791708e-03 2.122611e-01 0.7789472
## 198  1.307513e-02 2.846179e-01 0.7023070
## 199  8.355348e-03 2.039828e-01 0.7876619
## 205  4.146751e-03 1.134175e-01 0.8824357
## 206  9.170630e-03 2.193009e-01 0.7715285
## 214  1.711891e-02 3.407260e-01 0.6421551
## 217  1.506632e-02 3.135305e-01 0.6714031
## 220  1.590816e-02 3.249858e-01 0.6591061
## 221  9.544482e-03 2.261146e-01 0.7643409
## 225  9.347716e-03 2.225445e-01 0.7681078
## 227  1.075964e-02 2.473990e-01 0.7418413
## 230  6.074475e-03 1.574831e-01 0.8364424
## 231  1.472157e-02 3.087120e-01 0.6765664
## 242  3.220833e-09 9.982913e-08 0.9999999
## 249  1.242794e-02 2.746276e-01 0.7129445
## 251  8.150875e-03 2.000389e-01 0.7918102
## 253  9.177859e-03 2.194338e-01 0.7713883
## 261  1.173248e-02 2.635432e-01 0.7247243
## 262  1.562836e-02 3.212264e-01 0.6631453
## 281  1.983936e-02 3.732190e-01 0.6069417
## 283  7.450707e-03 1.862105e-01 0.8063388
## 284  1.568524e-02 3.219945e-01 0.6623202
## 286  9.323924e-03 2.221104e-01 0.7685657
## 292  6.991200e-03 1.768535e-01 0.8161553
## 294  7.777828e-03 1.927344e-01 0.7994877
## 295  1.184092e-02 2.652960e-01 0.7228631
## 296  5.309485e-03 1.405611e-01 0.8541294
## 300  2.642827e-02 4.383892e-01 0.5351826
## 302  6.686751e-03 1.705264e-01 0.8227868
## 303  1.303639e-02 2.840284e-01 0.7029353
## 306  1.744288e-02 3.447976e-01 0.6377595
## 308  2.061178e-02 3.817843e-01 0.5976039
## 309  1.181514e-02 2.648801e-01 0.7233048
## 314  1.190379e-02 2.663080e-01 0.7217882
## 316  1.002932e-02 2.347619e-01 0.7552088
## 318  1.826405e-02 3.548656e-01 0.6268703
## 321  9.158520e-03 2.190780e-01 0.7717635
## 322  1.419687e-02 3.012317e-01 0.6845715
## 329  4.370152e-03 1.187722e-01 0.8768576
## 332  9.115574e-03 2.182865e-01 0.7725980
## 333  1.149195e-02 2.596225e-01 0.7288855
## 340  1.495362e-02 3.119637e-01 0.6730827
## 350  1.170355e-02 2.630740e-01 0.7252225
## 351  1.456775e-02 3.065377e-01 0.6788945
## 354  1.136618e-02 2.575540e-01 0.7310798
## 366  1.584165e-02 3.240964e-01 0.6600619
## 368  9.245348e-03 2.206730e-01 0.7700816
## 371  1.095642e-02 2.507267e-01 0.7383169
## 374  1.103376e-02 2.520258e-01 0.7369404
## 378  1.335851e-02 2.888973e-01 0.6977442
## 382  7.163979e-03 1.803987e-01 0.8124373
## 387  1.348999e-02 2.908636e-01 0.6956464
## 391  1.520115e-02 3.153945e-01 0.6694044
## 393  1.037007e-02 2.407151e-01 0.7489148
## 394  8.633568e-03 2.092825e-01 0.7820840
## 396  9.522470e-03 2.257170e-01 0.7647605
## 399  1.570414e-02 3.222492e-01 0.6620466
## 402  1.111378e-02 2.533649e-01 0.7355214
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## 413  1.815523e-02 3.535519e-01 0.6282929
## 414  1.065370e-02 2.455942e-01 0.7437521
## 416  1.204982e-02 2.686468e-01 0.7193034
## 417  1.034126e-02 2.402157e-01 0.7494430
## 421  6.723614e-03 1.712980e-01 0.8219784
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## 437  5.945528e-03 1.546804e-01 0.8393741
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## 473  1.046838e-02 2.424140e-01 0.7471176
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## 608  1.308484e-02 2.847655e-01 0.7021497
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## 623  1.498751e-02 3.124356e-01 0.6725769
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## 634  8.104125e-03 1.991313e-01 0.7927646
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## 697  3.211929e-03 9.024885e-02 0.9065392
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## 703  8.777931e-03 2.120026e-01 0.7792195
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## 714  4.843643e-03 1.298992e-01 0.8652571
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## 721  1.155227e-02 2.606099e-01 0.7278378
## 724  1.028239e-02 2.391928e-01 0.7505248
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## 738  1.047447e-02 2.425189e-01 0.7470066
## 743  3.375320e-03 9.438954e-02 0.9022351
## 744  4.665315e-03 1.257434e-01 0.8695912
## 746  1.065076e-02 2.455439e-01 0.7438053
## 747  1.109982e-02 2.531316e-01 0.7357686
## 751  7.510339e-03 1.874082e-01 0.8050815
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## 770  1.237295e-02 2.737645e-01 0.7138625
## 771  1.533039e-02 3.171707e-01 0.6674989
## 772  1.580592e-02 3.236176e-01 0.6605765
## 773  1.640302e-02 3.315211e-01 0.6520759
## 775  1.764331e-02 3.472881e-01 0.6350686
## 778  1.050856e-02 2.431060e-01 0.7463854
## 779  7.728110e-03 1.917501e-01 0.8005218
## 780  1.163182e-02 2.619079e-01 0.7264603
## 781  6.956978e-03 1.761474e-01 0.8168956
## 784  8.538997e-03 2.074896e-01 0.7839714
## 786  1.344420e-02 2.901802e-01 0.6963756
## 788  7.236301e-03 1.818730e-01 0.8108907
## 789  6.389273e-03 1.642433e-01 0.8293675
## 790  2.583150e-02 4.331569e-01 0.5410116
## 793  8.388159e-03 2.046118e-01 0.7870001
## 794  1.224610e-02 2.717649e-01 0.7159890
## 796  1.367345e-02 2.935872e-01 0.6927394
## 801  1.620263e-02 3.288920e-01 0.6549053
## 808  2.165743e-08 6.712676e-07 0.9999993
## 809  1.170871e-02 2.631578e-01 0.7251335
## 810  8.232653e-03 2.016213e-01 0.7901461
## 811  8.892764e-03 2.141519e-01 0.7769553
## 814  2.227441e-02 3.993237e-01 0.5784019
## 817  1.066778e-02 2.458345e-01 0.7434977
## 819  1.169905e-02 2.630010e-01 0.7252999
## 823  7.483475e-03 1.868691e-01 0.8056474
## 831  7.494937e-03 1.870992e-01 0.8054058
## 840  2.247587e-02 4.013697e-01 0.5761545
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## 842  1.704606e-02 3.398025e-01 0.6431515
## 848  7.003758e-03 1.771123e-01 0.8158839
## 851  2.493294e-02 4.250493e-01 0.5500177
## 853  1.096817e-02 2.509244e-01 0.7381074
## 854  5.226245e-03 1.386763e-01 0.8560975
## 855  1.112745e-02 2.535931e-01 0.7352794
## 856  4.074348e-03 1.116674e-01 0.8842583
## 858  1.772938e-02 3.483510e-01 0.6339196
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## 868  7.991122e-03 1.969283e-01 0.7950806
## 870  9.224940e-03 2.202987e-01 0.7704763
## 872  1.317708e-02 2.861640e-01 0.7006590
## 873  1.130713e-02 2.565785e-01 0.7321143
## 874  9.256968e-03 2.208859e-01 0.7698571
## 877  1.002206e-02 2.346341e-01 0.7553439
## 882  1.039469e-02 2.411414e-01 0.7484639
## 883  1.621540e-02 3.290602e-01 0.6547244
## 884  5.771321e-03 1.508623e-01 0.8433664
## 885  1.017293e-02 2.372833e-01 0.7525438
## 886  6.300684e-03 1.623525e-01 0.8313468
## 887  1.212593e-02 2.698594e-01 0.7180147
## 889  5.635486e-03 1.478597e-01 0.8465048
## 890  1.151577e-02 2.600128e-01 0.7284714
## 893  1.083189e-02 2.486245e-01 0.7405436
## 897  9.752056e-03 2.298426e-01 0.7604053
## 898  1.263298e-02 2.778258e-01 0.7095412
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## 901  1.589030e-02 3.247472e-01 0.6593625
## 904  3.772073e-03 1.042817e-01 0.8919463
## 908  9.468342e-03 2.247373e-01 0.7657943
## 911  6.110203e-03 1.582562e-01 0.8356336
## 915  7.829917e-03 1.937630e-01 0.7984071
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## 919  1.039734e-02 2.411872e-01 0.7484154
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## 934  6.753539e-03 1.719233e-01 0.8213232
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## 945  1.382042e-02 2.957525e-01 0.6904271
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## 952  7.995188e-03 1.970078e-01 0.7949970
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## 958  3.578863e-03 9.949286e-02 0.8969283
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## 965  1.396581e-02 2.978799e-01 0.6881543
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## 987  1.136589e-02 2.575493e-01 0.7310848
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## 1453 6.026833e-03 1.564499e-01 0.8375233
## 1454 2.940323e-02 4.627893e-01 0.5078075
## 1465 9.434161e-03 2.241173e-01 0.7664485
## 1471 5.582630e-03 1.466853e-01 0.8477321
## 1472 1.539064e-02 3.179951e-01 0.6666143
## 1475 3.527608e-03 9.821346e-02 0.8982589
## 1477 9.879885e-03 2.321191e-01 0.7580010
## 1478 1.286452e-02 2.814003e-01 0.7057352
## 1479 1.562098e-02 3.211266e-01 0.6632524
## 1480 7.581665e-03 1.888358e-01 0.8035826
## 1483 7.728546e-03 1.917588e-01 0.8005127
## 1491 1.172164e-02 2.633674e-01 0.7249109
## 1498 7.688558e-03 1.909652e-01 0.8013462
## 1501 1.930990e-02 3.671863e-01 0.6135038
## 1505 9.965492e-03 2.336355e-01 0.7563990
## 1506 1.220451e-02 2.711066e-01 0.7166889
## 1507 1.245330e-02 2.750247e-01 0.7125220
## 1509 1.005687e-02 2.352471e-01 0.7546961
## 1510 1.243318e-02 2.747097e-01 0.7128571
## 1511 6.710040e-03 1.710141e-01 0.8222759
## 1519 1.113820e-02 2.537724e-01 0.7350894
## 1525 8.169260e-03 2.003953e-01 0.7914355
## 1526 6.349968e-03 1.634055e-01 0.8302445
## 1534 7.423203e-03 1.856568e-01 0.8069200
## 1535 1.198511e-02 2.676124e-01 0.7204025
## 1537 7.860902e-03 1.943734e-01 0.7977657
## 1538 1.280688e-02 2.805142e-01 0.7066790
## 1540 1.466347e-02 3.078927e-01 0.6774439
## 1542 2.310514e-02 4.076551e-01 0.5692397
## 1543 9.828889e-03 2.312127e-01 0.7589585
## 1545 9.726620e-03 2.293879e-01 0.7608855
## 1559 1.160439e-02 2.614609e-01 0.7269347
## 1560 7.706011e-03 1.913118e-01 0.8009822
## 1561 8.438681e-03 2.055782e-01 0.7859832
## 1562 1.261354e-02 2.775239e-01 0.7098626
## 1566 1.307217e-02 2.845729e-01 0.7023549
## 1568 2.379184e-03 6.851452e-02 0.9291063
## 1573 1.084225e-02 2.487999e-01 0.7403578
## 1582 8.081585e-03 1.986929e-01 0.7932255
## 1593 1.059288e-02 2.445535e-01 0.7448536
## 1603 1.322590e-02 2.869017e-01 0.6998724
## 1604 1.148526e-02 2.595128e-01 0.7290020
## 1610 1.198077e-02 2.675430e-01 0.7204762
## 1614 6.151247e-03 1.591424e-01 0.8347063
## 1622 1.431504e-02 3.029321e-01 0.6827529
## 1623 9.731340e-03 2.294723e-01 0.7607964
## 1625 5.300218e-03 1.403517e-01 0.8543481
## 1627 1.523614e-02 3.158763e-01 0.6688875
## 1633 1.143524e-02 2.586915e-01 0.7298733
## 1635 1.715207e-02 3.411454e-01 0.6417026
## 1637 3.854817e-03 1.063162e-01 0.8898290
## 1645 1.112868e-02 2.536135e-01 0.7352579
## 1647 5.582941e-03 1.466922e-01 0.8477248
## 1648 4.329664e-03 1.178068e-01 0.8778635
## 1652 1.007407e-02 2.355496e-01 0.7543763
## 1653 6.976518e-03 1.765508e-01 0.8164727
## 1659 8.442619e-03 2.056534e-01 0.7859040
## 1664 7.728916e-03 1.917661e-01 0.8005050
## 1665 1.388630e-02 2.967182e-01 0.6893955
## 1670 1.184966e-02 2.654368e-01 0.7227135
## 1672 2.471653e-02 4.230543e-01 0.5522292
## 1673 1.517368e-02 3.150156e-01 0.6698107
## 1688 1.193713e-02 2.668435e-01 0.7212194
## 1691 1.845199e-02 3.571204e-01 0.6244277
## 1695 1.459512e-02 3.069258e-01 0.6784791
## 1700 1.292059e-02 2.822600e-01 0.7048194
## 1702 1.128177e-02 2.561589e-01 0.7325594
## 1703 1.410164e-02 2.998546e-01 0.6860438
## 1709 1.308602e-02 2.847834e-01 0.7021306
## 1725 9.503791e-03 2.253792e-01 0.7651170
## 1735 8.524636e-03 2.072165e-01 0.7842588
## 1738 2.038153e-02 3.792598e-01 0.6003587
## 1743 8.365433e-03 2.041762e-01 0.7874583
## 1748 1.399090e-02 2.982456e-01 0.6877635
## 1750 7.661214e-03 1.904216e-01 0.8019171
## 1755 8.427611e-03 2.053666e-01 0.7862058
## 1757 1.013013e-02 2.365336e-01 0.7533362
## 1758 6.862656e-03 1.741947e-01 0.8189427
## 1760 8.577776e-03 2.082258e-01 0.7831964
## 1761 1.022350e-02 2.381667e-01 0.7516098
## 1765 1.334908e-02 2.887558e-01 0.6978951
## 1769 1.692259e-02 3.382304e-01 0.6448470
## 1771 1.059288e-02 2.445535e-01 0.7448536
## 1772 9.789171e-03 2.305051e-01 0.7597058
## 1777 1.253066e-02 2.762337e-01 0.7112356
## 1781 1.255379e-02 2.765942e-01 0.7108520
## 1787 7.611828e-03 1.894379e-01 0.8029503
## 1789 1.100134e-02 2.514819e-01 0.7375167
## 1790 1.559464e-02 3.207702e-01 0.6636351
## 1798 1.030844e-02 2.396458e-01 0.7500458
## 1803 5.544160e-03 1.458284e-01 0.8486275
## 1804 8.295025e-03 2.028236e-01 0.7888813
## 1807 1.592250e-02 3.251773e-01 0.6589002
## 1808 1.338463e-02 2.892889e-01 0.6973265
## 1809 1.319159e-02 2.863835e-01 0.7004249
## 1811 5.443387e-03 1.435749e-01 0.8509817
## 1820 9.155975e-03 2.190311e-01 0.7718129
## 1821 8.448209e-03 2.057601e-01 0.7857917
## 1828 9.903299e-03 2.325345e-01 0.7575622
## 1829 1.161975e-02 2.617113e-01 0.7266689
## 1834 1.316065e-02 2.859153e-01 0.7009240
## 1837 8.866910e-03 2.136691e-01 0.7774640
## 1838 1.593825e-02 3.253872e-01 0.6586745
## 1845 4.292321e-03 1.169144e-01 0.8787933
## 1848 1.095498e-02 2.507024e-01 0.7383426
## 1849 1.550393e-02 3.195394e-01 0.6649567
## 1855 5.342807e-03 1.413132e-01 0.8533440
## 1862 1.224820e-02 2.717981e-01 0.7159537
## 1865 2.927430e-02 4.617867e-01 0.5089390
## 1869 1.452451e-02 3.059238e-01 0.6795517
## 1870 1.319935e-02 2.865008e-01 0.7002998
## 1871 1.101241e-02 2.516678e-01 0.7373198
## 1875 1.266508e-02 2.783238e-01 0.7090111
## 1876 1.124859e-02 2.556088e-01 0.7331426
## 1878 1.116373e-02 2.541980e-01 0.7346383
## 1881 8.783325e-03 2.121038e-01 0.7791129
## 1883 5.036119e-03 1.343382e-01 0.8606257
## 1884 1.103701e-02 2.520802e-01 0.7368828
## 1885 6.675160e-03 1.702835e-01 0.8230414
## 1887 1.137832e-02 2.577543e-01 0.7308674
## 1890 8.251776e-03 2.019903e-01 0.7897579
## 1891 1.524524e-02 3.160016e-01 0.6687532
## 1893 6.458500e-03 1.657145e-01 0.8278270
## 1894 1.239757e-02 2.741511e-01 0.7134513
## 1895 1.873874e-02 3.605256e-01 0.6207356
## 1896 7.963762e-03 1.963929e-01 0.7956433
## 1898 7.372144e-03 1.846269e-01 0.8080010
## 1900 1.036095e-02 2.405571e-01 0.7490819
## 1901 4.024959e-03 1.104694e-01 0.8855056
## 1912 6.090437e-03 1.578287e-01 0.8360809
## 1914 1.145309e-02 2.589847e-01 0.7295622
## 1915 1.718226e-02 3.415266e-01 0.6412911
## 1917 1.092443e-02 2.501879e-01 0.7388877
## 1918 1.764995e-02 3.473702e-01 0.6349799
## 1919 1.159717e-02 2.613432e-01 0.7270596
## 1923 4.814799e-03 1.292298e-01 0.8659554
## 1924 8.163981e-03 2.002930e-01 0.7915431
## 1926 1.677173e-02 3.362981e-01 0.6469301
## 1929 1.080422e-02 2.481557e-01 0.7410400
## 1931 8.274045e-03 2.024196e-01 0.7893063
## 1933 1.346957e-02 2.905591e-01 0.6959714
## 1936 8.966851e-03 2.155319e-01 0.7755012
## 1937 9.517764e-03 2.256319e-01 0.7648503
## 1939 1.293113e-02 2.824214e-01 0.7046475
## 1940 1.028403e-02 2.392213e-01 0.7504946
## 1942 9.486494e-03 2.250662e-01 0.7654473
## 1948 1.148471e-02 2.595037e-01 0.7290116
## 1956 1.202469e-02 2.682455e-01 0.7197298
## 1957 9.565990e-03 2.265027e-01 0.7639313
## 1958 1.001433e-02 2.344977e-01 0.7554879
## 1961 1.023918e-02 2.384403e-01 0.7513205
## 1968 1.416517e-02 3.007739e-01 0.6850609
## 1969 9.365215e-03 2.228634e-01 0.7677713
## 1971 2.649436e-03 7.568599e-02 0.9216646
## 1972 1.000912e-02 2.344058e-01 0.7555850
## 1975 8.482378e-03 2.064120e-01 0.7851056
## 1979 8.704596e-03 2.106233e-01 0.7806721
## 1981 7.747329e-03 1.921309e-01 0.8001218
## 1985 6.888738e-03 1.747356e-01 0.8183756
## 1986 1.095124e-02 2.506395e-01 0.7384093
## 1988 7.447646e-03 1.861489e-01 0.8064034
## 1989 8.355793e-03 2.039913e-01 0.7876529
## 1990 4.133473e-03 1.130971e-01 0.8827694
## 1991 7.976809e-03 1.966483e-01 0.7953749
## 1994 1.075272e-02 2.472814e-01 0.7419659
## 1995 2.947681e-03 8.346771e-02 0.9135846
## 2000 8.503861e-03 2.068212e-01 0.7846749
## 2001 1.288581e-02 2.817270e-01 0.7053872
## 2002 1.034764e-02 2.403263e-01 0.7493261
## 2007 1.685274e-02 3.373374e-01 0.6458099
## 2014 1.268123e-02 2.785740e-01 0.7087448
## 2016 6.533624e-03 1.673048e-01 0.8261616
## 2024 2.114367e-02 3.875254e-01 0.5913309
## 2026 1.172328e-02 2.633941e-01 0.7248826
## 2027 6.147312e-03 1.590576e-01 0.8347951
## 2028 1.124740e-02 2.555890e-01 0.7331636
## 2029 1.131785e-02 2.567559e-01 0.7319263
## 2030 1.294596e-02 2.826483e-01 0.7044058
## 2032 1.094561e-02 2.505447e-01 0.7385097
## 2039 1.312632e-02 2.853951e-01 0.7014786
## 2045 1.370976e-02 2.941236e-01 0.6921667
## 2047 1.755860e-02 3.462382e-01 0.6362032
## 2049 1.755860e-02 3.462382e-01 0.6362032
## 2050 1.095929e-02 2.507750e-01 0.7382657
## 2051 6.435515e-03 1.652266e-01 0.8283379
## 2055 9.705537e-03 2.290105e-01 0.7612839
## 2062 6.471216e-03 1.659841e-01 0.8275447
## 2064 7.539439e-03 1.879913e-01 0.8044693
## 2065 1.184247e-02 2.653210e-01 0.7228366
## 2068 1.744201e-02 3.447868e-01 0.6377712
## 2070 1.041473e-02 2.414880e-01 0.7480973
## 2079 1.133525e-02 2.570435e-01 0.7316213
## 2089 1.127095e-02 2.559795e-01 0.7327496
## 2091 3.477027e-03 9.694714e-02 0.8995758
## 2096 1.338619e-02 2.893122e-01 0.6973016
## 2098 1.553089e-02 3.199057e-01 0.6645634
## 2106 1.051259e-02 2.431753e-01 0.7463121
## 2107 1.078440e-02 2.478195e-01 0.7413961
## 2111 7.150695e-03 1.801273e-01 0.8127220
## 2113 7.329956e-03 1.837737e-01 0.8088963
## 2116 7.004575e-03 1.771291e-01 0.8158663
## 2125 8.384830e-03 2.045480e-01 0.7870672
## 2127 1.194558e-02 2.669790e-01 0.7210754
## 2130 1.195021e-02 2.670533e-01 0.7209965
## 2133 1.714704e-02 3.410818e-01 0.6417711
## 2134 1.767734e-02 3.477088e-01 0.6346138
## 2136 8.944795e-03 2.151216e-01 0.7759336
## 2137 2.156244e-02 3.919583e-01 0.5864793
## 2142 1.006730e-02 2.354305e-01 0.7545022
## 2143 7.586168e-03 1.889257e-01 0.8034881
## 2148 2.765368e-03 7.872721e-02 0.9185074
## 2153 1.098838e-02 2.512642e-01 0.7377474
## 2155 1.242964e-02 2.746541e-01 0.7129162
## 2156 3.122242e-03 8.795910e-02 0.9089187
## 2160 9.009296e-03 2.163202e-01 0.7746705
## 2163 1.132476e-02 2.568701e-01 0.7318052
## 2164 1.063455e-02 2.452668e-01 0.7440986
## 2174 1.165749e-02 2.623257e-01 0.7260168
## 2182 2.146658e-02 3.909502e-01 0.5875832
## 2198 2.102763e-02 3.862836e-01 0.5926888
## 2205 6.053073e-03 1.570193e-01 0.8369276
## 2207 1.663818e-02 3.345768e-01 0.6487850
## 2210 1.293781e-02 2.825236e-01 0.7045386
## 2212 1.880995e-02 3.613650e-01 0.6198251
## 2214 7.521264e-03 1.876272e-01 0.8048515
## 2218 2.441986e-02 4.202918e-01 0.5552884
## 2219 4.964367e-03 1.326890e-01 0.8623466
## 2221 1.171553e-02 2.632684e-01 0.7250161
## 2223 5.654883e-03 1.482899e-01 0.8460552
## 2231 6.770752e-03 1.722825e-01 0.8209468
## 2233 6.487558e-03 1.663304e-01 0.8271821
## 2239 5.982041e-03 1.554760e-01 0.8385420
## 2246 9.705937e-03 2.290177e-01 0.7612764
## 2248 5.074309e-03 1.352133e-01 0.8597124
## 2250 6.853707e-03 1.740089e-01 0.8191374
## 2252 1.085695e-02 2.490487e-01 0.7400943
## 2255 1.289022e-02 2.817947e-01 0.7053151
## 2258 1.407111e-02 2.994118e-01 0.6865171
## 2259 9.380492e-03 2.231417e-01 0.7674779
## 2261 8.468979e-03 2.061565e-01 0.7853745
## 2264 1.412980e-02 3.002624e-01 0.6856078
## 2266 1.741833e-02 3.444911e-01 0.6380905
## 2269 8.474572e-03 2.062632e-01 0.7852623
## 2275 9.665244e-03 2.282882e-01 0.7620465
## 2280 8.577704e-03 2.082244e-01 0.7831979
## 2286 7.942022e-03 1.959670e-01 0.7960910
## 2288 7.228253e-03 1.817092e-01 0.8110626
## 2293 7.594192e-03 1.890859e-01 0.8033199
## 2297 1.391795e-02 2.971811e-01 0.6889009
## 2303 2.084276e-02 3.842929e-01 0.5948644
## 2305 7.757773e-03 1.923377e-01 0.7999045
## 2308 2.682023e-02 4.417617e-01 0.5314181
## 2309 5.661573e-03 1.484381e-01 0.8459003
## 2312 9.046995e-03 2.170189e-01 0.7739341
## 2313 1.948373e-02 3.691817e-01 0.6113345
## 2319 4.136073e-03 1.131599e-01 0.8827041
## 2323 6.920557e-03 1.753946e-01 0.8176849
## 2328 5.658870e-03 1.483782e-01 0.8459629
## 2332 7.024742e-03 1.775443e-01 0.8154309
## 2333 1.000052e-02 2.342541e-01 0.7557454
## 2334 4.734727e-03 1.273660e-01 0.8678993
## 2337 1.432145e-02 3.030241e-01 0.6826544
## 2339 4.049161e-03 1.110569e-01 0.8848940
## 2343 9.217004e-03 2.201531e-01 0.7706299
## 2344 1.097697e-02 2.510723e-01 0.7379507
## 2346 1.561294e-02 3.210179e-01 0.6633692
## 2352 1.430877e-02 3.028421e-01 0.6828491
## 2355 1.206461e-02 2.688829e-01 0.7190525
## 2359 2.310688e-02 4.076723e-01 0.5692208
## 2368 4.114546e-03 1.126400e-01 0.8832455
## 2371 1.717887e-02 3.414839e-01 0.6413372
## 2374 4.821762e-03 1.293915e-01 0.8657867
## 2375 4.810555e-03 1.291313e-01 0.8660582
## 2376 2.982854e-02 4.660633e-01 0.5041082
## 2381 5.269200e-03 1.396500e-01 0.8550808
## 2382 1.085340e-02 2.489886e-01 0.7401580
## 2383 3.447136e-03 9.619704e-02 0.9003558
## 2395 2.719956e-02 4.449782e-01 0.5278222
## 2396 1.148712e-02 2.595432e-01 0.7289696
## 2398 4.556214e-03 1.231802e-01 0.8722635
## 2401 5.624582e-03 1.476178e-01 0.8467577
## 2405 1.044478e-02 2.420068e-01 0.7475484
## 2411 1.125835e-02 2.557706e-01 0.7329710
## 2412 5.302159e-03 1.403956e-01 0.8543023
## 2418 1.708514e-02 3.402982e-01 0.6426166
## 2427 8.953882e-03 2.152907e-01 0.7757554
## 2430 4.810896e-03 1.291392e-01 0.8660499
## 2434 1.183413e-02 2.651866e-01 0.7229793
## 2435 5.415255e-03 1.429436e-01 0.8516411
## 2438 6.535101e-03 1.673360e-01 0.8261289
## 2439 1.302267e-02 2.838194e-01 0.7031579
## 2446 8.674253e-03 2.100511e-01 0.7812746
## 2454 2.800730e-03 7.965067e-02 0.9175486
## 2456 9.822063e-03 2.310912e-01 0.7590868
## 2458 4.987794e-03 1.332282e-01 0.8617840
## 2459 1.249314e-02 2.756480e-01 0.7118589
## 2462 9.085846e-03 2.177375e-01 0.7731766
## 2466 1.206893e-02 2.689517e-01 0.7189794
## 2472 1.113575e-02 2.537316e-01 0.7351327
## 2475 1.031320e-02 2.397285e-01 0.7499583
## 2476 5.335591e-03 1.411505e-01 0.8535139
## 2478 2.571473e-02 4.321191e-01 0.5421661
## 2481 7.673679e-03 1.906695e-01 0.8016568
## 2484 1.313111e-02 2.854678e-01 0.7014011
## 2491 7.477814e-03 1.867554e-01 0.8057668
## 2495 8.835778e-03 2.130869e-01 0.7780773
## 2496 1.396056e-02 2.978033e-01 0.6882361
## 2498 1.073131e-02 2.469173e-01 0.7423514
## 2499 7.028454e-03 1.776207e-01 0.8153509
## 2500 2.314741e-02 4.080718e-01 0.5687808
## 2501 4.531110e-03 1.225882e-01 0.8728807
## 2504 1.253154e-02 2.762474e-01 0.7112211
## 2505 8.956114e-03 2.153323e-01 0.7757116
## 2507 7.139543e-03 1.798993e-01 0.8129612
## 2510 1.107503e-02 2.527171e-01 0.7362079
## 2511 5.544874e-03 1.458443e-01 0.8486108
## 2516 1.037179e-02 2.407449e-01 0.7488833
## 2518 1.610334e-02 3.275805e-01 0.6563161
## 2519 1.067633e-02 2.459805e-01 0.7433432
## 2522 1.110280e-02 2.531814e-01 0.7357158
## 2524 1.265331e-02 2.781412e-01 0.7092055
## 2526 1.036312e-02 2.405947e-01 0.7490422
## 2530 9.896845e-03 2.324200e-01 0.7576831
## 2537 1.388948e-02 2.967647e-01 0.6893458
## 2546 3.860232e-03 1.064490e-01 0.8896908
## 2553 4.140097e-03 1.132570e-01 0.8826029
## 2564 1.389882e-02 2.969014e-01 0.6891997
## 2566 1.370000e-02 2.939794e-01 0.6923206
## 2567 4.421709e-03 1.199983e-01 0.8755800
## 2568 1.357939e-02 2.921937e-01 0.6942269
## 2573 4.646817e-03 1.253100e-01 0.8700432
## 2576 1.582458e-02 3.238678e-01 0.6603076
## 2587 4.379331e-03 1.189908e-01 0.8766299
## 2588 1.209067e-02 2.692981e-01 0.7186112
## 2589 4.522973e-03 1.223961e-01 0.8730809
## 2590 1.134393e-02 2.571869e-01 0.7314691
## 2591 1.351586e-02 2.912490e-01 0.6952352
## 2594 1.255212e-02 2.765683e-01 0.7108796
## 2595 1.801671e-02 3.518705e-01 0.6301128
## 2597 8.141657e-03 1.998601e-01 0.7919982
## 2599 5.835070e-03 1.522637e-01 0.8419012
## 2602 3.182240e-03 8.949222e-02 0.9073255
## 2604 8.306867e-03 2.030515e-01 0.7886417
## 2606 2.080688e-03 6.045744e-02 0.9374619
## 2608 6.706345e-03 1.709367e-01 0.8223569
## 2609 1.548844e-02 3.193287e-01 0.6651828
## 2613 1.659720e-02 3.340465e-01 0.6493563
## 2617 9.358507e-03 2.227412e-01 0.7679003
## 2619 1.084239e-02 2.488023e-01 0.7403553
## 2631 1.668110e-02 3.351311e-01 0.6481878
## 2634 1.006422e-02 2.353764e-01 0.7545594
## 2635 1.442444e-02 3.044982e-01 0.6810774
## 2636 1.214199e-02 2.701147e-01 0.7177433
## 2637 1.379892e-02 2.954365e-01 0.6907645
## 2641 5.775677e-03 1.509582e-01 0.8432661
## 2642 5.031755e-03 1.342381e-01 0.8607302
## 2644 8.850140e-03 2.133556e-01 0.7777943
## 2649 3.356656e-03 9.391855e-02 0.9027248
## 2653 8.885034e-03 2.140076e-01 0.7771073
## 2654 1.720939e-02 3.418689e-01 0.6409217
## 2660 1.185166e-02 2.654690e-01 0.7226793
## 2662 2.734147e-03 7.791023e-02 0.9193556
## 2663 1.082012e-02 2.484252e-01 0.7407546
## 2664 6.676537e-03 1.703124e-01 0.8230111
## 2669 8.961920e-03 2.154402e-01 0.7755978
## 2670 1.706180e-02 3.400022e-01 0.6429360
## 2672 1.004577e-02 2.350516e-01 0.7549026
## 2675 4.121960e-03 1.128191e-01 0.8830589
## 2676 1.452914e-02 3.059895e-01 0.6794813
## 2680 4.218679e-03 1.151490e-01 0.8806323
## 2682 1.106340e-02 2.525224e-01 0.7364142
## 2683 1.289021e-02 2.817945e-01 0.7053153
## 2684 2.062077e-02 3.818824e-01 0.5974968
## 2685 1.059934e-02 2.446642e-01 0.7447364
## 2688 9.112462e-03 2.182290e-01 0.7726585
## 2698 1.297752e-02 2.831306e-01 0.7038918
## 2699 5.308705e-03 1.405435e-01 0.8541478
## 2704 1.141116e-02 2.582953e-01 0.7302935
## 2709 9.386354e-03 2.232484e-01 0.7673653
## 2710 1.208757e-02 2.692488e-01 0.7186636
## 2713 1.870816e-02 3.601644e-01 0.6211274
## 2717 6.364546e-03 1.637164e-01 0.8299190
## 2719 8.930209e-03 2.148501e-01 0.7762197
## 2730 9.415370e-03 2.237760e-01 0.7668086
## 2735 2.187745e-03 6.336381e-02 0.9344484
## 2740 8.626611e-03 2.091509e-01 0.7822225
## 2748 1.119069e-02 2.546469e-01 0.7341625
## 2749 6.470602e-03 1.659711e-01 0.8275583
## 2751 1.428966e-02 3.025676e-01 0.6831427
## 2754 1.627126e-02 3.297950e-01 0.6539338
## 2762 3.580562e-03 9.953520e-02 0.8968842
## 2768 7.403930e-03 1.852684e-01 0.8073277
## 2769 1.105730e-02 2.524203e-01 0.7365224
## 2777 3.642236e-03 1.010695e-01 0.8952883
## 2784 1.967587e-02 3.713705e-01 0.6089536
## 2786 8.340853e-03 2.037046e-01 0.7879545
## 2788 7.440972e-03 1.860146e-01 0.8065444
## 2792 1.267541e-02 2.784838e-01 0.7088408
## 2799 8.368878e-03 2.042423e-01 0.7873888
## 2801 1.316486e-02 2.859790e-01 0.7008561
## 2806 4.836042e-03 1.297229e-01 0.8654410
## 2813 2.676943e-03 7.640947e-02 0.9209136
## 2814 3.181432e-03 8.947161e-02 0.9073470
## 2815 1.146718e-02 2.592161e-01 0.7293168
## 2819 4.496021e-03 1.217593e-01 0.8737447
## 2824 8.673328e-03 2.100337e-01 0.7812930
## 2825 7.935780e-03 1.958446e-01 0.7962196
## 2828 7.304177e-03 1.832515e-01 0.8094444
## 2831 8.243312e-03 2.018270e-01 0.7899297
## 2835 5.504390e-03 1.449405e-01 0.8495551
## 2848 1.077330e-02 2.476310e-01 0.7415957
## 2852 1.474416e-02 3.090301e-01 0.6762257
## 2853 8.709128e-03 2.107087e-01 0.7805822
## 2857 6.112594e-03 1.583079e-01 0.8355795
## 2861 1.150465e-02 2.598307e-01 0.7286647
## 2864 1.412513e-02 3.001948e-01 0.6856800
## 2868 1.048217e-02 2.426516e-01 0.7468663
## 2869 7.640253e-03 1.900044e-01 0.8023553
## 2880 1.469134e-02 3.082861e-01 0.6770226
## 2888 8.865442e-03 2.136417e-01 0.7774929
## 2889 5.662520e-03 1.484591e-01 0.8458784
## 2890 5.632028e-03 1.477830e-01 0.8465850
## 2892 1.354668e-02 2.917077e-01 0.6947457
## 2894 4.298289e-03 1.170572e-01 0.8786445
## 2900 4.754249e-03 1.278212e-01 0.8674246
## 2909 4.429241e-03 1.201771e-01 0.8753936
## 2916 1.124631e-02 2.555709e-01 0.7331828
## 2920 1.373727e-02 2.945292e-01 0.6917335
## 2927 1.662375e-02 3.343903e-01 0.6489860
## 2930 7.981376e-03 1.967377e-01 0.7952810
## 2932 1.061956e-02 2.450104e-01 0.7443700
## 2939 5.922177e-03 1.541707e-01 0.8399071
## 2942 1.570626e-02 3.222777e-01 0.6620160
## 2947 1.484056e-02 3.103837e-01 0.6747758
## 2948 1.063071e-02 2.452011e-01 0.7441682
## 2952 1.546744e-02 3.190429e-01 0.6654897
## 2956 1.225169e-02 2.718532e-01 0.7158951
## 2963 6.905659e-03 1.750862e-01 0.8180081
## 2965 1.444368e-02 3.047727e-01 0.6807837
## 2970 6.789807e-03 1.726797e-01 0.8205305
## 2972 1.348152e-02 2.907373e-01 0.6957812
## 2975 2.107562e-02 3.867979e-01 0.5921265
## 2976 1.130948e-02 2.566175e-01 0.7320730
## 2980 1.015500e-02 2.369695e-01 0.7528755
## 2984 1.494447e-02 3.118360e-01 0.6732195
## 2991 1.146509e-02 2.591818e-01 0.7293531
## 2997 1.539640e-02 3.180738e-01 0.6665298
## 3002 1.674076e-02 3.358999e-01 0.6473593
## 3008 1.642109e-02 3.317570e-01 0.6518219
## 3010 1.017107e-02 2.372508e-01 0.7525782
## 3013 7.225213e-03 1.816473e-01 0.8111275
## 3015 1.363630e-02 2.930375e-01 0.6933262
## 3021 1.854112e-02 3.581833e-01 0.6232756
## 3023 7.471646e-03 1.866315e-01 0.8058969
## 3024 1.670574e-02 3.354488e-01 0.6478455
## 3026 5.415478e-03 1.429486e-01 0.8516359
## 3032 1.599823e-02 3.261861e-01 0.6578157
## 3038 1.101498e-02 2.517109e-01 0.7372742
## 3041 3.586795e-03 9.969053e-02 0.8967227
## 3046 1.015501e-02 2.369697e-01 0.7528753
## 3047 3.866548e-03 1.066039e-01 0.8895296
## 3055 9.926077e-03 2.329381e-01 0.7571358
## 3062 8.552713e-03 2.077501e-01 0.7836971
## 3063 2.809842e-02 4.524196e-01 0.5194819
## 3072 7.966694e-03 1.964503e-01 0.7955830
## 3074 9.777798e-03 2.303022e-01 0.7599200
## 3084 6.108105e-03 1.582108e-01 0.8356811
## 3091 1.965614e-02 3.711465e-01 0.6091973
## 3098 6.724599e-03 1.713186e-01 0.8219568
## 3099 9.483601e-03 2.250138e-01 0.7655026
## 3104 5.995007e-03 1.557582e-01 0.8382468
## 3109 1.323564e-02 2.870487e-01 0.6997157
## 3110 1.717665e-02 3.414559e-01 0.6413675
## 3117 6.943642e-03 1.758719e-01 0.8171844
## 3118 3.178657e-02 4.805024e-01 0.4877111
## 3120 1.031839e-02 2.398186e-01 0.7498630
## 3129 1.129762e-02 2.564212e-01 0.7322812
## 3133 1.621244e-02 3.290212e-01 0.6547664
## 3140 1.310266e-08 4.061144e-07 0.9999996
## 3141 3.472162e-03 9.682516e-02 0.8997027
## 3143 1.232681e-02 2.730385e-01 0.7146347
## 3145 9.863637e-03 2.318305e-01 0.7583058
## 3148 2.308565e-02 4.074628e-01 0.5694515
## 3151 1.142593e-02 2.585383e-01 0.7300358
## 3152 1.102192e-02 2.518273e-01 0.7371508
## 3155 5.651185e-03 1.482079e-01 0.8461409
## 3156 4.645908e-03 1.252886e-01 0.8700655
## 3163 4.764391e-03 1.280575e-01 0.8671781
## 3165 1.376827e-02 2.949859e-01 0.6912459
## 3167 5.343384e-03 1.413262e-01 0.8533304
## 3169 1.325459e-02 2.873346e-01 0.6994108
## 3174 1.553525e-02 3.199649e-01 0.6644998
## 3175 1.661783e-02 3.343136e-01 0.6490686
## 3178 1.151496e-02 2.599995e-01 0.7284856
## 3181 9.555498e-03 2.263134e-01 0.7641311
## 3182 7.133595e-03 1.797776e-01 0.8130888
## 3186 1.491215e-02 3.113850e-01 0.6737028
## 3188 5.571366e-03 1.464346e-01 0.8479941
## 3189 4.091690e-03 1.120872e-01 0.8838211
## 3191 2.045125e-02 3.800267e-01 0.5995220
## 3196 1.304787e-02 2.842033e-01 0.7027489
## 3200 5.058429e-03 1.348496e-01 0.8600919
## 3201 1.372780e-02 2.943896e-01 0.6918826
## 3205 2.648555e-03 7.566281e-02 0.9216886
## 3207 1.359433e-02 2.924154e-01 0.6939903
## 3208 2.425161e-03 6.974276e-02 0.9278321
## 3209 7.522980e-03 1.876616e-01 0.8048154
## 3210 1.970721e-02 3.717258e-01 0.6085670
## 3212 1.633484e-02 3.306292e-01 0.6530360
## 3214 5.233916e-03 1.388503e-01 0.8559157
## 3218 4.575311e-03 1.236300e-01 0.8717946
## 3222 1.252310e-02 2.761158e-01 0.7113611
## 3234 4.358189e-03 1.184872e-01 0.8771546
## 3235 9.531699e-03 2.258838e-01 0.7645845
## 3238 1.250857e-02 2.758890e-01 0.7116025
## 3246 1.602052e-02 3.264823e-01 0.6574972
## 3249 1.307052e-02 2.845479e-01 0.7023816
## 3250 1.048016e-02 2.426170e-01 0.7469029
## 3252 1.837206e-02 3.561636e-01 0.6254644
## 3253 4.102667e-03 1.123528e-01 0.8835445
## 3255 1.432182e-02 3.030294e-01 0.6826488
## 3257 1.509283e-02 3.138979e-01 0.6710093
## 3262 5.801158e-09 1.798058e-07 0.9999998
## 3264 8.832011e-03 2.130164e-01 0.7781516
## 3266 4.599472e-03 1.241984e-01 0.8712021
## 3267 5.552099e-03 1.460054e-01 0.8484425
## 3268 6.352353e-03 1.634564e-01 0.8301912
## 3270 7.493079e-03 1.870619e-01 0.8054450
## 3271 2.038324e-02 3.792786e-01 0.6003381
## 3275 6.432288e-03 1.651581e-01 0.8284096
## 3281 1.496692e-02 3.121490e-01 0.6728841
## 3282 5.073535e-03 1.351955e-01 0.8597309
## 3283 2.169582e-02 3.933543e-01 0.5849498
## 3287 4.087917e-03 1.119959e-01 0.8839161
## 3288 1.036415e-02 2.406125e-01 0.7490234
## 3289 5.157792e-03 1.371197e-01 0.8577225
## 3295 2.322187e-02 4.088039e-01 0.5679742
## 3298 1.352863e-02 2.914392e-01 0.6950322
## 3300 1.432176e-02 3.030285e-01 0.6826498
## 3314 7.287457e-03 1.829124e-01 0.8098002
## 3316 1.220978e-02 2.711901e-01 0.7166001
## 3319 4.609104e-03 1.244248e-01 0.8709661
## 3320 4.110724e-03 1.125476e-01 0.8833417
## 3327 1.065445e-02 2.456069e-01 0.7437387
## 3329 6.788665e-03 1.726559e-01 0.8205554
## 3331 7.647478e-03 1.901483e-01 0.8022043
## 3340 7.584145e-03 1.888853e-01 0.8035305
## 3341 8.485468e-03 2.064709e-01 0.7850437
## 3344 5.203586e-03 1.381617e-01 0.8566347
## 3345 7.338046e-03 1.839375e-01 0.8087245
## 3346 2.081429e-02 3.839850e-01 0.5952007
## 3347 1.394732e-02 2.976101e-01 0.6884426
## 3354 1.329324e-02 2.879167e-01 0.6987901
## 3357 1.851712e-02 3.578974e-01 0.6235855
## 3359 6.953568e-03 1.760770e-01 0.8169694
## 3361 1.521157e-02 3.155381e-01 0.6692503
## 3363 2.789155e-03 7.934862e-02 0.9178622
## 3366 6.005297e-03 1.559819e-01 0.8380128
## 3370 1.782009e-02 3.494668e-01 0.6327131
## 3372 3.145240e-03 8.854741e-02 0.9083074
## 3376 2.738281e-03 7.801849e-02 0.9192432
## 3384 1.099614e-02 2.513945e-01 0.7376093
## 3386 4.082936e-03 1.118754e-01 0.8840417
## 3389 8.232870e-03 2.016255e-01 0.7901417
## 3390 6.264233e-03 1.615719e-01 0.8321638
## 3394 2.034729e-02 3.788823e-01 0.6007704
## 3398 5.208932e-03 1.382832e-01 0.8565079
## 3402 1.197308e-02 2.674198e-01 0.7206072
## 3405 3.073052e-03 8.669812e-02 0.9102288
## 3408 5.580120e-03 1.466294e-01 0.8477904
## 3413 7.168808e-03 1.804973e-01 0.8123339
## 3419 4.263757e-03 1.162305e-01 0.8795057
## 3421 3.444674e-03 9.613520e-02 0.9004201
## 3425 4.336334e-03 1.179660e-01 0.8776977
## 3426 4.120663e-03 1.127878e-01 0.8830916
## 3428 4.775557e-03 1.283175e-01 0.8669070
## 3431 4.337298e-03 1.179890e-01 0.8776737
## 3432 2.537774e-03 7.273691e-02 0.9247253
## 3445 1.611930e-02 3.277918e-01 0.6560889
## 3448 1.077758e-02 2.477037e-01 0.7415187
## 3451 2.631918e-02 4.374416e-01 0.5362392
## 3456 2.122148e-02 3.883548e-01 0.5904238
## 3457 2.965757e-02 4.647533e-01 0.5055891
## 3458 1.492588e-02 3.115768e-01 0.6734974
## 3463 1.325560e-02 2.873498e-01 0.6993946
## 3469 7.701855e-03 1.912293e-01 0.8010689
## 3471 7.457079e-03 1.863387e-01 0.8062042
## 3475 1.221266e-02 2.712358e-01 0.7165515
## 3476 1.362384e-02 2.928530e-01 0.6935232
## 3481 1.095150e-02 2.506439e-01 0.7384046
## 3482 1.343119e-02 2.899857e-01 0.6965831
## 3486 1.250376e-02 2.758139e-01 0.7116824
## 3489 1.245704e-02 2.750834e-01 0.7124596
## 3492 1.069176e-02 2.462436e-01 0.7430646
## 3494 5.809341e-03 1.516987e-01 0.8424920
## 3498 7.658783e-03 1.903733e-01 0.8019680
## 3499 4.621368e-03 1.247128e-01 0.8706658
## 3503 9.639014e-03 2.278172e-01 0.7625438
## 3504 1.187138e-02 2.657867e-01 0.7223419
## 3505 1.597741e-02 3.259091e-01 0.6581135
## 3506 9.202347e-03 2.198840e-01 0.7709137
## 3508 1.249399e-02 2.756613e-01 0.7118447
## 3511 5.720268e-03 1.497364e-01 0.8445433
## 3513 1.074893e-02 2.472170e-01 0.7420341
## 3515 8.351228e-03 2.039037e-01 0.7877450
## 3516 1.094145e-02 2.504746e-01 0.7385839
## 3518 1.426852e-02 3.022638e-01 0.6834677
## 3521 8.285212e-03 2.026347e-01 0.7890801
## 3525 1.141972e-02 2.584361e-01 0.7301442
## 3526 1.985422e-02 3.733864e-01 0.6067594
## 3530 1.027885e-02 2.391313e-01 0.7505898
## 3533 1.692537e-02 3.382660e-01 0.6448087
## 3535 1.522957e-02 3.157860e-01 0.6689844
## 3539 9.662201e-03 2.282336e-01 0.7621042
## 3540 2.238473e-02 4.004462e-01 0.5771691
## 3543 1.659688e-02 3.340424e-01 0.6493607
## 3544 4.743163e-03 1.275628e-01 0.8676941
## 3547 8.603931e-03 2.087215e-01 0.7826745
## 3549 1.426852e-02 3.022638e-01 0.6834677
## 3550 9.646951e-03 2.279598e-01 0.7623932
## 3553 6.581208e-03 1.683087e-01 0.8251100
## 3556 6.643697e-03 1.696233e-01 0.8237330
## 3561 9.368919e-03 2.229309e-01 0.7677002
## 3567 5.032806e-03 1.342622e-01 0.8607050
## 3573 1.314182e-02 2.856301e-01 0.7012280
## 3577 1.795730e-02 3.511464e-01 0.6308963
## 3581 1.679856e-02 3.366427e-01 0.6465587
## 3586 1.075015e-02 2.472377e-01 0.7420121
## 3587 3.243867e-02 4.850908e-01 0.4824705
## 3589 6.929300e-03 1.755754e-01 0.8174953
## 3590 1.542525e-02 3.184677e-01 0.6661070
## 3591 1.603935e-02 3.267323e-01 0.6572283
## 3601 7.433072e-03 1.858556e-01 0.8067113
## 3606 1.246535e-02 2.752134e-01 0.7123212
## 3608 1.131097e-02 2.566421e-01 0.7320469
## 3610 1.071870e-02 2.467027e-01 0.7425786
## 3620 7.231469e-03 1.817746e-01 0.8109939
## 3621 7.808782e-03 1.933460e-01 0.7988452
## 3623 1.483321e-02 3.102808e-01 0.6748860
## 3631 7.970389e-03 1.965227e-01 0.7955069
## 3633 1.108491e-02 2.528823e-01 0.7360328
## 3634 7.542604e-03 1.880546e-01 0.8044028
## 3640 6.818193e-03 1.732707e-01 0.8199111
## 3641 6.057123e-03 1.571071e-01 0.8368358
## 3646 1.227200e-02 2.721741e-01 0.7155539
## 3650 2.521425e-02 4.276178e-01 0.5471679
## 3651 5.599163e-03 1.470530e-01 0.8473478
## 3652 2.240155e-02 4.006168e-01 0.5769816
## 3660 8.679520e-03 2.101505e-01 0.7811700
## 3662 9.266597e-03 2.210623e-01 0.7696711
## 3663 1.051808e-02 2.432697e-01 0.7462122
## 3669 1.120328e-02 2.548562e-01 0.7339405
## 3689 1.411706e-02 3.000780e-01 0.6858050
## 3690 5.536370e-03 1.456546e-01 0.8488090
## 3691 1.330417e-02 2.880810e-01 0.6986148
## 3693 4.923955e-03 1.317572e-01 0.8633188
## 3694 4.328783e-03 1.177858e-01 0.8778854
## 3697 1.671750e-02 3.356003e-01 0.6476822
## 3699 3.944700e-03 1.085153e-01 0.8875400
## 3702 8.957117e-03 2.153509e-01 0.7756920
## 3711 1.201350e-02 2.680666e-01 0.7199199
## 3721 9.621924e-03 2.275100e-01 0.7628681
## 3722 1.764852e-02 3.473525e-01 0.6349990
## 3723 1.589388e-02 3.247950e-01 0.6593111
## 3726 1.548159e-02 3.192355e-01 0.6652830
## 3727 2.280024e-02 4.046294e-01 0.5725704
## 3731 3.259486e-03 9.145813e-02 0.9052824
## 3734 9.795374e-03 2.306157e-01 0.7595889
## 3735 5.509106e-03 1.450459e-01 0.8494450
## 3737 1.801054e-02 3.517954e-01 0.6301941
## 3742 1.582067e-02 3.238153e-01 0.6603640
## 3744 7.032384e-03 1.777015e-01 0.8152661
## 3750 1.203501e-02 2.684105e-01 0.7195545
## 3751 9.406089e-03 2.236073e-01 0.7669866
## 3752 1.506779e-02 3.135509e-01 0.6713814
## 3756 1.030427e-02 2.395733e-01 0.7501224
## 3760 1.841920e-02 3.567282e-01 0.6248526
## 3761 5.762494e-03 1.506678e-01 0.8435697
## 3765 2.325467e-02 4.091257e-01 0.5676197
## 3770 1.087848e-02 2.494125e-01 0.7397090
## 3776 1.097872e-02 2.511019e-01 0.7379194
## 3777 1.759595e-02 3.467016e-01 0.6357025
## 3784 1.148585e-02 2.595225e-01 0.7289917
## 3785 7.313983e-03 1.834502e-01 0.8092358
## 3788 1.582067e-02 3.238153e-01 0.6603640
## 3791 1.819233e-02 3.540004e-01 0.6278073
## 3797 1.238138e-02 2.738968e-01 0.7137218
## 3799 5.293541e-03 1.402008e-01 0.8545057
## 3802 1.722907e-02 3.421170e-01 0.6406540
## 3803 9.720285e-03 2.292745e-01 0.7610052
## 3808 8.927600e-03 2.148015e-01 0.7762709
## 3809 5.300762e-03 1.403640e-01 0.8543352
## 3811 9.331219e-03 2.222435e-01 0.7684252
## 3822 3.231226e-02 4.842096e-01 0.4834782
## 3823 2.271083e-03 6.561331e-02 0.9321156
## 3824 8.445587e-03 2.057101e-01 0.7858443
## 3828 1.610223e-02 3.275659e-01 0.6563319
## 3829 9.601833e-03 2.271485e-01 0.7632496
## 3833 9.919698e-03 2.328251e-01 0.7572552
## 3839 1.178768e-02 2.644366e-01 0.7237757
## 3841 9.820245e-03 2.310588e-01 0.7591210
## 3842 6.872164e-03 1.743920e-01 0.8187359
## 3843 9.757932e-03 2.299476e-01 0.7602945
## 3847 8.185559e-03 2.007109e-01 0.7911036
## 3850 5.118354e-03 1.362202e-01 0.8586615
## 3851 9.425287e-03 2.239562e-01 0.7666185
## 3855 6.436743e-03 1.652527e-01 0.8283106
## 3856 5.492295e-03 1.446702e-01 0.8498375
## 3858 1.206011e-02 2.688111e-01 0.7191288
## 3860 6.161305e-03 1.593593e-01 0.8344794
## 3862 1.208612e-02 2.692257e-01 0.7186882
## 3863 1.630732e-03 4.803398e-02 0.9503353
## 3873 1.694056e-02 3.384597e-01 0.6445997
## 3876 7.542604e-03 1.880546e-01 0.8044028
## 3877 1.133291e-02 2.570049e-01 0.7316622
## 3886 1.830779e-02 3.553920e-01 0.6263002
## 3889 9.429268e-03 2.240285e-01 0.7665422
## 3891 1.447776e-02 3.052586e-01 0.6802637
## 3894 6.612982e-03 1.689777e-01 0.8244093
## 3898 1.037190e-02 2.407468e-01 0.7488813
## 3900 1.303932e-02 2.840731e-01 0.7028876
## 3902 1.242698e-02 2.746125e-01 0.7129605
## 3903 1.540671e-02 3.182147e-01 0.6663786
## 3907 1.043874e-02 2.419026e-01 0.7476586
## 3912 1.174154e-02 2.636900e-01 0.7245684
## 3916 4.673869e-03 1.259437e-01 0.8693824
## 3918 1.582169e-02 3.238290e-01 0.6603493
## 3930 8.018981e-03 1.974726e-01 0.7945084
## 3935 1.312337e-02 2.853504e-01 0.7015263
## 3936 1.777424e-02 3.489033e-01 0.6333225
## 3938 1.407015e-02 2.993979e-01 0.6865320
## 3939 3.945578e-03 1.085368e-01 0.8875177
## 3940 1.355242e-02 2.917930e-01 0.6946546
## 3941 7.137953e-03 1.798667e-01 0.8129953
## 3945 1.206848e-02 2.689446e-01 0.7189869
## 3949 1.110308e-02 2.531861e-01 0.7357108
## 3953 6.575934e-03 1.681976e-01 0.8252265
## 3957 5.762212e-03 1.506616e-01 0.8435761
## 3960 1.499833e-02 3.125862e-01 0.6724155
## 3961 1.102507e-02 2.518801e-01 0.7370948
## 3977 1.110308e-02 2.531861e-01 0.7357108
## 3978 9.926417e-03 2.329442e-01 0.7571294
## 3980 1.002588e-02 2.347013e-01 0.7552728
## 3982 9.068947e-03 2.174251e-01 0.7735060
## 3985 6.611405e-03 1.689445e-01 0.8244441
## 3986 5.650958e-03 1.482029e-01 0.8461462
## 3988 1.090947e-02 2.499357e-01 0.7391548
## 3990 1.073293e-02 2.469449e-01 0.7423222
## 3991 4.308213e-03 1.172944e-01 0.8783974
## 3995 5.361974e-03 1.417452e-01 0.8528928
## 3997 4.925022e-03 1.317819e-01 0.8632931
## 4000 4.316209e-03 1.174855e-01 0.8781983
## 4001 1.337158e-02 2.890932e-01 0.6975352
## 4006 5.405012e-03 1.427135e-01 0.8518815
## 4010 7.988494e-03 1.968769e-01 0.7951346
## 4011 4.366544e-03 1.186863e-01 0.8769472
## 4012 9.988320e-03 2.340388e-01 0.7559729
## 4014 4.365856e-03 1.186699e-01 0.8769643
## 4023 5.895541e-03 1.535885e-01 0.8405159
## 4025 6.051597e-03 1.569873e-01 0.8369611
## 4029 1.073293e-02 2.469449e-01 0.7423222
## 4038 4.163634e-03 1.138246e-01 0.8820118
## 4040 2.243839e-03 6.487917e-02 0.9328770
## 4044 8.403243e-03 2.049006e-01 0.7866962
## 4045 1.065107e-02 2.455492e-01 0.7437998
## 4051 1.633828e-02 3.306742e-01 0.6529876
## 4052 1.168210e-02 2.627257e-01 0.7255922
## 4054 9.093781e-03 2.178841e-01 0.7730221
## 4070 1.448096e-02 3.053041e-01 0.6802150
## 4071 1.246382e-02 2.751894e-01 0.7123468
## 4074 1.764852e-02 3.473525e-01 0.6349990
## 4077 6.557485e-03 1.678085e-01 0.8256340
## 4083 5.024699e-03 1.340762e-01 0.8608991
## 4089 1.747332e-02 3.451773e-01 0.6373493
## 4092 3.732368e-03 1.033019e-01 0.8929657
## 4096 8.225440e-03 2.014820e-01 0.7902926
## 4097 1.128202e-02 2.561630e-01 0.7325550
## 4098 5.978686e-03 1.554030e-01 0.8386184
## 4103 7.985430e-03 1.968170e-01 0.7951976
## 4113 7.066135e-03 1.783951e-01 0.8145388
## 4116 1.289214e-02 2.818241e-01 0.7052837
## 4124 1.251311e-02 2.759599e-01 0.7115270
## 4126 2.503615e-02 4.259950e-01 0.5489688
## 4130 1.110308e-02 2.531861e-01 0.7357108
## 4135 6.499919e-03 1.665921e-01 0.8269080
## 4136 1.405291e-02 2.991476e-01 0.6867995
## 4138 1.106693e-02 2.525815e-01 0.7363516
## 4141 8.310184e-03 2.031153e-01 0.7885746
## 4142 1.098593e-02 2.512231e-01 0.7377910
## 4146 4.093167e-03 1.121230e-01 0.8837838
## 4152 1.329698e-02 2.879729e-01 0.6987301
## 4154 7.308526e-03 1.833396e-01 0.8093519
## 4156 3.963166e-03 1.089657e-01 0.8870711
## 4157 9.034939e-03 2.167956e-01 0.7741695
## 4159 1.110308e-02 2.531861e-01 0.7357108
## 4160 1.128009e-02 2.561309e-01 0.7325890
## 4170 1.784365e-02 3.497560e-01 0.6324004
## 4173 4.719211e-03 1.270038e-01 0.8682770
## 4175 1.427041e-02 3.022910e-01 0.6834386
## 4178 7.026296e-03 1.775763e-01 0.8153974
## 4180 2.025093e-02 3.778171e-01 0.6019320
## 4184 1.211924e-02 2.697530e-01 0.7181278
## 4191 4.939731e-03 1.321212e-01 0.8629390
## 4193 1.246382e-02 2.751894e-01 0.7123468
## 4194 1.466433e-02 3.079047e-01 0.6774310
## 4197 1.052724e-02 2.434271e-01 0.7460456
## 4199 1.763602e-02 3.471979e-01 0.6351661
## 4200 5.695908e-03 1.491981e-01 0.8451060
## 4203 1.026546e-02 2.388981e-01 0.7508364
## 4204 4.265279e-03 1.162670e-01 0.8794677
## 4212 1.291292e-02 2.821426e-01 0.7049445
## 4214 2.511502e-02 4.267150e-01 0.5481699
## 4215 1.687154e-02 3.375780e-01 0.6455505
## 4219 1.200462e-02 2.679247e-01 0.7200707
## 4223 1.370587e-02 2.940661e-01 0.6922280
## 4225 2.024155e-03 5.891509e-02 0.9390608
## 4227 9.398804e-03 2.234748e-01 0.7671263
## 4228 1.422172e-02 3.015899e-01 0.6841883
## 4231 2.233667e-02 3.999578e-01 0.5777055
## 4234 1.037914e-02 2.408721e-01 0.7487488
## 4242 4.882839e-03 1.308070e-01 0.8643101
## 4254 1.355672e-02 2.918569e-01 0.6945864
## 4256 1.518446e-02 3.151644e-01 0.6696511
## 4258 4.236330e-03 1.155728e-01 0.8801908
## 4271 8.206928e-03 2.011242e-01 0.7906688
## 4274 2.877314e-03 8.164406e-02 0.9154786
## 4278 9.605843e-03 2.272207e-01 0.7631734
## 4279 1.359181e-02 2.923781e-01 0.6940301
## 4281 1.044223e-02 2.419629e-01 0.7475949
## 4282 1.481189e-02 3.099818e-01 0.6752063
## 4286 1.582507e-02 3.238743e-01 0.6603007
## 4287 1.579546e-02 3.234772e-01 0.6607273
## 4289 1.438329e-02 3.039099e-01 0.6817068
## 4291 7.506612e-03 1.873334e-01 0.8051599
## 4293 1.162854e-02 2.618546e-01 0.7265168
## 4297 6.871881e-03 1.743861e-01 0.8187420
## 4300 5.282317e-03 1.399469e-01 0.8547708
## 4302 8.508237e-03 2.069045e-01 0.7845872
## 4305 6.388632e-08 1.980141e-06 0.9999980
## 4307 1.242111e-02 2.745204e-01 0.7130585
## 4309 4.236330e-03 1.155728e-01 0.8801908
## 4310 1.295536e-02 2.827919e-01 0.7042527
## 4312 1.624453e-02 3.294436e-01 0.6543119
## 4315 1.170924e-02 2.631664e-01 0.7251244
## 4323 7.894364e-03 1.950316e-01 0.7970740
## 4325 6.907038e-03 1.751148e-01 0.8179782
## 4328 5.355054e-03 1.415893e-01 0.8530557
## 4331 8.959909e-03 2.154029e-01 0.7756372
## 4332 7.164187e-03 1.804029e-01 0.8124329
## 4337 1.320850e-02 2.866391e-01 0.7001524
## 4341 9.798407e-03 2.306697e-01 0.7595319
## 4342 9.570820e-03 2.265898e-01 0.7638394
## 4344 2.152711e-03 6.241476e-02 0.9354325
## 4345 1.040209e-02 2.412694e-01 0.7483285
## 4346 1.342866e-02 2.899478e-01 0.6966235
## 4350 1.118511e-02 2.545540e-01 0.7342609
## 4354 1.365565e-02 2.933240e-01 0.6930203
## 4360 4.096238e-03 1.121973e-01 0.8837065
## 4364 1.715821e-02 3.412229e-01 0.6416188
## 4367 1.071575e-02 2.466523e-01 0.7426320
## 4370 4.817790e-03 1.292993e-01 0.8658829
## 4376 1.799306e-03 5.272822e-02 0.9454725
## 4378 1.603949e-02 3.267343e-01 0.6572262
## 4386 1.414791e-02 3.005245e-01 0.6853276
## 4387 4.280430e-02 5.458015e-01 0.4113942
## 4389 1.553120e-02 3.199099e-01 0.6645589
## 4395 2.446232e-02 4.206891e-01 0.5548486
## 4401 1.840005e-02 3.564990e-01 0.6251009
## 4404 1.624961e-02 3.295105e-01 0.6542399
## 4407 2.945997e-02 4.632290e-01 0.5073110
## 4411 9.359707e-03 2.227631e-01 0.7678772
## 4412 8.996869e-03 2.160896e-01 0.7749135
## 4413 1.658958e-02 3.339479e-01 0.6494625
## 4414 1.146747e-02 2.592209e-01 0.7293117
## 4418 1.498299e-02 3.123727e-01 0.6726443
## 4420 2.075492e-02 3.833417e-01 0.5959034
## 4422 1.498956e-02 3.124641e-01 0.6725463
## 4442 1.314648e-02 2.857007e-01 0.7011528
## 4444 9.860925e-03 2.317824e-01 0.7583567
## 4450 1.655037e-02 3.334395e-01 0.6500102
## 4451 1.847152e-02 3.573535e-01 0.6241750
## 4457 9.623554e-03 2.275393e-01 0.7628371
## 4462 9.138794e-03 2.187146e-01 0.7721466
## 4467 9.675751e-03 2.284767e-01 0.7618475
## 4475 8.578461e-03 2.082388e-01 0.7831827
## 4477 1.383448e-02 2.959588e-01 0.6902068
## 4479 7.952837e-03 1.961789e-01 0.7958682
## 4487 6.469247e-03 1.659424e-01 0.8275884
## 4499 8.167370e-03 2.003586e-01 0.7914740
## 4500 1.278870e-02 2.802341e-01 0.7069772
## 4503 1.276451e-02 2.798611e-01 0.7073743
## 4506 9.520449e-03 2.256805e-01 0.7647991
## 4515 1.592140e-02 3.251625e-01 0.6589161
## 4520 3.725853e-03 1.031410e-01 0.8931332
## 4525 1.216025e-02 2.704046e-01 0.7174351
## 4534 7.870858e-03 1.945694e-01 0.7975598
## 4536 1.281408e-02 2.806249e-01 0.7065610
## 4541 9.258789e-03 2.209193e-01 0.7698219
## 4542 1.129473e-02 2.563734e-01 0.7323319
## 4544 1.143080e-02 2.586183e-01 0.7299509
## 4545 1.029156e-02 2.393524e-01 0.7503561
## 4547 1.083976e-02 2.487578e-01 0.7404025
## 4548 7.649456e-03 1.901876e-01 0.8021629
## 4552 1.613698e-02 3.280256e-01 0.6558374
## 4554 1.368865e-02 2.938118e-01 0.6924996
## 4557 5.242858e-03 1.390532e-01 0.8557040
## 4560 6.052001e-03 1.569960e-01 0.8369520
## 4573 1.011048e-02 2.361890e-01 0.7537005
## 4574 4.347424e-03 1.182305e-01 0.8774220
## 4575 3.115077e-03 8.777565e-02 0.9091093
## 4576 5.060137e-03 1.348887e-01 0.8600511
## 4577 1.167180e-02 2.625584e-01 0.7257698
## 4580 5.896044e-03 1.535995e-01 0.8405044
## 4583 4.222683e-03 1.152452e-01 0.8805321
## 4585 1.086410e-02 2.491695e-01 0.7399664
## 4591 1.030422e-02 2.395725e-01 0.7501233
## 4593 2.476236e-03 7.110324e-02 0.9264205
## 4600 1.109329e-02 2.530225e-01 0.7358842
## 4601 1.050183e-02 2.429902e-01 0.7465080
## 4603 1.121231e-02 2.550062e-01 0.7337815
## 4604 9.215060e-03 2.201174e-01 0.7706675
## 4606 7.379685e-03 1.847792e-01 0.8078412
## 4607 1.450743e-02 3.056809e-01 0.6798116
## 4608 7.379685e-03 1.847792e-01 0.8078412
## 4619 3.989032e-03 1.095958e-01 0.8864152
## 4622 1.086410e-02 2.491695e-01 0.7399664
## 4624 1.182171e-02 2.649862e-01 0.7231921
## 4625 4.832760e-03 1.296468e-01 0.8655205
## 4626 1.023666e-02 2.383964e-01 0.7513670
## 4630 1.021162e-02 2.379593e-01 0.7518290
## 4632 1.418917e-02 3.011205e-01 0.6846903
## 4638 1.681788e-02 3.368906e-01 0.6462916
## 4639 1.104984e-02 2.522954e-01 0.7366548
## 4640 2.472647e-02 4.231462e-01 0.5521273
## 4641 1.775867e-02 3.487117e-01 0.6335296
## 4643 1.285629e-02 2.812739e-01 0.7058699
## 4646 1.564300e-02 3.214242e-01 0.6629328
## 4649 3.046946e-03 8.602742e-02 0.9109256
## 4650 1.918283e-02 3.657184e-01 0.6150988
## 4652 1.310131e-02 2.850156e-01 0.7018831
## 4660 8.732780e-03 2.111540e-01 0.7801132
## 4673 1.392913e-02 2.973445e-01 0.6887264
## 4674 1.872076e-02 3.603134e-01 0.6209658
## 4675 4.763458e-03 1.280357e-01 0.8672008
## 4680 1.066434e-02 2.457758e-01 0.7435599
## 4683 7.367826e-03 1.845396e-01 0.8080925
## 4687 1.609830e-02 3.275139e-01 0.6563878
## 4689 2.199429e-02 3.964511e-01 0.5815546
## 4692 7.191929e-03 1.809691e-01 0.8118390
## 4693 1.141250e-02 2.583173e-01 0.7302702
## 4695 1.773043e-02 3.483639e-01 0.6339057
## 4696 6.617191e-03 1.690662e-01 0.8243166
## 4697 1.161100e-02 2.615687e-01 0.7268203
## 4701 6.601476e-03 1.687356e-01 0.8246629
## 4704 1.693603e-02 3.384020e-01 0.6446620
## 4706 4.362261e-03 1.185842e-01 0.8770535
## 4707 2.216950e-02 3.982516e-01 0.5795789
## 4713 1.493028e-02 3.116382e-01 0.6734315
## 4714 6.451952e-03 1.655756e-01 0.8279725
## 4717 1.888634e-02 3.622624e-01 0.6188513
## 4726 1.276313e-02 2.798399e-01 0.7073969
## 4729 7.272118e-03 1.826010e-01 0.8101269
## 4730 5.998966e-03 1.558443e-01 0.8381568
## 4733 4.584252e-03 1.238405e-01 0.8715753
## 4734 1.463745e-02 3.075249e-01 0.6778377
## 4749 1.219923e-02 2.710229e-01 0.7167778
## 4753 8.958485e-03 2.153764e-01 0.7756652
## 4754 1.228289e-02 2.723461e-01 0.7153710
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## 4757 1.255848e-02 2.766674e-01 0.7107742
## 4758 6.236143e-03 1.609693e-01 0.8327945
## 4763 1.075377e-02 2.472993e-01 0.7419469
## 4764 4.205935e-03 1.148428e-01 0.8809513
## 4765 1.093765e-02 2.504107e-01 0.7386516
## 4771 3.452948e-03 9.634300e-02 0.9002041
## 4773 1.225188e-02 2.718563e-01 0.7158918
## 4774 9.727247e-03 2.293991e-01 0.7608737
## 4778 2.284246e-02 4.050506e-01 0.5721070
## 4783 1.259702e-02 2.772671e-01 0.7101359
## 4784 1.564107e-02 3.213982e-01 0.6629607
## 4785 1.596922e-02 3.257999e-01 0.6582308
## 4786 1.654344e-02 3.333495e-01 0.6501070
## 4787 9.501073e-03 2.253301e-01 0.7651689
## 4798 5.079773e-03 1.353383e-01 0.8595819
## 4799 6.448851e-03 1.655097e-01 0.8280414
## 4800 6.031416e-03 1.565494e-01 0.8374192
## 4806 1.047806e-02 2.425807e-01 0.7469412
## 4812 3.984590e-03 1.094876e-01 0.8865278
## 4815 4.069487e-03 1.115497e-01 0.8843809
## 4816 1.077935e-02 2.477338e-01 0.7414868
## 4818 2.902297e-03 8.229239e-02 0.9148053
## 4822 5.209393e-03 1.382936e-01 0.8564970
## 4826 2.893984e-03 8.207676e-02 0.9150293
## 4827 1.051110e-02 2.431497e-01 0.7463392
## 4833 7.691103e-03 1.910158e-01 0.8012931
## 4834 1.375056e-02 2.947251e-01 0.6915243
## 4839 1.461579e-02 3.072184e-01 0.6781658
## 4842 4.714223e-03 1.268873e-01 0.8683984
## 4844 5.665550e-03 1.485262e-01 0.8458082
## 4845 8.105169e-03 1.991516e-01 0.7927432
## 4850 4.817634e-03 1.292957e-01 0.8658867
## 4851 4.878775e-03 1.307130e-01 0.8644082
## 4854 1.079468e-02 2.479939e-01 0.7412114
## 4855 2.068696e-02 3.826034e-01 0.5967096
## 4864 1.841341e-02 3.566590e-01 0.6249276
## 4870 4.591728e-03 1.240163e-01 0.8713919
## 4872 7.045043e-03 1.779618e-01 0.8149932
## 4873 9.352384e-03 2.226296e-01 0.7680180
## 4875 9.641402e-03 2.278601e-01 0.7624985
## 4878 6.609887e-03 1.689126e-01 0.8244775
## 4880 7.099758e-03 1.790848e-01 0.8138155
## 4886 1.951691e-02 3.695610e-01 0.6109221
## 4892 9.490868e-03 2.251454e-01 0.7653638
## 4895 4.813973e-03 1.292107e-01 0.8659754
## 4898 1.205569e-02 2.687406e-01 0.7192037
## 4900 8.476387e-03 2.062978e-01 0.7852258
## 4902 9.263094e-03 2.209981e-01 0.7697388
## 4906 6.012403e-03 1.561364e-01 0.8378512
## 4907 5.073806e-03 1.352017e-01 0.8597245
## 4909 4.214563e-03 1.150501e-01 0.8807353
## 4915 3.747296e-03 1.036705e-01 0.8925822
## 4916 2.302537e-02 4.068671e-01 0.5701075
## 4918 6.514752e-03 1.669059e-01 0.8265794
## 4919 1.231602e-02 2.728686e-01 0.7148154
## 4922 9.478240e-03 2.249167e-01 0.7656051
## 4923 4.767561e-03 1.281313e-01 0.8671012
## 4926 4.918585e-03 1.316332e-01 0.8634482
## 4937 5.203466e-03 1.381589e-01 0.8566376
## 4938 8.550080e-03 2.077001e-01 0.7837498
## 4940 4.842087e-03 1.298631e-01 0.8652948
## 4946 6.445512e-03 1.654389e-01 0.8281156
## 4950 1.299733e-02 2.834330e-01 0.7035697
## 4954 1.288590e-03 3.835621e-02 0.9603552
## 4956 9.479108e-03 2.249324e-01 0.7655885
## 4958 3.845488e-03 1.060873e-01 0.8900672
## 4961 1.155025e-02 2.605769e-01 0.7278728
## 4962 8.107207e-03 1.991912e-01 0.7927016
## 4964 5.145664e-03 1.368433e-01 0.8580110
## 4967 6.849827e-03 1.739283e-01 0.8192218
## 4970 4.770825e-03 1.282073e-01 0.8670219
## 4971 1.234247e-02 2.732851e-01 0.7143724
## 4977 1.277000e-02 2.799458e-01 0.7072842
## 4979 3.581067e-03 9.954780e-02 0.8968711
## 4981 5.328175e-03 1.409831e-01 0.8536887
## 4990 3.821531e-03 1.054989e-01 0.8906796
## 4995 8.978864e-03 2.157552e-01 0.7752659
## 4996 1.339058e-02 2.893779e-01 0.6972315
## 5002 2.720650e-03 7.755661e-02 0.9197227
## 5005 2.765406e-03 7.872820e-02 0.9185064
## 5006 1.009002e-02 2.358299e-01 0.7540801
## 5007 4.720476e-03 1.270334e-01 0.8682461
## 5008 1.900364e-02 3.636349e-01 0.6173614
## 5009 1.115912e-02 2.541211e-01 0.7347198
## 5010 4.995673e-03 1.334094e-01 0.8615950
## 5013 2.572274e-03 7.365019e-02 0.9237775
## 5016 8.378188e-03 2.044207e-01 0.7872011
## 5017 5.206630e-03 1.382308e-01 0.8565625
## 5018 5.732504e-03 1.500066e-01 0.8442609
## 5025 1.459674e-02 3.069487e-01 0.6784545
## 5028 4.235295e-03 1.155480e-01 0.8802167
## 5031 1.454032e-02 3.061483e-01 0.6793113
## 5032 3.506634e-03 9.768883e-02 0.8988045
## 5034 4.578549e-03 1.237063e-01 0.8717152
## 5037 4.923574e-03 1.317484e-01 0.8633280
## 5041 5.801374e-03 1.515236e-01 0.8426751
## 5046 8.033794e-03 1.977617e-01 0.7942045
## 5049 5.328808e-03 1.409974e-01 0.8536738
## 5056 4.953522e-03 1.324392e-01 0.8626073
## 5059 1.637479e-02 3.311521e-01 0.6524731
## 5061 7.619586e-03 1.895926e-01 0.8027878
## 5062 3.675752e-03 1.019010e-01 0.8944232
## 5064 9.084467e-03 2.177120e-01 0.7732035
## 5067 4.707077e-03 1.267204e-01 0.8685725
## 5069 3.091640e-03 8.717504e-02 0.9097333
## 5088 1.357624e-02 2.921469e-01 0.6942769
## 5092 1.170598e-02 2.631134e-01 0.7251806
## 5093 1.342628e-02 2.899123e-01 0.6966614
## 5094 1.219412e-02 2.709420e-01 0.7168639
## 5100 1.773587e-02 3.484309e-01 0.6338333
## 5101 1.312606e-02 2.853912e-01 0.7014827
## 5104 1.842147e-02 3.567554e-01 0.6248231
## 5110 6.767311e-03 1.722107e-01 0.8210220
## 5112 6.076219e-03 1.575209e-01 0.8364029
## 5116 6.115403e-03 1.583686e-01 0.8355160
## 5119 9.583271e-03 2.268142e-01 0.7636025
## 5120 7.935751e-03 1.958441e-01 0.7962202
## 5121 7.426097e-03 1.857151e-01 0.8068588
## 5125 7.456269e-03 1.863224e-01 0.8062213
## 5131 1.986482e-02 3.735058e-01 0.6066294
## 5144 1.079468e-02 2.479939e-01 0.7412114
## 5146 7.485863e-03 1.869171e-01 0.8055971
## 5151 6.194140e-03 1.600665e-01 0.8337393
## 5155 1.210416e-02 2.695130e-01 0.7183829
## 5157 1.046398e-02 2.423382e-01 0.7471979
## 5158 5.119632e-03 1.362494e-01 0.8586310
## 5159 1.184310e-02 2.653310e-01 0.7228259
## 5166 9.304104e-03 2.217484e-01 0.7689475
## 5168 1.518950e-02 3.152339e-01 0.6695766
## 5170 5.607041e-03 1.472281e-01 0.8471648
## 5171 1.462352e-02 3.073278e-01 0.6780486
## 5173 1.408264e-02 2.995791e-01 0.6863382
## 5183 3.554879e-03 9.889466e-02 0.8975505
## 5185 1.445794e-02 3.049761e-01 0.6805660
## 5188 3.444889e-03 9.614060e-02 0.9004145
## 5190 1.100678e-02 2.515732e-01 0.7374200
## 5193 8.423705e-03 2.052920e-01 0.7862843
## 5196 1.015524e-02 2.369736e-01 0.7528712
## 5199 1.437736e-02 3.038251e-01 0.6817976
## 5205 1.253539e-02 2.763075e-01 0.7111571
## 5207 1.626437e-02 3.297045e-01 0.6540311
## 5212 1.205569e-02 2.687406e-01 0.7192037
## 5213 1.458332e-02 3.067586e-01 0.6786581
## 5214 1.080860e-02 2.482300e-01 0.7409614
## 5216 1.140244e-02 2.581517e-01 0.7304458
## 5218 1.261060e-02 2.774783e-01 0.7099111
## 5222 2.158116e-02 3.921546e-01 0.5862642
## 5226 1.446218e-02 3.050366e-01 0.6805012
## 5230 8.827624e-03 2.129342e-01 0.7782381
## 5237 4.545631e-03 1.229308e-01 0.8725236
## 5242 1.422123e-02 3.015829e-01 0.6841959
## 5245 5.303186e-03 1.404188e-01 0.8542780
## 5248 4.259512e-03 1.161288e-01 0.8796117
## 5252 5.825802e-03 1.520603e-01 0.8421139
## 5255 6.353334e-03 1.634773e-01 0.8301693
## 5257 4.870167e-03 1.305138e-01 0.8646161
## 5259 5.323821e-03 1.408849e-01 0.8537913
## 5263 3.747010e-03 1.036635e-01 0.8925895
## 5265 1.179541e-02 2.645614e-01 0.7236432
## 5266 1.473938e-02 3.089629e-01 0.6762978
## 5267 1.171449e-02 2.632515e-01 0.7250340
## 5275 1.151771e-02 2.600445e-01 0.7284378
## 5277 4.720476e-03 1.270334e-01 0.8682461
## 5279 1.483170e-02 3.102595e-01 0.6749088
## 5280 1.770457e-02 3.480450e-01 0.6342504
## 5283 2.411268e-02 4.173975e-01 0.5584898
## 5284 6.115403e-03 1.583686e-01 0.8355160
## 5289 1.608991e-02 3.274027e-01 0.6565074
## 5291 3.879182e-03 1.069135e-01 0.8892073
## 5293 4.455482e-03 1.207996e-01 0.8747450
## 5294 1.974702e-02 3.721765e-01 0.6080765
## 5296 3.253882e-03 9.131581e-02 0.9054303
## 5301 1.220448e-02 2.711061e-01 0.7166894
## 5304 1.072407e-02 2.467940e-01 0.7424819
## 5306 1.703965e-02 3.397211e-01 0.6432393
## 5308 9.821863e-03 2.310876e-01 0.7590905
## 5310 1.466686e-02 3.079405e-01 0.6773926
## 5312 2.729738e-03 7.779476e-02 0.9194755
## 5319 1.926565e-02 3.666760e-01 0.6140583
## 5321 1.945126e-02 3.688101e-01 0.6117387
## 5328 1.519007e-02 3.152417e-01 0.6695682
## 5329 3.362029e-03 9.405420e-02 0.9025838
## 5331 1.483170e-02 3.102595e-01 0.6749088
## 5335 1.714962e-02 3.411144e-01 0.6417360
## 5337 1.116124e-02 2.541564e-01 0.7346824
## 5339 1.502405e-02 3.129437e-01 0.6720322
## 5341 1.459471e-02 3.069199e-01 0.6784854
## 5342 2.381166e-02 4.145273e-01 0.5616611
## 5343 8.369242e-03 2.042493e-01 0.7873815
## 5352 1.640487e-02 3.315452e-01 0.6520500
## 5356 1.112148e-02 2.534934e-01 0.7353851
## 5358 1.310147e-02 2.850180e-01 0.7018806
## 5360 1.340267e-02 2.895590e-01 0.6970383
## 5361 9.276864e-03 2.212502e-01 0.7694729
## 5364 2.144332e-02 3.907050e-01 0.5878516
## 5365 5.556754e-03 1.461091e-01 0.8483341
## 5366 7.471714e-03 1.866329e-01 0.8058954
## 5371 1.599757e-02 3.261772e-01 0.6578252
## 5374 1.855800e-02 3.583841e-01 0.6230579
## 5375 9.449202e-03 2.243903e-01 0.7661605
## 5376 4.613931e-03 1.245382e-01 0.8708479
## 5377 9.326710e-03 2.221613e-01 0.7685120
## 5379 1.095917e-02 2.507730e-01 0.7382679
## 5380 7.309611e-03 1.833616e-01 0.8093288
## 5385 1.209351e-02 2.693434e-01 0.7185631
## 5389 8.496845e-03 2.066876e-01 0.7848155
## 5390 1.562560e-02 3.211891e-01 0.6631853
## 5392 4.952322e-03 1.324115e-01 0.8626362
## 5397 3.468629e-03 9.673652e-02 0.8997948
## 5398 1.808795e-02 3.527365e-01 0.6291756
## 5407 7.369517e-03 1.845738e-01 0.8080567
## 5414 1.404586e-02 2.990452e-01 0.6869090
## 5417 7.312866e-03 1.834276e-01 0.8092596
## 5418 1.358666e-02 2.923017e-01 0.6941117
## 5420 1.506625e-02 3.135295e-01 0.6714042
## 5431 2.652743e-02 4.392471e-01 0.5342255
## 5433 3.858808e-02 5.236166e-01 0.4377953
## 5437 4.519463e-03 1.223132e-01 0.8731673
## 5438 8.528891e-03 2.072975e-01 0.7841736
## 5442 1.694099e-02 3.384652e-01 0.6445938
## 5445 1.181725e-02 2.649141e-01 0.7232686
## 5449 1.100017e-02 2.514622e-01 0.7375376
## 5450 7.774317e-03 1.926650e-01 0.7995607
## 5456 4.479978e-03 1.213797e-01 0.8741403
## 5464 1.312576e-02 2.853867e-01 0.7014876
## 5466 1.750462e-02 3.455672e-01 0.6369282
## 5472 1.419725e-02 3.012371e-01 0.6845656
## 5479 2.515430e-02 4.270728e-01 0.5477729
## 5483 6.162809e-03 1.593917e-01 0.8344455
## 5491 1.248721e-02 2.755552e-01 0.7119576
## 5493 9.265833e-03 2.210483e-01 0.7696859
## 5495 1.386547e-02 2.964131e-01 0.6897215
## 5496 1.513791e-02 3.145217e-01 0.6703404
## 5498 1.473894e-02 3.089567e-01 0.6763043
## 5500 1.171630e-02 2.632809e-01 0.7250028
## 5501 8.570715e-03 2.080919e-01 0.7833374
## 5507 5.332594e-03 1.410829e-01 0.8535845
## 5508 8.187848e-03 2.007552e-01 0.7910570
## 5509 1.639804e-02 3.314560e-01 0.6521460
## 5510 1.877207e-02 3.609188e-01 0.6203091
## 5514 2.376856e-02 4.141136e-01 0.5621179
## 5515 1.555247e-02 3.201985e-01 0.6642490
## 5520 7.524780e-03 1.876976e-01 0.8047776
## 5526 1.277516e-02 2.800254e-01 0.7071995
## 5527 1.140482e-02 2.581909e-01 0.7304043
## 5528 1.583686e-02 3.240323e-01 0.6601309
## 5529 4.860728e-03 1.302952e-01 0.8648441
## 5531 1.140799e-02 2.582430e-01 0.7303490
## 5533 9.729579e-03 2.294408e-01 0.7608296
## 5534 1.406350e-02 2.993014e-01 0.6866351
## 5536 1.883339e-02 3.616406e-01 0.6195260
## 5541 2.216447e-02 3.982001e-01 0.5796354
## 5551 1.082149e-02 2.484485e-01 0.7407300
## 5555 1.401927e-02 2.986586e-01 0.6873221
## 5556 1.831598e-02 3.554905e-01 0.6261935
## 5559 1.663137e-02 3.344887e-01 0.6488799
## 5560 1.315437e-02 2.858203e-01 0.7010253
## 5565 1.170342e-02 2.630720e-01 0.7252246
## 5567 2.686291e-02 4.421259e-01 0.5310112
## 5568 1.521202e-02 3.155443e-01 0.6692437
## 5584 1.366990e-02 2.935347e-01 0.6927954
## 5585 1.590610e-02 3.249583e-01 0.6591356
## 5588 1.476084e-02 3.092648e-01 0.6759743
## 5589 1.398025e-02 2.980904e-01 0.6879294
## 5596 1.928285e-02 3.668745e-01 0.6138427
## 5607 1.093700e-02 2.503998e-01 0.7386632
## 5619 5.676926e-03 1.487781e-01 0.8455449
## 5620 2.329430e-03 6.718155e-02 0.9304890
## 5621 7.521932e-03 1.876406e-01 0.8048375
## 5626 1.199760e-02 2.678124e-01 0.7201900
## 5630 1.259786e-02 2.772802e-01 0.7101219
## 5632 3.425342e-02 4.973193e-01 0.4684273
## 5633 3.705088e-03 1.026275e-01 0.8936675
## 5634 2.112416e-02 3.873170e-01 0.5915588
## 5636 5.637655e-03 1.479079e-01 0.8464545
## 5637 1.764754e-02 3.473404e-01 0.6350121
## 5639 1.370870e-02 2.941079e-01 0.6921834
## 5640 1.187101e-02 2.657807e-01 0.7223483
## 5641 1.421113e-02 3.014373e-01 0.6843515
## 5643 4.644963e-03 1.252665e-01 0.8700885
## 5645 9.119329e-03 2.183557e-01 0.7725249
## 5647 1.056460e-02 2.440687e-01 0.7453667
## 5663 3.162457e-03 8.898730e-02 0.9078502
## 5666 6.320771e-03 1.627820e-01 0.8308972
## 5669 4.807681e-03 1.290645e-01 0.8661278
## 5673 1.129189e-02 2.563263e-01 0.7323818
## 5681 5.615914e-03 1.474253e-01 0.8469588
## 5684 1.407266e-02 2.994342e-01 0.6864931
## 5686 7.709381e-03 1.913786e-01 0.8009120
## 5687 1.183825e-02 2.652530e-01 0.7229087
## 5688 1.468103e-02 3.081406e-01 0.6771784
## 5690 5.060075e-03 1.348873e-01 0.8600526
## 5693 4.146161e-03 1.134033e-01 0.8824505
## 5697 1.753780e-02 3.459797e-01 0.6364825
## 5700 6.414805e-03 1.647865e-01 0.8287987
## 5706 2.058683e-02 3.815119e-01 0.5979013
## 5707 6.319954e-03 1.627646e-01 0.8309154
## 5715 4.617587e-03 1.246241e-01 0.8707584
## 5719 5.068881e-03 1.350890e-01 0.8598421
## 5723 4.413182e-03 1.197958e-01 0.8757910
## 5731 4.180240e-03 1.142246e-01 0.8815952
## 5732 1.137254e-02 2.576589e-01 0.7309685
## 5742 4.762735e-03 1.280189e-01 0.8672184
## 5755 1.677149e-02 3.362950e-01 0.6469335
## 5757 1.187998e-02 2.659250e-01 0.7221950
## 5761 1.098944e-02 2.512819e-01 0.7377286
## 5768 1.160804e-02 2.615204e-01 0.7268715
## 5771 1.271153e-02 2.790429e-01 0.7082456
## 5772 7.609671e-03 1.893948e-01 0.8029955
## 5773 1.080470e-02 2.481638e-01 0.7410315
## 5776 1.900995e-02 3.637085e-01 0.6172815
## 5781 8.552509e-03 2.077463e-01 0.7837012
## 5785 8.786501e-03 2.121634e-01 0.7790501
## 5789 2.406462e-03 6.924363e-02 0.9283499
## 5794 1.322156e-02 2.868363e-01 0.6999422
## 5801 1.257373e-02 2.769048e-01 0.7105215
## 5810 8.426636e-03 2.053480e-01 0.7862254
## 5815 4.413182e-03 1.197958e-01 0.8757910
## 5817 5.877751e-03 1.531992e-01 0.8409230
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## 5830 3.357656e-03 9.394381e-02 0.9026985
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## 5842 1.176478e-02 2.640662e-01 0.7241690
## 5844 9.659566e-03 2.281863e-01 0.7621541
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## 5888 8.106497e-03 1.991774e-01 0.7927161
## 5891 2.034277e-03 5.919164e-02 0.9387741
## 5893 8.132680e-03 1.996859e-01 0.7921814
## 5894 1.547936e-02 3.192051e-01 0.6653155
## 5898 4.044445e-03 1.109425e-01 0.8850131
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## 5906 4.330217e-03 1.178200e-01 0.8778498
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## 5916 1.419622e-02 3.012222e-01 0.6845816
## 5921 1.026681e-02 2.389217e-01 0.7508115
## 5922 1.306838e-02 2.845153e-01 0.7024163
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## 5926 1.982452e-02 3.730517e-01 0.6071238
## 5927 6.962703e-03 1.762657e-01 0.8167716
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## 5935 1.246671e-02 2.752346e-01 0.7122987
## 5939 3.046640e-03 8.601955e-02 0.9109338
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## 5959 1.652348e-02 3.330903e-01 0.6503862
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## 5965 5.620276e-03 1.475221e-01 0.8468576
## 5968 1.396107e-02 2.978107e-01 0.6882282
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## 5999 1.486706e-02 3.107547e-01 0.6743782
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## 6013 1.538374e-02 3.179009e-01 0.6667154
## 6015 1.232770e-02 2.730525e-01 0.7146198
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## 6039 1.493758e-02 3.117400e-01 0.6733224
## 6041 1.540274e-02 3.181604e-01 0.6664369
## 6042 8.817928e-03 2.127526e-01 0.7784294
## 6053 6.942533e-03 1.758490e-01 0.8172084
## 6054 6.026020e-03 1.564322e-01 0.8375418
## 6055 1.098044e-02 2.511307e-01 0.7378889
## 6061 1.538851e-02 3.179661e-01 0.6666454
## 6062 1.562529e-02 3.211848e-01 0.6631899
## 6064 1.999426e-02 3.749589e-01 0.6050469
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## 6069 1.460335e-02 3.070424e-01 0.6783543
## 6077 5.910581e-03 1.539174e-01 0.8401721
## 6080 8.633348e-03 2.092783e-01 0.7820883
## 6089 3.460623e-03 9.653565e-02 0.9000037
## 6092 9.328624e-03 2.221962e-01 0.7684752
## 6094 8.310169e-03 2.031150e-01 0.7885748
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## 6098 2.020649e-02 3.773243e-01 0.6024692
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## 6106 9.013466e-03 2.163975e-01 0.7745890
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## 6111 3.244948e-03 9.108881e-02 0.9056662
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## 6121 3.572362e-03 9.933082e-02 0.8970968
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## 6128 1.208249e-02 2.691679e-01 0.7187496
## 6129 1.558581e-02 3.206505e-01 0.6637637
## 6130 4.551681e-03 1.230734e-01 0.8723749
## 6134 2.000360e-02 3.750634e-01 0.6049330
## 6138 1.457117e-02 3.065862e-01 0.6788426
## 6140 1.129334e-02 2.563504e-01 0.7323562
## 6141 1.577180e-02 3.231596e-01 0.6610686
## 6142 1.226470e-02 2.720588e-01 0.7156765
## 6143 7.683926e-03 1.908732e-01 0.8014429
## 6145 1.077012e-02 2.475771e-01 0.7416528
## 6150 1.441074e-02 3.043024e-01 0.6812869
## 6151 1.077012e-02 2.475771e-01 0.7416528
## 6153 1.063404e-02 2.452581e-01 0.7441079
## 6156 1.046896e-02 2.424239e-01 0.7471071
## 6164 1.836568e-02 3.560871e-01 0.6255472
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## 6172 7.585089e-03 1.889042e-01 0.8035107
## 6178 1.866934e-02 3.597053e-01 0.6216253
## 6181 3.978699e-02 5.302395e-01 0.4299735
## 6188 8.503155e-03 2.068078e-01 0.7846891
## 6191 1.574100e-02 3.227456e-01 0.6615134
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## 6200 2.773504e-03 7.893985e-02 0.9182866
## 6203 1.853928e-02 3.581614e-01 0.6232993
## 6210 8.440636e-03 2.056155e-01 0.7859438
## 6214 1.200523e-02 2.679345e-01 0.7200603
## 6215 7.303867e-03 1.832452e-01 0.8094509
## 6216 8.540888e-03 2.075255e-01 0.7839336
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## 6224 2.016170e-02 3.768268e-01 0.6030115
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## 6236 1.196570e-02 2.673015e-01 0.7207328
## 6237 8.806116e-03 2.125313e-01 0.7786626
## 6238 1.276249e-02 2.798299e-01 0.7074076
## 6240 8.144852e-03 1.999221e-01 0.7919330
## 6243 9.148895e-03 2.189007e-01 0.7719504
## 6246 7.083190e-03 1.787451e-01 0.8141717
## 6247 6.424846e-03 1.650000e-01 0.8285752
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## 6275 1.553301e-02 3.199345e-01 0.6645325
## 6276 5.740180e-03 1.501759e-01 0.8440839
## 6279 2.188129e-03 6.337420e-02 0.9344377
## 6281 6.402403e-03 1.645227e-01 0.8290749
## 6283 6.003084e-03 1.559338e-01 0.8380631
## 6284 1.191147e-02 2.664314e-01 0.7216571
## 6287 2.044298e-02 3.799359e-01 0.5996211
## 6288 1.413874e-02 3.003918e-01 0.6854694
## 6290 1.159115e-02 2.612449e-01 0.7271639
## 6292 8.236453e-03 2.016947e-01 0.7900689
## 6294 1.137972e-02 2.577773e-01 0.7308430
## 6301 1.526029e-02 3.162086e-01 0.6685311
## 6305 9.174678e-03 2.193753e-01 0.7714500
## 6308 1.303739e-02 2.840436e-01 0.7029190
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## 6323 1.272877e-02 2.793094e-01 0.7079618
## 6334 1.110793e-02 2.532671e-01 0.7356250
## 6336 4.875753e-03 1.306431e-01 0.8644812
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## 6341 1.079517e-02 2.480022e-01 0.7412026
## 6342 1.220003e-02 2.710356e-01 0.7167643
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## 6368 1.283423e-02 2.809349e-01 0.7062309
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## 6377 1.042595e-02 2.416818e-01 0.7478923
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## 6407 2.151508e-02 3.914607e-01 0.5870243
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## 6433 1.036100e-02 2.405579e-01 0.7490811
## 6434 8.979678e-03 2.157703e-01 0.7752500
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## 6438 5.920599e-03 1.541362e-01 0.8399432
## 6439 1.633216e-02 3.305941e-01 0.6530737
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## 6493 1.368010e-02 2.936855e-01 0.6926344
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## 6496 6.031899e-03 1.565599e-01 0.8374082
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## 6503 8.572105e-03 2.081182e-01 0.7833097
## 6508 1.504870e-02 3.132860e-01 0.6716653
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## 6512 1.337955e-02 2.892127e-01 0.6974077
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## 6522 9.910508e-03 2.326623e-01 0.7574272
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## 6534 1.325804e-02 2.873865e-01 0.6993554
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## 6536 3.584320e-03 9.962886e-02 0.8967868
## 6537 7.347577e-03 1.841303e-01 0.8085221
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## 6547 1.487134e-02 3.108147e-01 0.6743140
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## 6554 1.388141e-02 2.966465e-01 0.6894721
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## 6561 1.952435e-02 3.696459e-01 0.6108297
## 6562 1.231743e-02 2.728907e-01 0.7147918
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## 6570 1.970544e-02 3.717057e-01 0.6085888
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## 6578 7.890471e-03 1.949551e-01 0.7971544
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## 6590 1.284240e-02 2.810605e-01 0.7060970
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## 6592 7.683217e-03 1.908591e-01 0.8014577
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## 6605 1.395492e-02 2.977211e-01 0.6883240
## 6607 7.160780e-03 1.803333e-01 0.8125059
## 6609 6.679477e-03 1.703740e-01 0.8229466
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## 6612 1.543132e-02 3.185506e-01 0.6660181
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## 6622 4.169964e-03 1.139771e-01 0.8818529
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## 6640 1.828899e-02 3.551659e-01 0.6265451
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## 6651 1.086685e-02 2.492160e-01 0.7399171
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## 6678 8.962119e-03 2.154439e-01 0.7755939
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## 6680 1.057939e-02 2.443225e-01 0.7450981
## 6687 1.185771e-02 2.655665e-01 0.7225758
## 6689 2.520677e-02 4.275499e-01 0.5472433
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## 6729 1.065099e-02 2.455478e-01 0.7438012
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## 6740 1.123929e-02 2.554544e-01 0.7333064
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## 6746 5.973573e-03 1.552916e-01 0.8387348
## 6748 1.498258e-02 3.123670e-01 0.6726504
## 6751 6.768779e-03 1.722413e-01 0.8209899
## 6752 7.314428e-03 1.834592e-01 0.8092263
## 6755 1.317352e-02 2.861102e-01 0.7007163
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## 6766 1.630591e-02 3.302499e-01 0.6534442
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## 6783 3.696199e-03 1.024075e-01 0.8938963
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## 6788 1.933987e-02 3.675314e-01 0.6131287
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## 6801 9.516118e-03 2.256022e-01 0.7648817
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## 6807 1.434266e-02 3.033282e-01 0.6823291
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## 6813 8.940033e-03 2.150330e-01 0.7760270
## 6814 1.721681e-02 3.419625e-01 0.6408207
## 6822 6.410403e-03 1.646929e-01 0.8288967
## 6823 5.745569e-03 1.502948e-01 0.8439597
## 6824 7.324384e-03 1.836609e-01 0.8090147
## 6825 5.736417e-03 1.500929e-01 0.8441707
## 6827 8.302681e-03 2.029709e-01 0.7887264
## 6832 7.544222e-03 1.880870e-01 0.8043688
## 6834 1.022037e-02 2.381122e-01 0.7516674
## 6838 1.209705e-02 2.693998e-01 0.7185032
## 6839 1.033438e-02 2.400962e-01 0.7495694
## 6842 1.026179e-02 2.388343e-01 0.7509039
## 6843 1.193353e-02 2.667856e-01 0.7212809
## 6845 5.725922e-03 1.498613e-01 0.8444128
## 6852 1.771430e-02 3.481650e-01 0.6341207
## 6854 4.444091e-03 1.205295e-01 0.8750264
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## 6863 1.206195e-02 2.688405e-01 0.7190976
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## 6872 1.039564e-02 2.411578e-01 0.7484466
## 6875 1.298261e-02 2.832083e-01 0.7038091
## 6885 1.922908e-02 3.662535e-01 0.6145174
## 6889 5.092202e-03 1.356226e-01 0.8592852
## 6891 1.304871e-02 2.842160e-01 0.7027352
## 6893 1.063927e-02 2.453475e-01 0.7440132
## 6897 1.484194e-02 3.104030e-01 0.6747550
## 6898 6.334699e-03 1.630796e-01 0.8305857
## 6907 8.172383e-03 2.004557e-01 0.7913719
## 6910 1.059886e-02 2.446561e-01 0.7447450
## 6913 7.074428e-03 1.785653e-01 0.8143603
## 6916 4.563799e-03 1.233589e-01 0.8720773
## 6918 1.572544e-02 3.225362e-01 0.6617384
## 6923 7.763978e-03 1.924605e-01 0.7997755
## 6926 1.198854e-02 2.676674e-01 0.7203441
## 6928 1.420002e-02 3.012772e-01 0.6845228
## 6930 1.031521e-02 2.397634e-01 0.7499214
## 6936 2.133274e-02 3.895361e-01 0.5891311
## 6937 1.120752e-02 2.549266e-01 0.7338659
## 6939 7.832545e-03 1.938148e-01 0.7983527
## 6945 7.634318e-03 1.898862e-01 0.8024795
## 6949 9.233355e-03 2.204531e-01 0.7703135
## 6950 5.028648e-03 1.341668e-01 0.8608046
## 6951 1.189184e-02 2.661159e-01 0.7219923
## 6952 1.054967e-02 2.438125e-01 0.7456378
## 6954 1.286839e-02 2.814597e-01 0.7056719
## 6957 1.334863e-02 2.887491e-01 0.6979023
## 6959 1.828295e-02 3.550932e-01 0.6266238
## 6960 5.999427e-03 1.558543e-01 0.8381463
## 6961 1.234271e-02 2.732889e-01 0.7143684
## 6962 2.534716e-02 4.288217e-01 0.5458311
## 6966 9.352656e-03 2.226346e-01 0.7680128
## 6968 1.007299e-02 2.355306e-01 0.7543964
## 6971 1.074248e-02 2.471073e-01 0.7421502
## 6974 1.384389e-02 2.960968e-01 0.6900593
## 6978 9.503422e-03 2.253725e-01 0.7651240
## 6980 1.088450e-02 2.495142e-01 0.7396013
## 6984 1.149771e-02 2.597169e-01 0.7287854
## 6985 1.138601e-02 2.578810e-01 0.7307329
## 6987 6.123322e-03 1.585397e-01 0.8353370
## 6992 5.478890e-03 1.443703e-01 0.8501509
## 6993 5.804672e-03 1.515961e-01 0.8425993
## 6995 9.983570e-03 2.339549e-01 0.7560615
## 6998 8.495633e-03 2.066645e-01 0.7848398
## 6999 1.121104e-02 2.549852e-01 0.7338038
## 7001 1.055715e-02 2.439410e-01 0.7455018
## 7004 1.167904e-02 2.626761e-01 0.7256449
## 7005 8.698731e-03 2.105128e-01 0.7807885
## 7006 1.407462e-02 2.994627e-01 0.6864626
## 7008 2.175717e-02 3.939939e-01 0.5842489
## 7009 6.854601e-03 1.740275e-01 0.8191179
## 7012 1.005903e-02 2.352851e-01 0.7546559
## 7014 8.414908e-03 2.051237e-01 0.7864613
## 7015 1.229526e-02 2.725412e-01 0.7151635
## 7016 5.279512e-03 1.398834e-01 0.8548370
## 7019 1.388860e-02 2.967519e-01 0.6893595
## 7026 1.182492e-02 2.650380e-01 0.7231371
## 7028 8.264645e-03 2.022385e-01 0.7894969
## 7029 4.707915e-03 1.267400e-01 0.8685521
## 7036 2.131590e-02 3.893577e-01 0.5893264
## 7043 1.176136e-02 2.640109e-01 0.7242278
## 7048 1.598000e-02 3.259435e-01 0.6580765
## 7051 4.646207e-03 1.252956e-01 0.8700582
## 7055 1.047780e-02 2.425763e-01 0.7469459
## 7058 1.059886e-02 2.446561e-01 0.7447450
## 7065 1.236092e-02 2.735753e-01 0.7140638
## 7066 1.041808e-02 2.415457e-01 0.7480362
## 7069 4.467437e-09 1.384674e-07 0.9999999
## 7073 1.205015e-02 2.686521e-01 0.7192978
## 7077 1.172703e-02 2.634549e-01 0.7248181
## 7079 1.230319e-02 2.726663e-01 0.7150305
## 7082 1.355555e-02 2.918396e-01 0.6946049
## 7083 1.064056e-02 2.453695e-01 0.7439900
## 7088 1.216193e-02 2.704315e-01 0.7174066
## 7091 1.681815e-02 3.368941e-01 0.6462877
## 7094 1.096444e-02 2.508617e-01 0.7381739
## 7100 5.853398e-03 1.526657e-01 0.8414809
## 7103 8.940302e-03 2.150380e-01 0.7760217
## 7106 6.654845e-03 1.698573e-01 0.8234878
## 7109 1.434273e-02 3.033293e-01 0.6823280
## 7110 9.745081e-03 2.297180e-01 0.7605370
## 7112 1.305292e-02 2.842801e-01 0.7026670
## 7114 1.263951e-02 2.779272e-01 0.7094333
## 7115 9.239764e-03 2.205706e-01 0.7701896
## 7116 6.840553e-03 1.737356e-01 0.8194238
## 7120 3.283062e-03 9.205640e-02 0.9046605
## 7130 7.764452e-03 1.924699e-01 0.7997657
## 7133 9.181603e-03 2.195027e-01 0.7713157
## 7139 1.076018e-02 2.474082e-01 0.7418316
## 7141 1.089476e-02 2.496874e-01 0.7394179
## 7144 1.094689e-02 2.505662e-01 0.7384869
## 7152 1.215329e-02 2.702941e-01 0.7175526
## 7155 8.174009e-03 2.004872e-01 0.7913388
## 7157 1.906897e-02 3.643962e-01 0.6165348
## 7158 1.230194e-02 2.726466e-01 0.7150514
## 7160 6.228431e-03 1.608037e-01 0.8329679
## 7161 4.862254e-03 1.303305e-01 0.8648072
## 7166 1.096878e-02 2.509346e-01 0.7380966
## 7167 1.494435e-02 3.118344e-01 0.6732213
## 7168 7.145785e-03 1.800269e-01 0.8128273
## 7178 1.473651e-02 3.089225e-01 0.6763410
## 7179 1.852381e-02 3.579771e-01 0.6234991
## 7181 6.265987e-03 1.616095e-01 0.8321245
## 7182 1.694448e-02 3.385097e-01 0.6445458
## 7186 1.110404e-02 2.532021e-01 0.7356938
## 7188 1.529322e-02 3.166609e-01 0.6680459
## 7191 1.190086e-02 2.662609e-01 0.7218383
## 7192 1.662546e-02 3.344123e-01 0.6489622
## 7196 2.250270e-02 4.016409e-01 0.5758564
## 7197 1.760644e-02 3.468316e-01 0.6355620
## 7202 8.708887e-03 2.107042e-01 0.7805869
## 7203 8.160765e-03 2.002307e-01 0.7916086
## 7207 1.436591e-02 3.036612e-01 0.6819729
## 7209 8.740287e-03 2.112952e-01 0.7799645
## 7210 1.202516e-02 2.682530e-01 0.7197219
## 7221 3.696824e-03 1.024230e-01 0.8938802
## 7222 7.132315e-03 1.797514e-01 0.8131163
## 7226 7.042914e-03 1.779180e-01 0.8150391
## 7228 1.451263e-02 3.057549e-01 0.6797325
## 7229 1.005685e-02 2.352467e-01 0.7546965
## 7237 1.407029e-02 2.993999e-01 0.6865298
## 7238 1.404597e-02 2.990467e-01 0.6869073
## 7241 1.606783e-02 3.271101e-01 0.6568220
## 7247 9.902925e-03 2.325279e-01 0.7575692
## 7248 7.337151e-03 1.839193e-01 0.8087435
## 7250 8.556981e-03 2.078312e-01 0.7836118
## 7270 1.328353e-02 2.877705e-01 0.6989460
## 7273 9.742162e-03 2.296658e-01 0.7605920
## 7275 1.076286e-02 2.474536e-01 0.7417835
## 7279 1.531457e-02 3.169538e-01 0.6677317
## 7280 6.438078e-03 1.652810e-01 0.8282809
## 7281 5.656703e-03 1.483302e-01 0.8460131
## 7282 1.503871e-02 3.131473e-01 0.6718140
## 7283 1.056968e-02 2.441560e-01 0.7452743
## 7285 1.100634e-02 2.515659e-01 0.7374278
## 7287 1.341449e-02 2.897360e-01 0.6968495
## 7294 1.027230e-02 2.390173e-01 0.7507104
## 7299 7.532980e-03 1.878619e-01 0.8046051
## 7302 9.451127e-03 2.244252e-01 0.7661237
## 7305 8.087850e-03 1.988148e-01 0.7930973
## 7314 1.136602e-02 2.575515e-01 0.7310824
## 7315 1.561393e-02 3.210312e-01 0.6633549
## 7317 1.096161e-02 2.508141e-01 0.7382243
## 7320 1.331881e-02 2.883012e-01 0.6983799
## 7330 1.071703e-03 3.211488e-02 0.9668134
## 7332 5.660039e-03 1.484041e-01 0.8459358
## 7337 4.052483e-03 1.111374e-01 0.8848101
## 7338 1.289877e-02 2.819257e-01 0.7051755
## 7339 1.082963e-02 2.485863e-01 0.7405841
## 7341 1.128877e-02 2.562747e-01 0.7324365
## 7342 7.276304e-03 1.826860e-01 0.8100377
## 7344 1.061723e-02 2.449706e-01 0.7444122
## 7346 7.413351e-03 1.854583e-01 0.8071283
## 7350 1.365371e-03 4.054577e-02 0.9580889
## 7355 4.052444e-03 1.111365e-01 0.8848110
## 7360 1.878163e-02 3.610314e-01 0.6201869
## 7364 7.173938e-03 1.806020e-01 0.8122240
## 7365 6.894626e-03 1.748577e-01 0.8182477
## 7366 1.042342e-02 2.416380e-01 0.7479386
## 7371 9.277104e-03 2.212546e-01 0.7694683
## 7373 1.116245e-02 2.541767e-01 0.7346608
## 7376 5.693040e-03 1.491347e-01 0.8451723
## 7380 4.161083e-03 1.137631e-01 0.8820758
## 7381 1.097941e-02 2.511135e-01 0.7379071
## 7387 9.028500e-03 2.166763e-01 0.7742952
## 7389 5.454305e-03 1.438197e-01 0.8507260
## 7392 4.590250e-03 1.239816e-01 0.8714282
## 7399 1.092936e-02 2.502710e-01 0.7387997
## 7402 1.087382e-02 2.493338e-01 0.7397924
## 7403 6.153429e-03 1.591895e-01 0.8346571
## 7408 3.705748e-03 1.026438e-01 0.8936504
## 7410 1.330898e-02 2.881534e-01 0.6985377
## 7412 1.420590e-02 3.013619e-01 0.6844322
## 7416 1.056494e-02 2.440745e-01 0.7453605
## 7419 9.138282e-03 2.187052e-01 0.7721565
## 7426 1.332584e-02 2.884068e-01 0.6982674
## 7428 1.026945e-02 2.389677e-01 0.7507628
## 7431 5.528640e-03 1.454821e-01 0.8489892
## 7432 7.492943e-03 1.870592e-01 0.8054479
## 7433 9.399437e-03 2.234864e-01 0.7671142
## 7436 6.462210e-03 1.657932e-01 0.8277446
## 7438 4.464432e-03 1.210116e-01 0.8745240
## 7440 1.163385e-02 2.619410e-01 0.7264252
## 7441 1.554682e-02 3.201220e-01 0.6643312
## 7447 7.478130e-03 1.867617e-01 0.8057601
## 7456 1.012738e-02 2.364855e-01 0.7533871
## 7457 1.222142e-02 2.713744e-01 0.7164042
## 7458 1.271767e-02 2.791379e-01 0.7081445
## 7462 1.142751e-02 2.585642e-01 0.7300083
## 7463 8.981228e-03 2.157991e-01 0.7752197
## 7466 1.236555e-02 2.736481e-01 0.7139864
## 7467 1.191945e-02 2.665596e-01 0.7215210
## 7472 1.089701e-02 2.497254e-01 0.7393776
## 7475 9.731820e-03 2.294809e-01 0.7607873
## 7484 8.031434e-03 1.977157e-01 0.7942529
## 7485 3.754800e-03 1.038557e-01 0.8923895
## 7487 8.005410e-03 1.972076e-01 0.7947870
## 7488 1.555038e-02 3.201702e-01 0.6642794
## 7490 1.270369e-02 2.789216e-01 0.7083747
## 7497 4.122073e-03 1.128218e-01 0.8830561
## 7498 1.424057e-02 3.018616e-01 0.6838979
## 7502 1.663556e-02 3.345429e-01 0.6488216
## 7507 1.040130e-02 2.412557e-01 0.7483430
## 7511 1.155742e-02 2.606942e-01 0.7277484
## 7519 4.939561e-03 1.321173e-01 0.8629431
## 7520 1.417510e-02 3.009173e-01 0.6849076
## 7523 1.106693e-02 2.525815e-01 0.7363516
## 7525 7.529792e-03 1.877981e-01 0.8046721
## 7526 9.808218e-03 2.308446e-01 0.7593472
## 7529 1.773814e-02 3.484589e-01 0.6338030
## 7530 8.271406e-03 2.023688e-01 0.7893598
## 7531 7.262920e-03 1.824142e-01 0.8103229
## 7532 4.314633e-03 1.174478e-01 0.8782375
## 7533 1.529015e-02 3.166188e-01 0.6680911
## 7534 5.563938e-03 1.462692e-01 0.8481669
## 7536 1.320952e-02 2.866545e-01 0.7001360
## 7538 1.763370e-02 3.471692e-01 0.6351971
## 7539 8.010309e-03 1.973033e-01 0.7946864
## 7543 1.255711e-02 2.766460e-01 0.7107969
## 7547 1.457628e-02 3.066587e-01 0.6787650
## 7549 5.403164e-03 1.426720e-01 0.8519249
## 7551 1.194648e-02 2.669934e-01 0.7210602
## 7552 1.336309e-02 2.889660e-01 0.6976709
## 7553 4.625410e-03 1.248077e-01 0.8705668
## 7556 1.328556e-02 2.878010e-01 0.6989134
## 7560 1.154330e-02 2.604634e-01 0.7279933
## 7566 1.179019e-02 2.644772e-01 0.7237326
## 7569 4.314633e-03 1.174478e-01 0.8782375
## 7570 9.464386e-03 2.246656e-01 0.7658700
## 7573 8.450847e-03 2.058105e-01 0.7857386
## 7580 7.149176e-03 1.800962e-01 0.8127546
## 7586 1.145202e-02 2.589671e-01 0.7295808
## 7597 9.120886e-03 2.183844e-01 0.7724947
## 7598 7.256741e-03 1.822886e-01 0.8104547
## 7601 1.222487e-02 2.714290e-01 0.7163461
## 7606 9.761834e-03 2.300172e-01 0.7602209
## 7612 5.220647e-03 1.385492e-01 0.8562301
## 7615 2.167084e-02 3.930934e-01 0.5852357
## 7616 1.274859e-02 2.796155e-01 0.7076359
## 7620 1.440296e-02 3.041912e-01 0.6814058
## 7626 1.459692e-02 3.069513e-01 0.6784518
## 7627 1.038726e-02 2.410128e-01 0.7486000
## 7629 1.537798e-02 3.178221e-01 0.6667999
## 7631 1.333659e-02 2.885682e-01 0.6980952
## 7633 1.663556e-02 3.345429e-01 0.6488216
## 7640 1.064818e-02 2.454998e-01 0.7438520
## 7645 1.714680e-02 3.410788e-01 0.6417744
## 7650 1.519628e-02 3.153273e-01 0.6694764
## 7651 1.372609e-02 2.943644e-01 0.6919096
## 7652 2.119699e-02 3.880940e-01 0.5907090
## 7654 7.701787e-03 1.912279e-01 0.8010703
## 7655 1.005158e-02 2.351540e-01 0.7547945
## 7659 1.212831e-02 2.698972e-01 0.7179745
## 7660 8.593793e-03 2.085295e-01 0.7828767
## 7665 5.894897e-03 1.535744e-01 0.8405307
## 7673 1.481038e-02 3.099606e-01 0.6752290
## 7674 1.056494e-02 2.440745e-01 0.7453605
## 7676 3.590645e-03 9.978644e-02 0.8966229
## 7677 1.443038e-02 3.045829e-01 0.6809867
## 7678 1.090183e-02 2.498068e-01 0.7392913
## 7685 7.144900e-03 1.800088e-01 0.8128463
## 7692 1.951470e-02 3.695357e-01 0.6109496
## 7697 9.133437e-03 2.186159e-01 0.7722507
## 7700 2.132760e-02 3.894817e-01 0.5891908
## 7704 2.734511e-02 4.462002e-01 0.5264546
## 7709 8.181485e-03 2.006320e-01 0.7911865
## 7712 1.152183e-02 2.601120e-01 0.7283662
## 7720 9.568444e-03 2.265470e-01 0.7638846
## 7721 1.328636e-02 2.878132e-01 0.6989005
## 7729 9.562514e-03 2.264400e-01 0.7639975
## 7730 5.512881e-03 1.451303e-01 0.8493569
## 7736 9.494696e-03 2.252147e-01 0.7652907
## 7739 1.270328e-02 2.789153e-01 0.7083815
## 7740 1.868993e-02 3.599490e-01 0.6213611
## 7741 1.555038e-02 3.201702e-01 0.6642794
## 7742 1.233236e-02 2.731260e-01 0.7145416
## 7743 5.215642e-03 1.384356e-01 0.8563488
## 7750 2.200035e-02 3.965136e-01 0.5814861
## 7753 1.418863e-02 3.011127e-01 0.6846987
## 7755 1.092936e-02 2.502710e-01 0.7387997
## 7757 1.092936e-02 2.502710e-01 0.7387997
## 7759 1.228648e-02 2.724027e-01 0.7153109
## 7761 1.714863e-02 3.411019e-01 0.6417495
## 7763 1.008324e-02 2.357108e-01 0.7542060
## 7764 3.935630e-03 1.082939e-01 0.8877704
## 7774 1.776052e-02 3.487345e-01 0.6335049
## 7778 7.148900e-03 1.800906e-01 0.8127605
## 7785 1.401254e-02 2.985606e-01 0.6874269
## 7788 9.640678e-03 2.278471e-01 0.7625122
## 7791 1.255478e-02 2.766097e-01 0.7108355
## 7793 2.815321e-03 8.003117e-02 0.9171535
## 7796 5.533156e-03 1.455829e-01 0.8488839
## 7797 5.531016e-03 1.455352e-01 0.8489338
## 7802 9.496704e-03 2.252510e-01 0.7652523
## 7805 2.247926e-02 4.014040e-01 0.5761168
## 7807 1.037062e-02 2.407246e-01 0.7489048
## 7811 9.298868e-03 2.216527e-01 0.7690485
## 7813 7.452580e-03 1.862482e-01 0.8062992
## 7814 1.754876e-02 3.461159e-01 0.6363353
## 7815 1.181436e-02 2.648676e-01 0.7233181
## 7826 2.774835e-03 7.897461e-02 0.9182506
## 7831 1.678803e-02 3.365076e-01 0.6467044
## 7837 1.294487e-02 2.826315e-01 0.7044236
## 7838 9.488445e-03 2.251015e-01 0.7654101
## 7842 1.632921e-03 4.809524e-02 0.9502718
## 7844 1.239992e-02 2.741881e-01 0.7134120
## 7846 1.810419e-02 3.529335e-01 0.6289623
## 7847 1.322266e-02 2.868529e-01 0.6999244
## 7849 1.124820e-02 2.556023e-01 0.7331495
## 7855 1.332997e-02 2.884688e-01 0.6982012
## 7857 1.162190e-02 2.617463e-01 0.7266318
## 7862 1.740093e-02 3.442736e-01 0.6383255
## 7869 1.710903e-02 3.406009e-01 0.6422901
## 7871 1.019673e-02 2.376993e-01 0.7521040
## 7876 1.421964e-02 3.015599e-01 0.6842204
## 7882 4.078948e-02 5.355801e-01 0.4236304
## 7883 1.651038e-02 3.329200e-01 0.6505696
## 7884 1.332244e-02 2.883557e-01 0.6983219
## 7888 1.096820e-02 2.509249e-01 0.7381069
## 7891 9.406753e-03 2.236194e-01 0.7669739
## 7892 9.928560e-03 2.329821e-01 0.7570893
## 7894 1.201321e-02 2.680620e-01 0.7199248
## 7896 1.162235e-02 2.617538e-01 0.7266239
## 7898 1.627852e-02 3.298905e-01 0.6538310
## 7910 2.595207e-02 4.342237e-01 0.5398242
## 7911 5.087560e-03 1.355165e-01 0.8593960
## 7921 1.114205e-02 2.538365e-01 0.7350214
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## 7984 1.931281e-02 3.672198e-01 0.6134674
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## 7989 1.733945e-02 3.435039e-01 0.6391566
## 7991 7.194964e-03 1.810310e-01 0.8117740
## 7999 1.259252e-02 2.771971e-01 0.7102103
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## 8013 1.765318e-02 3.474102e-01 0.6349366
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## 8018 1.492988e-02 3.116325e-01 0.6734376
## 8019 1.066957e-02 2.458650e-01 0.7434654
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## 8030 1.104785e-02 2.522619e-01 0.7366902
## 8034 6.243227e-03 1.611214e-01 0.8326354
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## 8054 8.294456e-03 2.028127e-01 0.7888929
## 8065 1.408980e-02 2.996828e-01 0.6862274
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## 8067 1.274736e-02 2.795965e-01 0.7076562
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## 8083 1.102556e-02 2.518883e-01 0.7370862
## 8089 1.852949e-02 3.580448e-01 0.6234258
## 8090 1.254911e-02 2.765214e-01 0.7109295
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## 8111 1.007063e-02 2.354891e-01 0.7544402
## 8113 1.311752e-02 2.852617e-01 0.7016208
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## 8128 2.385185e-02 4.149124e-01 0.5612357
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## 8150 5.293069e-03 1.401901e-01 0.8545168
## 8156 9.264581e-03 2.210254e-01 0.7697101
## 8167 1.331169e-02 2.881941e-01 0.6984942
## 8174 1.182757e-02 2.650807e-01 0.7230917
## 8176 1.619908e-02 3.288452e-01 0.6549557
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## 8208 1.417124e-02 3.008616e-01 0.6849671
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## 8216 1.661893e-02 3.343278e-01 0.6490532
## 8218 9.005952e-03 2.162581e-01 0.7747359
## 8222 1.656496e-02 3.336287e-01 0.6498063
## 8223 1.236519e-02 2.736425e-01 0.7139923
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## 8226 1.685742e-02 3.373973e-01 0.6457453
## 8227 7.195982e-03 1.810518e-01 0.8117522
## 8230 6.929900e-03 1.755879e-01 0.8174822
## 8234 1.564503e-02 3.214516e-01 0.6629033
## 8235 4.467124e-03 1.210754e-01 0.8744575
## 8237 1.109267e-02 2.530121e-01 0.7358952
## 8239 2.418592e-02 4.180908e-01 0.5577233
## 8242 1.097825e-02 2.510939e-01 0.7379278
## 8243 1.065928e-02 2.456895e-01 0.7436512
## 8247 7.602419e-03 1.892502e-01 0.8031474
## 8248 1.386984e-02 2.964771e-01 0.6896531
## 8253 1.164052e-02 2.620496e-01 0.7263098
## 8256 6.923934e-03 1.754645e-01 0.8176116
## 8257 1.778616e-02 3.490500e-01 0.6331639
## 8259 1.034719e-02 2.403185e-01 0.7493343
## 8267 8.195198e-03 2.008974e-01 0.7909074
## 8271 2.233687e-02 3.999598e-01 0.5777033
## 8272 1.199596e-02 2.677861e-01 0.7202179
## 8282 7.393379e-03 1.850556e-01 0.8075511
## 8288 6.835410e-03 1.736288e-01 0.8195358
## 8290 4.804947e-03 1.290010e-01 0.8661941
## 8291 9.205621e-03 2.199441e-01 0.7708503
## 8294 5.026908e-03 1.341268e-01 0.8608463
## 8295 1.425142e-02 3.020178e-01 0.6837308
## 8302 1.321383e-02 2.867196e-01 0.7000666
## 8303 2.374912e-03 6.840023e-02 0.9292249
## 8306 3.261304e-03 9.150429e-02 0.9052344
## 8308 9.718445e-03 2.292416e-01 0.7610400
## 8319 3.519756e-03 9.801713e-02 0.8984631
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## 8322 1.504750e-02 3.132694e-01 0.6716831
## 8325 1.574941e-02 3.228587e-01 0.6613919
## 8326 2.186002e-02 3.950626e-01 0.5830774
## 8328 4.375796e-03 1.189066e-01 0.8767176
## 8337 1.086636e-02 2.492077e-01 0.7399259
## 8340 5.555934e-03 1.460908e-01 0.8483532
## 8344 1.056151e-02 2.440157e-01 0.7454227
## 8345 4.625409e-03 1.248077e-01 0.8705669
## 8352 4.329944e-03 1.178135e-01 0.8778566
## 8359 8.231630e-03 2.016015e-01 0.7901669
## 8364 5.990246e-03 1.556546e-01 0.8383552
## 8365 1.031623e-02 2.397812e-01 0.7499026
## 8370 1.201710e-02 2.681242e-01 0.7198587
## 8381 8.557576e-03 2.078425e-01 0.7835999
## 8385 3.574021e-03 9.937217e-02 0.8970538
## 8387 8.274959e-03 2.024372e-01 0.7892878
## 8391 1.113766e-02 2.537634e-01 0.7350989
## 8395 1.031351e-02 2.397340e-01 0.7499525
## 8396 6.764380e-03 1.721495e-01 0.8210861
## 8400 1.257856e-02 2.769800e-01 0.7104415
## 8405 1.052320e-02 2.433577e-01 0.7461191
## 8406 1.087694e-02 2.493865e-01 0.7397366
## 8408 1.117469e-02 2.543806e-01 0.7344447
## 8409 3.750379e-03 1.037466e-01 0.8925030
## 8413 1.975084e-02 3.722197e-01 0.6080294
## 8415 1.420588e-02 3.013616e-01 0.6844325
## 8417 6.539401e-03 1.674268e-01 0.8260338
## 8418 8.957710e-03 2.153619e-01 0.7756804
## 8419 2.223574e-03 6.433231e-02 0.9334441
## 8420 1.466549e-02 3.079211e-01 0.6774134
## 8425 9.218931e-03 2.201885e-01 0.7705926
## 8426 1.514847e-02 3.146676e-01 0.6701839
## 8428 5.467956e-03 1.441255e-01 0.8504066
## 8430 1.163026e-02 2.618825e-01 0.7264872
## 8433 1.159690e-02 2.613388e-01 0.7270643
## 8437 4.367708e-03 1.187140e-01 0.8769183
## 8439 9.215544e-03 2.201263e-01 0.7706582
## 8442 2.883321e-02 4.583205e-01 0.5128463
## 8445 4.750302e-03 1.277292e-01 0.8675205
## 8448 6.312480e-03 1.626048e-01 0.8310827
## 8449 5.168741e-03 1.373691e-01 0.8574622
## 8459 7.026172e-03 1.775737e-01 0.8154001
## 8460 1.064389e-02 2.454264e-01 0.7439297
## 8464 6.776668e-03 1.724059e-01 0.8208175
## 8466 1.091972e-02 2.501085e-01 0.7389718
## 8468 1.121765e-02 2.550951e-01 0.7336873
## 8471 2.506237e-02 4.262346e-01 0.5487030
## 8474 3.636292e-03 1.009219e-01 0.8954418
## 8475 7.021488e-03 1.774773e-01 0.8155012
## 8476 9.864252e-03 2.318415e-01 0.7582943
## 8477 6.759619e-03 1.720502e-01 0.8211902
## 8486 9.306677e-03 2.217954e-01 0.7688979
## 8488 1.524055e-02 3.159371e-01 0.6688224
## 8490 1.655623e-02 3.335155e-01 0.6499283
## 8496 2.197868e-02 3.962900e-01 0.5817313
## 8497 8.319704e-03 2.032983e-01 0.7883820
## 8498 9.673987e-03 2.284451e-01 0.7618809
## 8501 4.519341e-03 1.223104e-01 0.8731703
## 8502 8.324831e-03 2.033968e-01 0.7882783
## 8504 8.700989e-03 2.105553e-01 0.7807437
## 8505 6.095794e-03 1.579446e-01 0.8359596
## 8508 5.100443e-03 1.358110e-01 0.8590885
## 8509 1.407168e-02 2.994201e-01 0.6865082
## 8510 2.065480e-02 3.822534e-01 0.5970918
## 8511 4.367708e-03 1.187140e-01 0.8769183
## 8513 1.095066e-02 2.506297e-01 0.7384196
## 8514 6.847837e-03 1.738870e-01 0.8192652
## 8517 7.589393e-03 1.889901e-01 0.8034205
## 8527 1.031336e-02 2.397313e-01 0.7499553
## 8528 1.209831e-02 2.694200e-01 0.7184817
## 8534 1.202082e-02 2.681836e-01 0.7197955
## 8535 9.106510e-03 2.181192e-01 0.7727743
## 8540 1.082590e-02 2.485232e-01 0.7406509
## 8542 1.101841e-02 2.517685e-01 0.7372131
## 8543 5.446274e-03 1.436397e-01 0.8509141
## 8545 3.452985e-03 9.634394e-02 0.9002031
## 8546 9.354105e-03 2.226610e-01 0.7679849
## 8547 1.120187e-02 2.548327e-01 0.7339654
## 8548 9.667559e-03 2.283298e-01 0.7620027
## 8551 1.333997e-02 2.886190e-01 0.6980410
## 8560 4.545568e-03 1.229293e-01 0.8725252
## 8561 1.159474e-02 2.613035e-01 0.7271017
## 8566 4.682059e-03 1.261354e-01 0.8691825
## 8567 1.327524e-02 2.876456e-01 0.6990791
## 8569 4.589711e-02 5.602642e-01 0.3938387
## 8570 4.630097e-03 1.249177e-01 0.8704522
## 8571 1.215556e-02 2.703303e-01 0.7175142
## 8575 5.889156e-03 1.534489e-01 0.8406620
## 8580 6.073049e-03 1.574522e-01 0.8364747
## 8584 2.197624e-02 3.962648e-01 0.5817589
## 8587 1.360976e-02 2.926443e-01 0.6937460
## 8600 1.322790e-02 2.869320e-01 0.6998401
## 8603 2.108248e-03 6.120743e-02 0.9366843
## 8607 1.069407e-02 2.462830e-01 0.7430229
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## 8626 1.139063e-02 2.579572e-01 0.7306522
## 8627 8.604561e-03 2.087335e-01 0.7826620
## 8629 3.546907e-03 9.869564e-02 0.8977575
## 8630 6.559959e-03 1.678607e-01 0.8255793
## 8635 1.046178e-02 2.423001e-01 0.7472381
## 8637 1.032293e-02 2.398975e-01 0.7497795
## 8646 6.902236e-03 1.750153e-01 0.8180824
## 8649 6.737282e-03 1.715837e-01 0.8216790
## 8651 7.106301e-03 1.792189e-01 0.8136748
## 8652 8.662050e-03 2.098207e-01 0.7815172
## 8656 7.863011e-03 1.944149e-01 0.7977220
## 8664 9.655083e-03 2.281058e-01 0.7622391
## 8667 4.628560e-03 1.248817e-01 0.8704898
## 8669 1.834241e-02 3.558079e-01 0.6258497
## 8672 5.878848e-03 1.532232e-01 0.8408979
## 8680 7.638459e-03 1.899687e-01 0.8023929
## 8681 6.158267e-03 1.592938e-01 0.8345479
## 8682 1.403791e-02 2.989296e-01 0.6870325
## 8683 3.567695e-03 9.921442e-02 0.8972179
## 8691 1.584360e-02 3.241226e-01 0.6600338
## 8700 1.758844e-02 3.466084e-01 0.6358032
## 8701 9.118447e-03 2.183395e-01 0.7725421
## 8707 1.045572e-02 2.421957e-01 0.7473486
## 8711 1.011555e-02 2.362780e-01 0.7536065
## 8715 3.574930e-02 5.068356e-01 0.4574151
## 8716 6.518244e-03 1.669797e-01 0.8265020
## 8721 9.288956e-03 2.214714e-01 0.7692396
## 8722 1.453653e-02 3.060945e-01 0.6793690
## 8724 1.620179e-02 3.288810e-01 0.6549172
## 8725 1.540226e-02 3.181538e-01 0.6664439
## 8729 5.240841e-03 1.390074e-01 0.8557518
## 8730 9.463887e-03 2.246566e-01 0.7658795
## 8731 7.547276e-03 1.881481e-01 0.8043046
## 8733 4.733716e-03 1.273424e-01 0.8679239
## 8735 1.533800e-02 3.172748e-01 0.6673872
## 8743 1.776804e-02 3.488270e-01 0.6334050
## 8744 2.008807e-02 3.760070e-01 0.6039049
## 8747 1.156000e-02 2.607363e-01 0.7277037
## 8758 1.285865e-02 2.813102e-01 0.7058311
## 8759 1.515296e-02 3.147297e-01 0.6701174
## 8762 9.336102e-03 2.223327e-01 0.7683312
## 8764 7.668130e-03 1.905592e-01 0.8017727
## 8769 8.431213e-03 2.054355e-01 0.7861333
## 8772 8.474230e-03 2.062566e-01 0.7852691
## 8773 1.832214e-02 3.555644e-01 0.6261134
## 8774 3.855920e-03 1.063433e-01 0.8898008
## 8775 1.687077e-02 3.375681e-01 0.6455612
## 8783 1.981864e-02 3.729854e-01 0.6071960
## 8784 1.342537e-02 2.898987e-01 0.6966760
## 8786 1.792069e-02 3.506992e-01 0.6313801
## 8790 7.722146e-03 1.916319e-01 0.8006460
## 8796 7.922898e-03 1.955919e-01 0.7964852
## 8798 1.512968e-02 3.144078e-01 0.6704625
## 8799 4.124709e-03 1.128855e-01 0.8829898
## 8804 1.663876e-02 3.345842e-01 0.6487770
## 8805 4.987846e-03 1.332294e-01 0.8617828
## 8806 1.529202e-02 3.166444e-01 0.6680636
## 8807 1.538582e-02 3.179293e-01 0.6666849
## 8811 1.607055e-02 3.271462e-01 0.6567832
## 8817 1.715813e-02 3.412219e-01 0.6416200
## 8818 4.827646e-03 1.295281e-01 0.8656442
## 8819 1.686912e-02 3.375470e-01 0.6455839
## 8820 1.501071e-02 3.127584e-01 0.6722309
## 8826 1.104433e-02 2.522030e-01 0.7367527
## 8830 1.368060e-02 2.936930e-01 0.6926264
## 8832 2.253136e-03 6.512984e-02 0.9326170
## 8835 1.865800e-02 3.595710e-01 0.6217710
## 8836 7.197721e-03 1.810872e-01 0.8117151
## 8845 1.422285e-02 3.016063e-01 0.6841708
## 8847 6.992342e-03 1.768770e-01 0.8161306
## 8850 1.446034e-02 3.050104e-01 0.6805293
## 8851 9.919311e-03 2.328183e-01 0.7572624
## 8854 1.412650e-02 3.002146e-01 0.6856589
## 8860 1.098322e-02 2.511774e-01 0.7378394
## 8861 8.570147e-03 2.080811e-01 0.7833488
## 8862 1.675736e-02 3.361133e-01 0.6471293
## 8866 2.693596e-02 4.427479e-01 0.5303161
## 8867 2.120607e-03 6.154335e-02 0.9363360
## 8871 9.752304e-03 2.298470e-01 0.7604007
## 8872 1.153211e-02 2.602803e-01 0.7281876
## 8881 3.989857e-03 1.096159e-01 0.8863943
## 8882 1.399887e-02 2.983617e-01 0.6876395
## 8884 9.609791e-03 2.272918e-01 0.7630984
## 8891 8.978736e-03 2.157528e-01 0.7752684
## 8892 7.397364e-03 1.851360e-01 0.8074667
## 8893 1.117492e-02 2.543844e-01 0.7344407
## 8895 1.226575e-02 2.720755e-01 0.7156588
## 8896 1.949262e-02 3.692834e-01 0.6112239
## 8900 1.392294e-02 2.972541e-01 0.6888230
## 8903 1.650249e-02 3.328175e-01 0.6506800
## 8904 8.977211e-03 2.157245e-01 0.7752983
## 8905 1.239334e-02 2.740847e-01 0.7135220
## 8906 1.224321e-02 2.717192e-01 0.7160376
## 8907 7.348883e-03 1.841567e-01 0.8084944
## 8911 1.592803e-02 3.252510e-01 0.6588209
## 8919 1.224182e-02 2.716972e-01 0.7160610
## 8920 1.308614e-02 2.847852e-01 0.7021286
## 8922 8.714930e-03 2.108180e-01 0.7804671
## 8927 1.559145e-02 3.207269e-01 0.6636816
## 8935 9.290106e-03 2.214925e-01 0.7692174
## 8942 1.931612e-02 3.672580e-01 0.6134259
## 8945 4.382276e-03 1.190609e-01 0.8765569
## 8948 1.028103e-02 2.391692e-01 0.7505498
## 8949 7.431560e-03 1.858252e-01 0.8067433
## 8951 1.408893e-02 2.996704e-01 0.6862407
## 8952 1.059845e-02 2.446491e-01 0.7447525
## 8953 8.837946e-03 2.131275e-01 0.7780346
## 8955 1.361337e-02 2.926978e-01 0.6936888
## 8959 1.212130e-02 2.697858e-01 0.7180929
## 8961 6.198384e-03 1.601578e-01 0.8336438
## 8965 1.344814e-02 2.902391e-01 0.6963128
## 8967 1.954849e-02 3.699214e-01 0.6105301
## 8970 3.386921e-03 9.468204e-02 0.9019310
## 8971 3.739851e-03 1.034867e-01 0.8927734
## 8973 7.643512e-03 1.900693e-01 0.8022872
## 8978 1.337506e-02 2.891454e-01 0.6974795
## 8982 1.294722e-02 2.826675e-01 0.7043853
## 8984 1.097462e-02 2.510329e-01 0.7379925
## 8985 1.020166e-02 2.377855e-01 0.7520128
## 8986 1.195852e-02 2.671865e-01 0.7208550
## 8990 5.818719e-03 1.519047e-01 0.8422766
## 8992 1.511473e-02 3.142010e-01 0.6706842
## 8998 9.381556e-03 2.231610e-01 0.7674574
## 9001 7.817943e-03 1.935268e-01 0.7986553
## 9006 8.942183e-03 2.150730e-01 0.7759848
## 9011 1.205454e-02 2.687222e-01 0.7192232
## 9012 9.423062e-03 2.239158e-01 0.7666612
## 9013 7.600288e-03 1.892076e-01 0.8031921
## 9015 1.633299e-02 3.306049e-01 0.6530621
## 9017 1.436014e-02 3.035786e-01 0.6820612
## 9018 2.342328e-02 4.107734e-01 0.5658033
## 9021 1.022360e-02 2.381686e-01 0.7516078
## 9025 6.677090e-03 1.703239e-01 0.8229990
## 9033 1.077062e-02 2.475855e-01 0.7416438
## 9037 9.562528e-03 2.264403e-01 0.7639972
## 9041 1.037168e-02 2.407429e-01 0.7488854
## 9046 5.881558e-03 1.532826e-01 0.8408359
## 9049 5.769027e-03 1.508118e-01 0.8434192
## 9054 1.215308e-02 2.702909e-01 0.7175560
## 9057 1.023843e-02 2.384273e-01 0.7513343
## 9063 1.313305e-02 2.854971e-01 0.7013698
## 9076 6.523170e-03 1.670838e-01 0.8263930
## 9077 1.264840e-02 2.780651e-01 0.7092865
## 9079 1.083849e-02 2.487362e-01 0.7404253
## 9080 6.056599e-03 1.570957e-01 0.8368477
## 9083 9.952225e-03 2.334009e-01 0.7566468
## 9084 9.372972e-03 2.230047e-01 0.7676223
## 9090 1.057376e-02 2.442258e-01 0.7452004
## 9092 1.256751e-02 2.768080e-01 0.7106245
## 9095 1.741740e-02 3.444795e-01 0.6381031
## 9097 1.194148e-02 2.669133e-01 0.7211453
## 9098 2.240798e-02 4.006821e-01 0.5769099
## 9100 1.993652e-02 3.743116e-01 0.6057519
## 9101 5.999270e-03 1.558509e-01 0.8381499
## 9105 1.719372e-02 3.416713e-01 0.6411350
## 9108 2.064265e-02 3.821210e-01 0.5972364
## 9109 7.729744e-03 1.917825e-01 0.8004878
## 9117 1.063196e-02 2.452226e-01 0.7441454
## 9119 1.227689e-02 2.722514e-01 0.7154717
## 9127 2.311065e-03 6.668854e-02 0.9310004
## 9130 1.083372e-02 2.486555e-01 0.7405108
## 9133 1.115538e-02 2.540588e-01 0.7347859
## 9136 1.011879e-02 2.363348e-01 0.7535464
## 9139 1.487574e-02 3.108762e-01 0.6742481
## 9151 1.234198e-02 2.732774e-01 0.7143806
## 9153 1.463798e-02 3.075324e-01 0.6778296
## 9156 1.306780e-02 2.845064e-01 0.7024258
## 9158 1.267949e-02 2.785469e-01 0.7087736
## 9162 1.323968e-02 2.871098e-01 0.6996505
## 9163 1.849838e-02 3.576740e-01 0.6238276
## 9166 1.455143e-02 3.063061e-01 0.6791425
## 9170 1.699577e-02 3.391632e-01 0.6438410
## 9180 1.641147e-02 3.316314e-01 0.6519571
## 9182 4.468603e-03 1.211104e-01 0.8744210
## 9186 3.574585e-03 9.938623e-02 0.8970392
## 9187 1.593136e-02 3.252954e-01 0.6587732
## 9192 1.253610e-02 2.763186e-01 0.7111453
## 9194 9.729699e-03 2.294429e-01 0.7608274
## 9197 1.315601e-02 2.858450e-01 0.7009990
## 9199 1.659252e-02 3.339860e-01 0.6494215
## 9201 1.263825e-02 2.779076e-01 0.7094542
## 9202 1.457078e-02 3.065807e-01 0.6788485
## 9203 8.647419e-03 2.095443e-01 0.7818082
## 9205 1.662287e-02 3.343788e-01 0.6489984
## 9208 1.134422e-02 2.571916e-01 0.7314642
## 9209 4.214897e-03 1.150582e-01 0.8807269
## 9214 1.702248e-02 3.395029e-01 0.6434746
## 9216 8.104949e-03 1.991473e-01 0.7927477
## 9217 1.717182e-02 3.413949e-01 0.6414332
## 9219 1.084054e-02 2.487710e-01 0.7403885
## 9220 3.619193e-03 1.004969e-01 0.8958839
## 9224 9.146870e-03 2.188634e-01 0.7719897
## 9229 7.995555e-03 1.970150e-01 0.7949895
## 9234 2.165762e-02 3.929553e-01 0.5853871
## 9235 1.758187e-02 3.465270e-01 0.6358911
## 9237 5.599912e-03 1.470697e-01 0.8473304
## 9238 2.263970e-03 6.542175e-02 0.9323143
## 9246 1.963010e-02 3.708507e-01 0.6095192
## 9249 5.737523e-03 1.501173e-01 0.8441452
## 9252 3.390386e-03 9.476937e-02 0.9018402
## 9253 1.062111e-02 2.450370e-01 0.7443419
## 9254 1.649248e-02 3.326873e-01 0.6508202
## 9257 1.706979e-02 3.401036e-01 0.6428266
## 9262 1.565535e-02 3.215910e-01 0.6627536
## 9266 7.982565e-03 1.967609e-01 0.7952565
## 9267 7.736829e-03 1.919229e-01 0.8003403
## 9271 1.294595e-02 2.826482e-01 0.7044058
## 9272 1.083482e-02 2.486741e-01 0.7404910
## 9274 5.708898e-03 1.494853e-01 0.8448058
## 9277 9.215991e-03 2.201345e-01 0.7706495
## 9279 2.216832e-02 3.982395e-01 0.5795921
## 9280 1.379658e-02 2.954022e-01 0.6908012
## 9281 6.378667e-03 1.640174e-01 0.8296039
## 9282 9.196724e-03 2.197807e-01 0.7710226
## 9283 1.167785e-02 2.626566e-01 0.7256655
## 9288 1.074181e-02 2.470958e-01 0.7421624
## 9290 7.472525e-03 1.866492e-01 0.8058783
## 9294 5.261106e-03 1.394667e-01 0.8552722
## 9305 4.204436e-03 1.148067e-01 0.8809888
## 9318 1.156039e-02 2.607428e-01 0.7276968
## 9319 1.439758e-02 3.041144e-01 0.6814881
## 9323 5.300843e-03 1.403658e-01 0.8543333
## 9325 1.427681e-02 3.023829e-01 0.6833402
## 9328 1.010792e-02 2.361441e-01 0.7537480
## 9329 7.659920e-03 1.903959e-01 0.8019442
## 9330 6.748481e-03 1.718177e-01 0.8214339
## 9336 8.202284e-03 2.010344e-01 0.7907633
## 9338 2.634733e-02 4.376865e-01 0.5359662
## 9344 7.766896e-03 1.925182e-01 0.7997149
## 9345 1.002896e-02 2.347556e-01 0.7552154
## 9346 1.335743e-02 2.888810e-01 0.6977616
## 9351 9.400828e-03 2.235117e-01 0.7670875
## 9352 9.851130e-03 2.316083e-01 0.7585406
## 9353 9.578303e-03 2.267247e-01 0.7636970
## 9360 3.618962e-03 1.004912e-01 0.8958899
## 9362 1.458416e-02 3.067705e-01 0.6786454
## 9363 8.663505e-03 2.098482e-01 0.7814883
## 9366 1.814779e-02 3.534618e-01 0.6283904
## 9369 6.662640e-03 1.700209e-01 0.8233165
## 9373 1.705750e-02 3.399477e-01 0.6429948
## 9377 7.742140e-03 1.920281e-01 0.8002297
## 9378 1.038317e-02 2.409419e-01 0.7486749
## 9383 1.689618e-02 3.378931e-01 0.6452107
## 9384 9.164526e-03 2.191885e-01 0.7716469
## 9386 2.080209e-02 3.838530e-01 0.5953449
## 9387 9.341414e-03 2.224296e-01 0.7682290
## 9388 1.409447e-02 2.997507e-01 0.6861549
## 9390 2.285054e-02 4.051311e-01 0.5720183
## 9393 1.055740e-02 2.439452e-01 0.7454974
## 9401 9.003867e-03 2.162195e-01 0.7747767
## 9402 1.368480e-02 2.937549e-01 0.6925603
## 9404 1.026439e-02 2.388796e-01 0.7508560
## 9405 1.207557e-02 2.690576e-01 0.7188669
## 9409 1.273783e-02 2.794494e-01 0.7078128
## 9413 1.132992e-02 2.569555e-01 0.7317146
## 9414 8.565425e-03 2.079915e-01 0.7834431
## 9418 1.203510e-02 2.684119e-01 0.7195530
## 9419 1.390779e-02 2.970325e-01 0.6890597
## 9425 7.442341e-03 1.860422e-01 0.8065155
## 9430 2.251519e-02 4.017671e-01 0.5757177
## 9431 1.215705e-02 2.703539e-01 0.7174890
## 9434 1.562890e-02 3.212337e-01 0.6631374
## 9435 1.064519e-02 2.454488e-01 0.7439060
## 9436 9.770041e-03 2.301638e-01 0.7600662
## 9437 1.545190e-02 3.188312e-01 0.6657169
## 9439 1.736275e-02 3.437959e-01 0.6388413
## 9442 8.737751e-03 2.112475e-01 0.7800147
## 9443 1.511017e-02 3.141380e-01 0.6707518
## 9446 1.220129e-02 2.710557e-01 0.7167431
## 9447 1.044930e-02 2.420850e-01 0.7474657
## 9448 2.127883e-02 3.889643e-01 0.5897568
## 9450 2.060252e-02 3.816832e-01 0.5977143
## 9452 1.054132e-02 2.436691e-01 0.7457896
## 9454 1.981332e-02 3.729254e-01 0.6072612
## 9462 6.629031e-03 1.693152e-01 0.8240558
## 9464 1.240936e-02 2.743362e-01 0.7132544
## 9465 1.543412e-03 4.558335e-02 0.9528732
## 9466 1.566972e-02 3.217851e-01 0.6625451
## 9467 9.076807e-03 2.175704e-01 0.7733527
## 9472 1.389113e-02 2.967889e-01 0.6893200
## 9473 1.210377e-02 2.695068e-01 0.7183894
## 9482 1.751565e-02 3.457044e-01 0.6367800
## 9486 1.024971e-02 2.386239e-01 0.7511264
## 9491 8.095619e-03 1.989659e-01 0.7929385
## 9492 1.442552e-02 3.045135e-01 0.6810610
## 9497 2.180085e-02 3.944483e-01 0.5837509
## 9504 1.123775e-02 2.554288e-01 0.7333334
## 9505 8.226924e-03 2.015107e-01 0.7902624
## 9506 1.505227e-02 3.133356e-01 0.6716122
## 9510 1.282886e-02 2.808524e-01 0.7063187
## 9516 2.125276e-02 3.886874e-01 0.5900598
## 9517 1.062643e-02 2.451280e-01 0.7442456
## 9519 7.082735e-03 1.787357e-01 0.8141815
## 9521 7.110274e-03 1.793002e-01 0.8135895
## 9530 1.305998e-02 2.843875e-01 0.7025525
## 9534 7.313749e-03 1.834455e-01 0.8092408
## 9541 1.421570e-02 3.015032e-01 0.6842811
## 9545 1.458821e-02 3.068278e-01 0.6785840
## 9548 2.082796e-02 3.841329e-01 0.5950392
## 9549 1.135064e-02 2.572977e-01 0.7313517
view(predictions2_f)
#MNL best model of train data
# Convert the probability value into a category 
pred_class1_1_f <- ifelse(predictions1_f[,1] > 0.002, 1, 0 )
pred_class1_1_f #. If the probability is greater than 0.01, the prediction is a positive class (1), otherwise negative class (0)
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1    0 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    0    1    1    0    0    0    1    0    1    1    1    0    0    0    0 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    0    1    1    1    1    1    1    1    0    1    1    1    1    0 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    0    1    0    1    0    1    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    0    1    0    1    1    1    1    1    1    0    1    0    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    0    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    0    1    1    1    1    1    1    1    1    0    1    1    0    0    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    0    1    1    1    0    1    1    1    1    1    0    0    0    1    1    0 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    1    0    1    1    1    1    1    0    1    1    0    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    0    1    1    0    1    1    1    1    1    1    0    1    1    1    1    0 
##  588  591  593  595  598  605  606  608  614  619  620  621  622  623  627  628 
##    0    1    1    0    0    1    1    0    0    0    1    1    1    1    1    1 
##  630  632  634  654  658  663  664  666  674  683  686  691  693  696  697  701 
##    1    1    0    1    1    1    1    1    1    1    0    1    1    0    0    1 
##  703  713  714  716  717  721  724  727  735  738  743  744  746  747  751  769 
##    1    1    0    1    1    1    1    1    1    1    0    0    1    1    0    1 
##  770  771  772  773  775  778  779  780  781  784  786  788  789  790  793  794 
##    1    1    1    1    1    1    0    1    1    0    1    1    1    0    1    0 
##  796  801  808  809  810  811  814  817  819  823  831  840  841  842  848  851 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  853  854  855  856  858  861  868  870  872  873  874  877  882  883  884  885 
##    1    1    1    1    1    1    1    1    0    0    1    0    0    1    1    1 
##  886  887  889  890  893  897  898  900  901  904  908  911  915  917  919  923 
##    0    1    1    1    1    0    1    1    0    0    1    1    1    1    1    1 
##  934  937  942  943  945  949  952  953  957  958  963  964  965  969  970  975 
##    1    0    1    1    1    1    0    1    1    0    1    1    1    1    1    1 
##  982  983  985  986  987  988  990  991  994  995 1003 1004 1011 1012 1014 1016 
##    0    1    0    0    1    1    0    0    1    1    1    1    1    0    1    0 
## 1017 1021 1023 1024 1026 1027 1034 1035 1038 1042 1043 1044 1045 1047 1048 1051 
##    1    1    1    1    0    1    0    0    0    1    1    1    1    1    1    1 
## 1052 1053 1063 1069 1071 1072 1073 1074 1075 1076 1077 1092 1096 1103 1104 1108 
##    1    1    1    1    1    1    1    0    1    1    1    1    0    0    1    0 
## 1109 1110 1116 1119 1125 1126 1127 1131 1132 1143 1147 1150 1151 1160 1162 1168 
##    1    1    0    1    1    1    0    1    0    1    1    1    1    1    1    0 
## 1169 1170 1171 1173 1177 1178 1180 1181 1182 1196 1198 1199 1205 1206 1216 1218 
##    0    1    1    1    1    0    0    1    1    1    1    1    0    1    1    0 
## 1220 1226 1229 1236 1237 1238 1242 1243 1245 1251 1253 1255 1256 1258 1259 1261 
##    1    1    1    1    1    1    0    1    0    0    1    1    0    1    1    1 
## 1264 1265 1267 1270 1271 1275 1286 1298 1299 1305 1307 1312 1318 1322 1325 1327 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1335 1340 1343 1347 1348 1349 1353 1356 1370 1372 1376 1380 1381 1383 1386 1389 
##    1    0    0    1    1    1    1    0    1    0    1    1    0    1    1    0 
## 1395 1399 1405 1412 1413 1419 1425 1426 1427 1430 1439 1451 1453 1454 1465 1471 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 1472 1475 1477 1478 1479 1480 1483 1491 1498 1501 1505 1506 1507 1509 1510 1511 
##    1    0    1    1    1    1    1    1    0    1    1    1    1    0    1    1 
## 1519 1525 1526 1534 1535 1537 1538 1540 1542 1543 1545 1559 1560 1561 1562 1566 
##    0    1    1    1    1    1    0    1    1    1    0    1    0    1    1    1 
## 1568 1573 1582 1593 1603 1604 1610 1614 1622 1623 1625 1627 1633 1635 1637 1645 
##    0    1    0    1    1    1    1    0    1    1    1    1    1    1    0    0 
## 1647 1648 1652 1653 1659 1664 1665 1670 1672 1673 1688 1691 1695 1700 1702 1703 
##    0    1    0    1    1    1    0    1    0    1    1    1    1    1    1    1 
## 1709 1725 1735 1738 1743 1748 1750 1755 1757 1758 1760 1761 1765 1769 1771 1772 
##    1    1    1    1    1    0    1    1    1    0    1    1    1    1    1    0 
## 1777 1781 1787 1789 1790 1798 1803 1804 1807 1808 1809 1811 1820 1821 1828 1829 
##    0    1    1    1    1    1    0    1    1    1    1    0    1    1    1    1 
## 1834 1837 1838 1845 1848 1849 1855 1862 1865 1869 1870 1871 1875 1876 1878 1881 
##    1    1    1    0    1    1    1    1    1    0    0    0    1    1    0    1 
## 1883 1884 1885 1887 1890 1891 1893 1894 1895 1896 1898 1900 1901 1912 1914 1915 
##    1    1    1    1    0    1    1    1    0    1    1    1    0    1    1    1 
## 1917 1918 1919 1923 1924 1926 1929 1931 1933 1936 1937 1939 1940 1942 1948 1956 
##    1    1    1    0    0    0    1    1    0    1    1    1    1    1    1    1 
## 1957 1958 1961 1968 1969 1971 1972 1975 1979 1981 1985 1986 1988 1989 1990 1991 
##    0    1    1    1    1    1    1    1    1    0    1    1    1    0    0    1 
## 1994 1995 2000 2001 2002 2007 2014 2016 2024 2026 2027 2028 2029 2030 2032 2039 
##    1    0    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 2045 2047 2049 2050 2051 2055 2062 2064 2065 2068 2070 2079 2089 2091 2096 2098 
##    1    1    1    1    1    1    0    0    0    1    1    1    1    0    1    1 
## 2106 2107 2111 2113 2116 2125 2127 2130 2133 2134 2136 2137 2142 2143 2148 2153 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 2155 2156 2160 2163 2164 2174 2182 2198 2205 2207 2210 2212 2214 2218 2219 2221 
##    1    0    1    1    1    1    1    1    0    1    1    1    0    1    1    1 
## 2223 2231 2233 2239 2246 2248 2250 2252 2255 2258 2259 2261 2264 2266 2269 2275 
##    0    0    0    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 2280 2286 2288 2293 2297 2303 2305 2308 2309 2312 2313 2319 2323 2328 2332 2333 
##    1    0    0    0    0    1    1    0    0    0    1    0    0    0    0    1 
## 2334 2337 2339 2343 2344 2346 2352 2355 2359 2368 2371 2374 2375 2376 2381 2382 
##    1    1    0    0    1    1    1    1    1    0    1    0    0    1    0    1 
## 2383 2395 2396 2398 2401 2405 2411 2412 2418 2427 2430 2434 2435 2438 2439 2446 
##    0    1    1    0    0    1    1    0    0    0    0    1    0    0    1    0 
## 2454 2456 2458 2459 2462 2466 2472 2475 2476 2478 2481 2484 2491 2495 2496 2498 
##    0    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 2499 2500 2501 2504 2505 2507 2510 2511 2516 2518 2519 2522 2524 2526 2530 2537 
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## 9549 
##    1
#225个0,775个1
library(fpp3)
view(pred_class1_1_f)
pred_class1_1_f
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
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## 5380 5385 5389 5390 5392 5397 5398 5407 5414 5417 5418 5420 5431 5433 5437 5438 
##    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1    1 
## 5442 5445 5449 5450 5456 5464 5466 5472 5479 5483 5491 5493 5495 5496 5498 5500 
##    1    0    1    1    0    1    1    1    1    0    1    0    1    1    1    1 
## 5501 5507 5508 5509 5510 5514 5515 5520 5526 5527 5528 5529 5531 5533 5534 5536 
##    1    0    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 5541 5551 5555 5556 5559 5560 5565 5567 5568 5584 5585 5588 5589 5596 5607 5619 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 5620 5621 5626 5630 5632 5633 5634 5636 5637 5639 5640 5641 5643 5645 5647 5663 
##    0    0    1    1    1    0    1    0    1    1    1    1    0    1    1    0 
## 5666 5669 5673 5681 5684 5686 5687 5688 5690 5693 5697 5700 5706 5707 5715 5719 
##    0    0    1    0    1    1    1    0    0    0    1    1    1    1    0    1 
## 5723 5731 5732 5742 5755 5757 5761 5768 5771 5772 5773 5776 5781 5785 5789 5794 
##    0    0    1    0    1    1    1    1    1    0    1    1    1    1    0    1 
## 5801 5810 5815 5817 5819 5830 5833 5842 5844 5847 5859 5868 5880 5884 5887 5888 
##    1    1    0    0    1    1    1    1    1    0    1    1    1    0    0    1 
## 5891 5893 5894 5898 5899 5906 5910 5915 5916 5921 5922 5925 5926 5927 5933 5935 
##    1    0    1    0    1    0    1    1    1    1    1    1    1    0    1    1 
## 5939 5943 5947 5958 5959 5964 5965 5968 5978 5981 5984 5995 5999 6002 6004 6006 
##    0    1    1    1    1    1    0    1    1    0    1    1    1    1    0    0 
## 6008 6013 6015 6020 6025 6033 6037 6039 6041 6042 6053 6054 6055 6061 6062 6064 
##    1    1    1    1    1    1    1    1    1    0    1    0    1    1    1    0 
## 6067 6069 6077 6080 6089 6092 6094 6097 6098 6100 6106 6110 6111 6116 6120 6121 
##    1    1    1    1    0    1    1    1    1    1    0    0    0    1    1    0 
## 6125 6127 6128 6129 6130 6134 6138 6140 6141 6142 6143 6145 6150 6151 6153 6156 
##    1    0    1    1    0    1    0    1    1    1    1    1    1    1    1    1 
## 6164 6171 6172 6178 6181 6188 6191 6197 6200 6203 6210 6214 6215 6216 6221 6224 
##    1    0    0    0    0    1    1    1    0    1    0    1    0    1    1    1 
## 6231 6235 6236 6237 6238 6240 6243 6246 6247 6250 6262 6266 6270 6272 6275 6276 
##    1    1    1    1    1    0    0    1    1    1    1    1    1    0    1    1 
## 6279 6281 6283 6284 6287 6288 6290 6292 6294 6301 6305 6308 6311 6312 6313 6317 
##    0    0    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6319 6320 6322 6323 6334 6336 6339 6341 6342 6343 6345 6347 6349 6350 6351 6353 
##    1    0    1    1    1    0    1    1    1    0    1    1    1    1    0    1 
## 6354 6359 6362 6366 6367 6368 6375 6377 6384 6386 6387 6388 6395 6396 6406 6407 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 6411 6414 6418 6419 6420 6427 6428 6430 6433 6434 6435 6438 6439 6443 6445 6446 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 6447 6463 6465 6468 6476 6477 6478 6481 6486 6491 6493 6495 6496 6502 6503 6508 
##    1    1    1    1    0    1    1    1    1    1    1    1    0    0    1    1 
## 6511 6512 6521 6522 6524 6531 6534 6535 6536 6537 6544 6547 6551 6554 6558 6561 
##    1    1    1    1    0    1    1    1    0    0    1    1    1    1    1    1 
## 6562 6566 6569 6570 6571 6572 6573 6574 6578 6579 6585 6590 6591 6592 6597 6605 
##    1    1    1    1    1    1    1    1    0    1    0    1    1    1    1    1 
## 6607 6609 6611 6612 6616 6622 6625 6630 6636 6640 6641 6651 6653 6655 6663 6667 
##    0    0    0    1    1    0    1    1    1    1    1    1    1    1    0    1 
## 6673 6674 6676 6677 6678 6679 6680 6687 6689 6696 6697 6698 6700 6703 6709 6711 
##    0    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 6718 6721 6725 6727 6729 6731 6732 6740 6745 6746 6748 6751 6752 6755 6761 6764 
##    1    1    1    1    1    1    1    0    1    0    1    0    1    1    1    1 
## 6766 6777 6779 6780 6783 6786 6788 6797 6801 6803 6807 6812 6813 6814 6822 6823 
##    1    1    1    1    0    1    1    1    0    1    1    1    1    1    0    1 
## 6824 6825 6827 6832 6834 6838 6839 6842 6843 6845 6852 6854 6862 6863 6864 6872 
##    1    0    1    0    1    1    1    1    1    0    1    0    1    1    1    1 
## 6875 6885 6889 6891 6893 6897 6898 6907 6910 6913 6916 6918 6923 6926 6928 6930 
##    1    1    0    1    1    0    0    1    1    1    1    1    1    1    1    1 
## 6936 6937 6939 6945 6949 6950 6951 6952 6954 6957 6959 6960 6961 6962 6966 6968 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 6971 6974 6978 6980 6984 6985 6987 6992 6993 6995 6998 6999 7001 7004 7005 7006 
##    1    1    0    1    1    1    0    1    0    1    0    1    1    1    1    1 
## 7008 7009 7012 7014 7015 7016 7019 7026 7028 7029 7036 7043 7048 7051 7055 7058 
##    1    1    1    1    1    0    1    1    1    0    0    1    1    0    1    1 
## 7065 7066 7069 7073 7077 7079 7082 7083 7088 7091 7094 7100 7103 7106 7109 7110 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 7112 7114 7115 7116 7120 7130 7133 7139 7141 7144 7152 7155 7157 7158 7160 7161 
##    1    1    0    0    1    1    1    1    1    1    1    1    1    1    1    0 
## 7166 7167 7168 7178 7179 7181 7182 7186 7188 7191 7192 7196 7197 7202 7203 7207 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7209 7210 7221 7222 7226 7228 7229 7237 7238 7241 7247 7248 7250 7270 7273 7275 
##    1    1    0    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 7279 7280 7281 7282 7283 7285 7287 7294 7299 7302 7305 7314 7315 7317 7320 7330 
##    1    1    0    1    1    1    1    0    1    0    1    1    1    1    1    0 
## 7332 7337 7338 7339 7341 7342 7344 7346 7350 7355 7360 7364 7365 7366 7371 7373 
##    0    0    1    1    1    1    1    1    0    1    1    0    0    1    0    1 
## 7376 7380 7381 7387 7389 7392 7399 7402 7403 7408 7410 7412 7416 7419 7426 7428 
##    1    0    1    1    0    1    1    1    0    0    1    1    1    1    1    1 
## 7431 7432 7433 7436 7438 7440 7441 7447 7456 7457 7458 7462 7463 7466 7467 7472 
##    0    0    1    0    0    1    1    0    1    1    1    1    1    1    1    1 
## 7475 7484 7485 7487 7488 7490 7497 7498 7502 7507 7511 7519 7520 7523 7525 7526 
##    1    1    0    1    1    1    0    1    1    1    1    0    1    0    1    0 
## 7529 7530 7531 7532 7533 7534 7536 7538 7539 7543 7547 7549 7551 7552 7553 7556 
##    1    1    1    0    1    0    1    1    1    1    1    0    1    1    0    1 
## 7560 7566 7569 7570 7573 7580 7586 7597 7598 7601 7606 7612 7615 7616 7620 7626 
##    1    1    0    1    1    1    1    0    0    1    0    0    1    1    1    1 
## 7627 7629 7631 7633 7640 7645 7650 7651 7652 7654 7655 7659 7660 7665 7673 7674 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 7676 7677 7678 7685 7692 7697 7700 7704 7709 7712 7720 7721 7729 7730 7736 7739 
##    0    1    1    1    1    0    1    0    0    1    1    1    1    0    0    1 
## 7740 7741 7742 7743 7750 7753 7755 7757 7759 7761 7763 7764 7774 7778 7785 7788 
##    1    1    1    0    1    1    1    1    1    1    1    0    1    0    1    1 
## 7791 7793 7796 7797 7802 7805 7807 7811 7813 7814 7815 7826 7831 7837 7838 7842 
##    1    0    1    1    1    1    1    1    0    1    1    0    1    1    1    0 
## 7844 7846 7847 7849 7855 7857 7862 7869 7871 7876 7882 7883 7884 7888 7891 7892 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 7894 7896 7898 7910 7911 7921 7923 7926 7927 7928 7929 7933 7936 7937 7939 7949 
##    1    1    1    1    0    1    0    1    0    1    1    1    1    1    1    1 
## 7953 7955 7957 7960 7962 7964 7965 7966 7967 7971 7976 7981 7983 7984 7988 7989 
##    1    1    1    1    1    1    1    0    1    1    1    1    0    1    1    1 
## 7991 7999 8008 8012 8013 8015 8017 8018 8019 8023 8026 8030 8034 8035 8043 8044 
##    1    1    0    1    1    1    0    1    1    1    1    1    0    0    1    0 
## 8049 8054 8065 8066 8067 8076 8083 8089 8090 8104 8108 8110 8111 8113 8118 8125 
##    1    1    1    0    1    1    1    1    1    1    0    0    1    1    0    1 
## 8127 8128 8133 8137 8138 8147 8150 8156 8167 8174 8176 8182 8198 8199 8206 8207 
##    0    1    1    0    1    0    0    1    1    1    0    0    1    1    1    1 
## 8208 8214 8215 8216 8218 8222 8223 8224 8226 8227 8230 8234 8235 8237 8239 8242 
##    1    1    1    1    1    1    1    0    1    0    0    0    0    1    1    1 
## 8243 8247 8248 8253 8256 8257 8259 8267 8271 8272 8282 8288 8290 8291 8294 8295 
##    1    1    1    1    0    1    1    1    1    1    1    1    0    1    0    0 
## 8302 8303 8306 8308 8319 8321 8322 8325 8326 8328 8337 8340 8344 8345 8352 8359 
##    1    1    0    1    0    1    1    1    1    0    1    0    1    0    0    1 
## 8364 8365 8370 8381 8385 8387 8391 8395 8396 8400 8405 8406 8408 8409 8413 8415 
##    0    1    1    1    0    1    1    1    0    1    1    1    0    0    1    1 
## 8417 8418 8419 8420 8425 8426 8428 8430 8433 8437 8439 8442 8445 8448 8449 8459 
##    0    1    0    1    1    1    0    1    1    0    1    0    0    0    0    1 
## 8460 8464 8466 8468 8471 8474 8475 8476 8477 8486 8488 8490 8496 8497 8498 8501 
##    1    1    1    1    1    0    1    1    0    1    1    1    1    1    1    0 
## 8502 8504 8505 8508 8509 8510 8511 8513 8514 8517 8527 8528 8534 8535 8540 8542 
##    1    1    0    0    1    1    0    1    0    1    1    1    1    1    1    1 
## 8543 8545 8546 8547 8548 8551 8560 8561 8566 8567 8569 8570 8571 8575 8580 8584 
##    0    0    1    1    1    1    0    1    1    1    0    0    1    1    0    1 
## 8587 8600 8603 8607 8623 8626 8627 8629 8630 8635 8637 8646 8649 8651 8652 8656 
##    1    1    0    1    0    1    0    1    1    1    1    0    0    0    0    1 
## 8664 8667 8669 8672 8680 8681 8682 8683 8691 8700 8701 8707 8711 8715 8716 8721 
##    1    0    1    1    0    0    1    0    1    1    1    1    0    0    1    1 
## 8722 8724 8725 8729 8730 8731 8733 8735 8743 8744 8747 8758 8759 8762 8764 8769 
##    1    1    1    0    1    0    0    1    0    1    1    1    1    1    1    1 
## 8772 8773 8774 8775 8783 8784 8786 8790 8796 8798 8799 8804 8805 8806 8807 8811 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8817 8818 8819 8820 8826 8830 8832 8835 8836 8845 8847 8850 8851 8854 8860 8861 
##    1    0    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8862 8866 8867 8871 8872 8881 8882 8884 8891 8892 8893 8895 8896 8900 8903 8904 
##    1    1    0    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8905 8906 8907 8911 8919 8920 8922 8927 8935 8942 8945 8948 8949 8951 8952 8953 
##    1    1    1    1    1    1    0    0    1    1    0    1    0    1    0    1 
## 8955 8959 8961 8965 8967 8970 8971 8973 8978 8982 8984 8985 8986 8990 8992 8998 
##    1    0    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
## 9001 9006 9011 9012 9013 9015 9017 9018 9021 9025 9033 9037 9041 9046 9049 9054 
##    0    1    1    1    1    1    1    1    0    0    1    1    1    0    0    1 
## 9057 9063 9076 9077 9079 9080 9083 9084 9090 9092 9095 9097 9098 9100 9101 9105 
##    1    1    1    1    0    1    0    1    1    1    1    1    1    1    1    1 
## 9108 9109 9117 9119 9127 9130 9133 9136 9139 9151 9153 9156 9158 9162 9163 9166 
##    1    0    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    0    0    0    1    1    1    0    1    1    0    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    0    1    1    1    0    1    1    1    1    0    1    1    1    1    0 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    0    1    1    1    0    1    1    1    1    1    1    1    0    0 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
## 9404 9405 9409 9413 9414 9418 9419 9425 9430 9431 9434 9435 9436 9437 9439 9442 
##    1    0    1    1    1    1    1    0    1    1    1    1    1    1    1    0 
## 9443 9446 9447 9448 9450 9452 9454 9462 9464 9465 9466 9467 9472 9473 9482 9486 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 9549 
##    1
pred_class1_2_f <- ifelse(predictions1_f[,2] > 0.1126, 1, 0 )
pred_class1_2_f #. If the probability is greater than 0.24, the prediction is a positive class (1), otherwise negative class (0)
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    0    1 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    0 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
##  588  591  593  595  598  605  606  608  614  619  620  621  622  623  627  628 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  630  632  634  654  658  663  664  666  674  683  686  691  693  696  697  701 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  703  713  714  716  717  721  724  727  735  738  743  744  746  747  751  769 
##    1    1    1    0    1    1    1    1    1    1    0    1    1    1    1    1 
##  770  771  772  773  775  778  779  780  781  784  786  788  789  790  793  794 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  796  801  808  809  810  811  814  817  819  823  831  840  841  842  848  851 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  853  854  855  856  858  861  868  870  872  873  874  877  882  883  884  885 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
##  886  887  889  890  893  897  898  900  901  904  908  911  915  917  919  923 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  934  937  942  943  945  949  952  953  957  958  963  964  965  969  970  975 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  982  983  985  986  987  988  990  991  994  995 1003 1004 1011 1012 1014 1016 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 1017 1021 1023 1024 1026 1027 1034 1035 1038 1042 1043 1044 1045 1047 1048 1051 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1052 1053 1063 1069 1071 1072 1073 1074 1075 1076 1077 1092 1096 1103 1104 1108 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1109 1110 1116 1119 1125 1126 1127 1131 1132 1143 1147 1150 1151 1160 1162 1168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 1169 1170 1171 1173 1177 1178 1180 1181 1182 1196 1198 1199 1205 1206 1216 1218 
##    1    1    1    1    1    1    1    1    0    1    1    1    0    1    1    1 
## 1220 1226 1229 1236 1237 1238 1242 1243 1245 1251 1253 1255 1256 1258 1259 1261 
##    1    1    1    0    1    1    0    1    1    1    1    1    1    1    1    1 
## 1264 1265 1267 1270 1271 1275 1286 1298 1299 1305 1307 1312 1318 1322 1325 1327 
##    1    0    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1335 1340 1343 1347 1348 1349 1353 1356 1370 1372 1376 1380 1381 1383 1386 1389 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 1395 1399 1405 1412 1413 1419 1425 1426 1427 1430 1439 1451 1453 1454 1465 1471 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 1472 1475 1477 1478 1479 1480 1483 1491 1498 1501 1505 1506 1507 1509 1510 1511 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1519 1525 1526 1534 1535 1537 1538 1540 1542 1543 1545 1559 1560 1561 1562 1566 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1568 1573 1582 1593 1603 1604 1610 1614 1622 1623 1625 1627 1633 1635 1637 1645 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1647 1648 1652 1653 1659 1664 1665 1670 1672 1673 1688 1691 1695 1700 1702 1703 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1709 1725 1735 1738 1743 1748 1750 1755 1757 1758 1760 1761 1765 1769 1771 1772 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1777 1781 1787 1789 1790 1798 1803 1804 1807 1808 1809 1811 1820 1821 1828 1829 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1834 1837 1838 1845 1848 1849 1855 1862 1865 1869 1870 1871 1875 1876 1878 1881 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1883 1884 1885 1887 1890 1891 1893 1894 1895 1896 1898 1900 1901 1912 1914 1915 
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## 8208 8214 8215 8216 8218 8222 8223 8224 8226 8227 8230 8234 8235 8237 8239 8242 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8243 8247 8248 8253 8256 8257 8259 8267 8271 8272 8282 8288 8290 8291 8294 8295 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8302 8303 8306 8308 8319 8321 8322 8325 8326 8328 8337 8340 8344 8345 8352 8359 
##    1    0    0    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 8364 8365 8370 8381 8385 8387 8391 8395 8396 8400 8405 8406 8408 8409 8413 8415 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 8417 8418 8419 8420 8425 8426 8428 8430 8433 8437 8439 8442 8445 8448 8449 8459 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8460 8464 8466 8468 8471 8474 8475 8476 8477 8486 8488 8490 8496 8497 8498 8501 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8502 8504 8505 8508 8509 8510 8511 8513 8514 8517 8527 8528 8534 8535 8540 8542 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8543 8545 8546 8547 8548 8551 8560 8561 8566 8567 8569 8570 8571 8575 8580 8584 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8587 8600 8603 8607 8623 8626 8627 8629 8630 8635 8637 8646 8649 8651 8652 8656 
##    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8664 8667 8669 8672 8680 8681 8682 8683 8691 8700 8701 8707 8711 8715 8716 8721 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8722 8724 8725 8729 8730 8731 8733 8735 8743 8744 8747 8758 8759 8762 8764 8769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8772 8773 8774 8775 8783 8784 8786 8790 8796 8798 8799 8804 8805 8806 8807 8811 
##    1    1    0    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8817 8818 8819 8820 8826 8830 8832 8835 8836 8845 8847 8850 8851 8854 8860 8861 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8862 8866 8867 8871 8872 8881 8882 8884 8891 8892 8893 8895 8896 8900 8903 8904 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8905 8906 8907 8911 8919 8920 8922 8927 8935 8942 8945 8948 8949 8951 8952 8953 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8955 8959 8961 8965 8967 8970 8971 8973 8978 8982 8984 8985 8986 8990 8992 8998 
##    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
## 9001 9006 9011 9012 9013 9015 9017 9018 9021 9025 9033 9037 9041 9046 9049 9054 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9057 9063 9076 9077 9079 9080 9083 9084 9090 9092 9095 9097 9098 9100 9101 9105 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9108 9109 9117 9119 9127 9130 9133 9136 9139 9151 9153 9156 9158 9162 9163 9166 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    0    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    0    1    1    1    1    1    0    1    1    0    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    0 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9404 9405 9409 9413 9414 9418 9419 9425 9430 9431 9434 9435 9436 9437 9439 9442 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9443 9446 9447 9448 9450 9452 9454 9462 9464 9465 9466 9467 9472 9473 9482 9486 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9549 
##    1
#25个0,975个1
view(pred_class1_2_f)  

#19个0,981个1
pred_class1_3_f <- ifelse(predictions1_f[,3] > 0.6, 1, 0 )
pred_class1_3_f #. If the probability is greater than 0.75, the prediction is a positive class (1), otherwise negative class (0)
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    1    1    1    1    0    1    1    0    1    1    1    1    1    1 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    0    1    1    1    0    1    1    1    1    1    1    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
##  588  591  593  595  598  605  606  608  614  619  620  621  622  623  627  628 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  630  632  634  654  658  663  664  666  674  683  686  691  693  696  697  701 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  703  713  714  716  717  721  724  727  735  738  743  744  746  747  751  769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  770  771  772  773  775  778  779  780  781  784  786  788  789  790  793  794 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
##  796  801  808  809  810  811  814  817  819  823  831  840  841  842  848  851 
##    1    1    1    1    1    1    0    1    1    1    1    0    1    1    1    0 
##  853  854  855  856  858  861  868  870  872  873  874  877  882  883  884  885 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  886  887  889  890  893  897  898  900  901  904  908  911  915  917  919  923 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  934  937  942  943  945  949  952  953  957  958  963  964  965  969  970  975 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
##  982  983  985  986  987  988  990  991  994  995 1003 1004 1011 1012 1014 1016 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1017 1021 1023 1024 1026 1027 1034 1035 1038 1042 1043 1044 1045 1047 1048 1051 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1052 1053 1063 1069 1071 1072 1073 1074 1075 1076 1077 1092 1096 1103 1104 1108 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1109 1110 1116 1119 1125 1126 1127 1131 1132 1143 1147 1150 1151 1160 1162 1168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1169 1170 1171 1173 1177 1178 1180 1181 1182 1196 1198 1199 1205 1206 1216 1218 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1220 1226 1229 1236 1237 1238 1242 1243 1245 1251 1253 1255 1256 1258 1259 1261 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1264 1265 1267 1270 1271 1275 1286 1298 1299 1305 1307 1312 1318 1322 1325 1327 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 1335 1340 1343 1347 1348 1349 1353 1356 1370 1372 1376 1380 1381 1383 1386 1389 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1395 1399 1405 1412 1413 1419 1425 1426 1427 1430 1439 1451 1453 1454 1465 1471 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 1472 1475 1477 1478 1479 1480 1483 1491 1498 1501 1505 1506 1507 1509 1510 1511 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1519 1525 1526 1534 1535 1537 1538 1540 1542 1543 1545 1559 1560 1561 1562 1566 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1568 1573 1582 1593 1603 1604 1610 1614 1622 1623 1625 1627 1633 1635 1637 1645 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1647 1648 1652 1653 1659 1664 1665 1670 1672 1673 1688 1691 1695 1700 1702 1703 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1709 1725 1735 1738 1743 1748 1750 1755 1757 1758 1760 1761 1765 1769 1771 1772 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1777 1781 1787 1789 1790 1798 1803 1804 1807 1808 1809 1811 1820 1821 1828 1829 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1834 1837 1838 1845 1848 1849 1855 1862 1865 1869 1870 1871 1875 1876 1878 1881 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1883 1884 1885 1887 1890 1891 1893 1894 1895 1896 1898 1900 1901 1912 1914 1915 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1917 1918 1919 1923 1924 1926 1929 1931 1933 1936 1937 1939 1940 1942 1948 1956 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1957 1958 1961 1968 1969 1971 1972 1975 1979 1981 1985 1986 1988 1989 1990 1991 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1994 1995 2000 2001 2002 2007 2014 2016 2024 2026 2027 2028 2029 2030 2032 2039 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 2045 2047 2049 2050 2051 2055 2062 2064 2065 2068 2070 2079 2089 2091 2096 2098 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2106 2107 2111 2113 2116 2125 2127 2130 2133 2134 2136 2137 2142 2143 2148 2153 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 2155 2156 2160 2163 2164 2174 2182 2198 2205 2207 2210 2212 2214 2218 2219 2221 
##    1    1    1    1    1    1    0    0    1    1    1    1    1    0    1    1 
## 2223 2231 2233 2239 2246 2248 2250 2252 2255 2258 2259 2261 2264 2266 2269 2275 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2280 2286 2288 2293 2297 2303 2305 2308 2309 2312 2313 2319 2323 2328 2332 2333 
##    1    1    1    1    1    0    1    0    1    1    1    1    1    1    1    1 
## 2334 2337 2339 2343 2344 2346 2352 2355 2359 2368 2371 2374 2375 2376 2381 2382 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    0    1    1 
## 2383 2395 2396 2398 2401 2405 2411 2412 2418 2427 2430 2434 2435 2438 2439 2446 
##    1    0    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 2454 2456 2458 2459 2462 2466 2472 2475 2476 2478 2481 2484 2491 2495 2496 2498 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 2499 2500 2501 2504 2505 2507 2510 2511 2516 2518 2519 2522 2524 2526 2530 2537 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2546 2553 2564 2566 2567 2568 2573 2576 2587 2588 2589 2590 2591 2594 2595 2597 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2599 2602 2604 2606 2608 2609 2613 2617 2619 2631 2634 2635 2636 2637 2641 2642 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2644 2649 2653 2654 2660 2662 2663 2664 2669 2670 2672 2675 2676 2680 2682 2683 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2684 2685 2688 2698 2699 2704 2709 2710 2713 2717 2719 2730 2735 2740 2748 2749 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2751 2754 2762 2768 2769 2777 2784 2786 2788 2792 2799 2801 2806 2813 2814 2815 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2819 2824 2825 2828 2831 2835 2848 2852 2853 2857 2861 2864 2868 2869 2880 2888 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2889 2890 2892 2894 2900 2909 2916 2920 2927 2930 2932 2939 2942 2947 2948 2952 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2956 2963 2965 2970 2972 2975 2976 2980 2984 2991 2997 3002 3008 3010 3013 3015 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 3021 3023 3024 3026 3032 3038 3041 3046 3047 3055 3062 3063 3072 3074 3084 3091 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 3098 3099 3104 3109 3110 3117 3118 3120 3129 3133 3140 3141 3143 3145 3148 3151 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    0    1 
## 3152 3155 3156 3163 3165 3167 3169 3174 3175 3178 3181 3182 3186 3188 3189 3191 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3196 3200 3201 3205 3207 3208 3209 3210 3212 3214 3218 3222 3234 3235 3238 3246 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3249 3250 3252 3253 3255 3257 3262 3264 3266 3267 3268 3270 3271 3275 3281 3282 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3283 3287 3288 3289 3295 3298 3300 3314 3316 3319 3320 3327 3329 3331 3340 3341 
##    0    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 3344 3345 3346 3347 3354 3357 3359 3361 3363 3366 3370 3372 3376 3384 3386 3389 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3390 3394 3398 3402 3405 3408 3413 3419 3421 3425 3426 3428 3431 3432 3445 3448 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3451 3456 3457 3458 3463 3469 3471 3475 3476 3481 3482 3486 3489 3492 3494 3498 
##    0    0    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3499 3503 3504 3505 3506 3508 3511 3513 3515 3516 3518 3521 3525 3526 3530 3533 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3535 3539 3540 3543 3544 3547 3549 3550 3553 3556 3561 3567 3573 3577 3581 3586 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3587 3589 3590 3591 3601 3606 3608 3610 3620 3621 3623 3631 3633 3634 3640 3641 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3646 3650 3651 3652 3660 3662 3663 3669 3689 3690 3691 3693 3694 3697 3699 3702 
##    1    0    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 3711 3721 3722 3723 3726 3727 3731 3734 3735 3737 3742 3744 3750 3751 3752 3756 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 3760 3761 3765 3770 3776 3777 3784 3785 3788 3791 3797 3799 3802 3803 3808 3809 
##    1    1    0    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 3811 3822 3823 3824 3828 3829 3833 3839 3841 3842 3843 3847 3850 3851 3855 3856 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3858 3860 3862 3863 3873 3876 3877 3886 3889 3891 3894 3898 3900 3902 3903 3907 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3912 3916 3918 3930 3935 3936 3938 3939 3940 3941 3945 3949 3953 3957 3960 3961 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3977 3978 3980 3982 3985 3986 3988 3990 3991 3995 3997 4000 4001 4006 4010 4011 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4012 4014 4023 4025 4029 4038 4040 4044 4045 4051 4052 4054 4070 4071 4074 4077 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4083 4089 4092 4096 4097 4098 4103 4113 4116 4124 4126 4130 4135 4136 4138 4141 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 4142 4146 4152 4154 4156 4157 4159 4160 4170 4173 4175 4178 4180 4184 4191 4193 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 4194 4197 4199 4200 4203 4204 4212 4214 4215 4219 4223 4225 4227 4228 4231 4234 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    0    1 
## 4242 4254 4256 4258 4271 4274 4278 4279 4281 4282 4286 4287 4289 4291 4293 4297 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4300 4302 4305 4307 4309 4310 4312 4315 4323 4325 4328 4331 4332 4337 4341 4342 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4344 4345 4346 4350 4354 4360 4364 4367 4370 4376 4378 4386 4387 4389 4395 4401 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    0    1 
## 4404 4407 4411 4412 4413 4414 4418 4420 4422 4442 4444 4450 4451 4457 4462 4467 
##    1    0    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 4475 4477 4479 4487 4499 4500 4503 4506 4515 4520 4525 4534 4536 4541 4542 4544 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4545 4547 4548 4552 4554 4557 4560 4573 4574 4575 4576 4577 4580 4583 4585 4591 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4593 4600 4601 4603 4604 4606 4607 4608 4619 4622 4624 4625 4626 4630 4632 4638 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4639 4640 4641 4643 4646 4649 4650 4652 4660 4673 4674 4675 4680 4683 4687 4689 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 4692 4693 4695 4696 4697 4701 4704 4706 4707 4713 4714 4717 4726 4729 4730 4733 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 4734 4749 4753 4754 4755 4757 4758 4763 4764 4765 4771 4773 4774 4778 4783 4784 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 4785 4786 4787 4798 4799 4800 4806 4812 4815 4816 4818 4822 4826 4827 4833 4834 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4839 4842 4844 4845 4850 4851 4854 4855 4864 4870 4872 4873 4875 4878 4880 4886 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 4892 4895 4898 4900 4902 4906 4907 4909 4915 4916 4918 4919 4922 4923 4926 4937 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 4938 4940 4946 4950 4954 4956 4958 4961 4962 4964 4967 4970 4971 4977 4979 4981 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4990 4995 4996 5002 5005 5006 5007 5008 5009 5010 5013 5016 5017 5018 5025 5028 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5031 5032 5034 5037 5041 5046 5049 5056 5059 5061 5062 5064 5067 5069 5088 5092 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5093 5094 5100 5101 5104 5110 5112 5116 5119 5120 5121 5125 5131 5144 5146 5151 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5155 5157 5158 5159 5166 5168 5170 5171 5173 5183 5185 5188 5190 5193 5196 5199 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5205 5207 5212 5213 5214 5216 5218 5222 5226 5230 5237 5242 5245 5248 5252 5255 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 5257 5259 5263 5265 5266 5267 5275 5277 5279 5280 5283 5284 5289 5291 5293 5294 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 5296 5301 5304 5306 5308 5310 5312 5319 5321 5328 5329 5331 5335 5337 5339 5341 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5342 5343 5352 5356 5358 5360 5361 5364 5365 5366 5371 5374 5375 5376 5377 5379 
##    0    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 5380 5385 5389 5390 5392 5397 5398 5407 5414 5417 5418 5420 5431 5433 5437 5438 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    0    1    1 
## 5442 5445 5449 5450 5456 5464 5466 5472 5479 5483 5491 5493 5495 5496 5498 5500 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 5501 5507 5508 5509 5510 5514 5515 5520 5526 5527 5528 5529 5531 5533 5534 5536 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 5541 5551 5555 5556 5559 5560 5565 5567 5568 5584 5585 5588 5589 5596 5607 5619 
##    0    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 5620 5621 5626 5630 5632 5633 5634 5636 5637 5639 5640 5641 5643 5645 5647 5663 
##    1    1    1    1    0    1    0    1    1    1    1    1    1    1    1    1 
## 5666 5669 5673 5681 5684 5686 5687 5688 5690 5693 5697 5700 5706 5707 5715 5719 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 5723 5731 5732 5742 5755 5757 5761 5768 5771 5772 5773 5776 5781 5785 5789 5794 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5801 5810 5815 5817 5819 5830 5833 5842 5844 5847 5859 5868 5880 5884 5887 5888 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5891 5893 5894 5898 5899 5906 5910 5915 5916 5921 5922 5925 5926 5927 5933 5935 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5939 5943 5947 5958 5959 5964 5965 5968 5978 5981 5984 5995 5999 6002 6004 6006 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6008 6013 6015 6020 6025 6033 6037 6039 6041 6042 6053 6054 6055 6061 6062 6064 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6067 6069 6077 6080 6089 6092 6094 6097 6098 6100 6106 6110 6111 6116 6120 6121 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6125 6127 6128 6129 6130 6134 6138 6140 6141 6142 6143 6145 6150 6151 6153 6156 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6164 6171 6172 6178 6181 6188 6191 6197 6200 6203 6210 6214 6215 6216 6221 6224 
##    1    1    1    0    0    1    1    1    1    0    1    1    1    1    1    1 
## 6231 6235 6236 6237 6238 6240 6243 6246 6247 6250 6262 6266 6270 6272 6275 6276 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 6279 6281 6283 6284 6287 6288 6290 6292 6294 6301 6305 6308 6311 6312 6313 6317 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6319 6320 6322 6323 6334 6336 6339 6341 6342 6343 6345 6347 6349 6350 6351 6353 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6354 6359 6362 6366 6367 6368 6375 6377 6384 6386 6387 6388 6395 6396 6406 6407 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 6411 6414 6418 6419 6420 6427 6428 6430 6433 6434 6435 6438 6439 6443 6445 6446 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 6447 6463 6465 6468 6476 6477 6478 6481 6486 6491 6493 6495 6496 6502 6503 6508 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6511 6512 6521 6522 6524 6531 6534 6535 6536 6537 6544 6547 6551 6554 6558 6561 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6562 6566 6569 6570 6571 6572 6573 6574 6578 6579 6585 6590 6591 6592 6597 6605 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6607 6609 6611 6612 6616 6622 6625 6630 6636 6640 6641 6651 6653 6655 6663 6667 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6673 6674 6676 6677 6678 6679 6680 6687 6689 6696 6697 6698 6700 6703 6709 6711 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 6718 6721 6725 6727 6729 6731 6732 6740 6745 6746 6748 6751 6752 6755 6761 6764 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6766 6777 6779 6780 6783 6786 6788 6797 6801 6803 6807 6812 6813 6814 6822 6823 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6824 6825 6827 6832 6834 6838 6839 6842 6843 6845 6852 6854 6862 6863 6864 6872 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6875 6885 6889 6891 6893 6897 6898 6907 6910 6913 6916 6918 6923 6926 6928 6930 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6936 6937 6939 6945 6949 6950 6951 6952 6954 6957 6959 6960 6961 6962 6966 6968 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 6971 6974 6978 6980 6984 6985 6987 6992 6993 6995 6998 6999 7001 7004 7005 7006 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7008 7009 7012 7014 7015 7016 7019 7026 7028 7029 7036 7043 7048 7051 7055 7058 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7065 7066 7069 7073 7077 7079 7082 7083 7088 7091 7094 7100 7103 7106 7109 7110 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7112 7114 7115 7116 7120 7130 7133 7139 7141 7144 7152 7155 7157 7158 7160 7161 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7166 7167 7168 7178 7179 7181 7182 7186 7188 7191 7192 7196 7197 7202 7203 7207 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 7209 7210 7221 7222 7226 7228 7229 7237 7238 7241 7247 7248 7250 7270 7273 7275 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7279 7280 7281 7282 7283 7285 7287 7294 7299 7302 7305 7314 7315 7317 7320 7330 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7332 7337 7338 7339 7341 7342 7344 7346 7350 7355 7360 7364 7365 7366 7371 7373 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7376 7380 7381 7387 7389 7392 7399 7402 7403 7408 7410 7412 7416 7419 7426 7428 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7431 7432 7433 7436 7438 7440 7441 7447 7456 7457 7458 7462 7463 7466 7467 7472 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7475 7484 7485 7487 7488 7490 7497 7498 7502 7507 7511 7519 7520 7523 7525 7526 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7529 7530 7531 7532 7533 7534 7536 7538 7539 7543 7547 7549 7551 7552 7553 7556 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7560 7566 7569 7570 7573 7580 7586 7597 7598 7601 7606 7612 7615 7616 7620 7626 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 7627 7629 7631 7633 7640 7645 7650 7651 7652 7654 7655 7659 7660 7665 7673 7674 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 7676 7677 7678 7685 7692 7697 7700 7704 7709 7712 7720 7721 7729 7730 7736 7739 
##    1    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1 
## 7740 7741 7742 7743 7750 7753 7755 7757 7759 7761 7763 7764 7774 7778 7785 7788 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 7791 7793 7796 7797 7802 7805 7807 7811 7813 7814 7815 7826 7831 7837 7838 7842 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 7844 7846 7847 7849 7855 7857 7862 7869 7871 7876 7882 7883 7884 7888 7891 7892 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 7894 7896 7898 7910 7911 7921 7923 7926 7927 7928 7929 7933 7936 7937 7939 7949 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 7953 7955 7957 7960 7962 7964 7965 7966 7967 7971 7976 7981 7983 7984 7988 7989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7991 7999 8008 8012 8013 8015 8017 8018 8019 8023 8026 8030 8034 8035 8043 8044 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8049 8054 8065 8066 8067 8076 8083 8089 8090 8104 8108 8110 8111 8113 8118 8125 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8127 8128 8133 8137 8138 8147 8150 8156 8167 8174 8176 8182 8198 8199 8206 8207 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8208 8214 8215 8216 8218 8222 8223 8224 8226 8227 8230 8234 8235 8237 8239 8242 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 8243 8247 8248 8253 8256 8257 8259 8267 8271 8272 8282 8288 8290 8291 8294 8295 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8302 8303 8306 8308 8319 8321 8322 8325 8326 8328 8337 8340 8344 8345 8352 8359 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 8364 8365 8370 8381 8385 8387 8391 8395 8396 8400 8405 8406 8408 8409 8413 8415 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8417 8418 8419 8420 8425 8426 8428 8430 8433 8437 8439 8442 8445 8448 8449 8459 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 8460 8464 8466 8468 8471 8474 8475 8476 8477 8486 8488 8490 8496 8497 8498 8501 
##    1    1    1    1    0    1    1    1    1    1    1    1    0    1    1    1 
## 8502 8504 8505 8508 8509 8510 8511 8513 8514 8517 8527 8528 8534 8535 8540 8542 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8543 8545 8546 8547 8548 8551 8560 8561 8566 8567 8569 8570 8571 8575 8580 8584 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    0 
## 8587 8600 8603 8607 8623 8626 8627 8629 8630 8635 8637 8646 8649 8651 8652 8656 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8664 8667 8669 8672 8680 8681 8682 8683 8691 8700 8701 8707 8711 8715 8716 8721 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 8722 8724 8725 8729 8730 8731 8733 8735 8743 8744 8747 8758 8759 8762 8764 8769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8772 8773 8774 8775 8783 8784 8786 8790 8796 8798 8799 8804 8805 8806 8807 8811 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 8817 8818 8819 8820 8826 8830 8832 8835 8836 8845 8847 8850 8851 8854 8860 8861 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8862 8866 8867 8871 8872 8881 8882 8884 8891 8892 8893 8895 8896 8900 8903 8904 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8905 8906 8907 8911 8919 8920 8922 8927 8935 8942 8945 8948 8949 8951 8952 8953 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8955 8959 8961 8965 8967 8970 8971 8973 8978 8982 8984 8985 8986 8990 8992 8998 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9001 9006 9011 9012 9013 9015 9017 9018 9021 9025 9033 9037 9041 9046 9049 9054 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 9057 9063 9076 9077 9079 9080 9083 9084 9090 9092 9095 9097 9098 9100 9101 9105 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 9108 9109 9117 9119 9127 9130 9133 9136 9139 9151 9153 9156 9158 9162 9163 9166 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    1    1    1    1    0    1    1    0    1    1    1 
## 9404 9405 9409 9413 9414 9418 9419 9425 9430 9431 9434 9435 9436 9437 9439 9442 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 9443 9446 9447 9448 9450 9452 9454 9462 9464 9465 9466 9467 9472 9473 9482 9486 
##    1    1    1    0    0    1    1    1    1    1    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 9549 
##    1
view(pred_class1_3_f)  #0.5时全是1

pred_class1_f <- cbind(pred_class1_1_f, pred_class1_2_f,pred_class1_3_f)
pred_class1_f
##      pred_class1_1_f pred_class1_2_f pred_class1_3_f
## 2                  1               1               1
## 4                  1               1               1
## 8                  1               1               1
## 13                 1               1               1
## 16                 0               1               1
## 18                 0               1               1
## 29                 1               1               1
## 30                 1               1               1
## 32                 1               1               1
## 36                 1               1               1
## 39                 1               1               1
## 41                 1               1               1
## 43                 1               1               1
## 48                 1               1               1
## 49                 1               1               1
## 55                 0               1               1
## 58                 1               1               1
## 59                 0               1               1
## 60                 1               1               1
## 62                 1               1               1
## 63                 0               1               1
## 71                 0               1               1
## 73                 0               0               1
## 80                 1               1               1
## 84                 0               1               1
## 86                 1               1               1
## 87                 1               1               1
## 98                 1               1               1
## 102                0               1               1
## 104                0               1               1
## 107                0               0               1
## 109                0               1               1
## 110                1               1               1
## 113                1               1               1
## 123                0               1               1
## 125                1               1               1
## 136                1               1               1
## 137                1               1               1
## 138                1               1               0
## 143                1               1               1
## 145                1               1               1
## 147                1               1               0
## 149                0               0               1
## 151                1               1               1
## 153                1               1               1
## 160                1               1               1
## 162                1               1               1
## 165                0               0               1
## 167                1               1               1
## 168                1               1               1
## 171                1               1               1
## 175                1               1               1
## 177                1               1               1
## 184                0               1               1
## 187                1               1               1
## 188                0               1               1
## 198                1               1               1
## 199                0               1               1
## 205                1               0               1
## 206                1               1               1
## 214                1               1               1
## 217                1               1               1
## 220                1               1               1
## 221                1               1               1
## 225                1               1               1
## 227                1               1               1
## 230                0               1               1
## 231                1               1               1
## 242                0               0               1
## 249                1               1               1
## 251                1               1               1
## 253                1               1               1
## 261                1               1               1
## 262                1               1               1
## 281                1               1               1
## 283                0               1               1
## 284                1               1               1
## 286                0               1               1
## 292                1               1               1
## 294                1               1               1
## 295                1               1               1
## 296                0               1               1
## 300                1               1               0
## 302                1               1               1
## 303                1               1               1
## 306                1               1               1
## 308                1               1               1
## 309                1               1               1
## 314                1               1               1
## 316                0               1               1
## 318                1               1               1
## 321                1               1               1
## 322                1               1               1
## 329                1               0               1
## 332                1               1               1
## 333                1               1               1
## 340                1               1               1
## 350                0               1               1
## 351                1               1               1
## 354                1               1               1
## 366                1               1               1
## 368                1               1               1
## 371                1               1               1
## 374                1               1               1
## 378                1               1               1
## 382                1               1               1
## 387                0               1               1
## 391                1               1               1
## 393                1               1               1
## 394                0               1               1
## 396                0               1               1
## 399                1               1               1
## 402                0               1               1
## 408                1               1               1
## 412                1               1               1
## 413                1               1               1
## 414                0               1               1
## 416                1               1               1
## 417                1               1               1
## 421                1               1               1
## 423                1               1               1
## 426                1               1               1
## 429                0               1               1
## 430                0               1               1
## 437                0               1               1
## 441                1               1               1
## 444                1               1               1
## 450                0               1               1
## 456                1               1               1
## 460                1               1               1
## 462                1               1               1
## 463                1               1               1
## 465                1               1               0
## 469                0               1               1
## 473                1               1               1
## 481                1               1               1
## 484                1               1               0
## 487                1               1               1
## 493                1               1               1
## 500                0               1               1
## 507                1               1               1
## 525                1               1               1
## 527                0               1               1
## 532                1               1               1
## 535                0               1               1
## 537                1               1               1
## 538                1               1               1
## 541                0               1               1
## 544                1               1               1
## 549                1               0               1
## 552                1               1               0
## 553                1               1               1
## 555                1               1               1
## 558                1               1               1
## 559                0               1               1
## 562                1               1               1
## 566                1               1               1
## 571                1               1               1
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## 9506               1               1               1
## 9510               1               1               1
## 9516               1               1               0
## 9517               1               1               1
## 9519               1               1               1
## 9521               1               1               1
## 9530               1               1               1
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## 9541               1               1               1
## 9545               1               1               1
## 9548               0               1               1
## 9549               1               1               1
view(pred_class1_f)


#repeat
#OL best model of train data
# Convert the probability value into a category
pred_class2_1_f <- ifelse(predictions2_f[,1] > 0.0044, 1, 0 )
pred_class2_1_f #. If the probability is greater than 0.01, the prediction is a positive class (1), otherwise negative class (0)
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    0    1 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    0 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
##  588  591  593  595  598  605  606  608  614  619  620  621  622  623  627  628 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  630  632  634  654  658  663  664  666  674  683  686  691  693  696  697  701 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  703  713  714  716  717  721  724  727  735  738  743  744  746  747  751  769 
##    1    1    1    0    1    1    1    1    1    1    0    1    1    1    1    1 
##  770  771  772  773  775  778  779  780  781  784  786  788  789  790  793  794 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  796  801  808  809  810  811  814  817  819  823  831  840  841  842  848  851 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  853  854  855  856  858  861  868  870  872  873  874  877  882  883  884  885 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
##  886  887  889  890  893  897  898  900  901  904  908  911  915  917  919  923 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  934  937  942  943  945  949  952  953  957  958  963  964  965  969  970  975 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  982  983  985  986  987  988  990  991  994  995 1003 1004 1011 1012 1014 1016 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 1017 1021 1023 1024 1026 1027 1034 1035 1038 1042 1043 1044 1045 1047 1048 1051 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1052 1053 1063 1069 1071 1072 1073 1074 1075 1076 1077 1092 1096 1103 1104 1108 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1109 1110 1116 1119 1125 1126 1127 1131 1132 1143 1147 1150 1151 1160 1162 1168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 1169 1170 1171 1173 1177 1178 1180 1181 1182 1196 1198 1199 1205 1206 1216 1218 
##    1    1    1    1    1    0    1    1    0    1    1    1    0    1    1    1 
## 1220 1226 1229 1236 1237 1238 1242 1243 1245 1251 1253 1255 1256 1258 1259 1261 
##    1    1    1    0    1    1    0    1    1    1    1    1    1    1    1    1 
## 1264 1265 1267 1270 1271 1275 1286 1298 1299 1305 1307 1312 1318 1322 1325 1327 
##    1    0    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1335 1340 1343 1347 1348 1349 1353 1356 1370 1372 1376 1380 1381 1383 1386 1389 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 1395 1399 1405 1412 1413 1419 1425 1426 1427 1430 1439 1451 1453 1454 1465 1471 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 1472 1475 1477 1478 1479 1480 1483 1491 1498 1501 1505 1506 1507 1509 1510 1511 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1519 1525 1526 1534 1535 1537 1538 1540 1542 1543 1545 1559 1560 1561 1562 1566 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1568 1573 1582 1593 1603 1604 1610 1614 1622 1623 1625 1627 1633 1635 1637 1645 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 1647 1648 1652 1653 1659 1664 1665 1670 1672 1673 1688 1691 1695 1700 1702 1703 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1709 1725 1735 1738 1743 1748 1750 1755 1757 1758 1760 1761 1765 1769 1771 1772 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1777 1781 1787 1789 1790 1798 1803 1804 1807 1808 1809 1811 1820 1821 1828 1829 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1834 1837 1838 1845 1848 1849 1855 1862 1865 1869 1870 1871 1875 1876 1878 1881 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 1883 1884 1885 1887 1890 1891 1893 1894 1895 1896 1898 1900 1901 1912 1914 1915 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 1917 1918 1919 1923 1924 1926 1929 1931 1933 1936 1937 1939 1940 1942 1948 1956 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1957 1958 1961 1968 1969 1971 1972 1975 1979 1981 1985 1986 1988 1989 1990 1991 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    0    1 
## 1994 1995 2000 2001 2002 2007 2014 2016 2024 2026 2027 2028 2029 2030 2032 2039 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2045 2047 2049 2050 2051 2055 2062 2064 2065 2068 2070 2079 2089 2091 2096 2098 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 2106 2107 2111 2113 2116 2125 2127 2130 2133 2134 2136 2137 2142 2143 2148 2153 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
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## 9549 
##    1
view(pred_class2_1_f)
#39个0,961个1
pred_class2_1_f
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##    1    0    1    1    1    1    1    1    1    1    0    1    1    0    1    1 
## 5093 5094 5100 5101 5104 5110 5112 5116 5119 5120 5121 5125 5131 5144 5146 5151 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5155 5157 5158 5159 5166 5168 5170 5171 5173 5183 5185 5188 5190 5193 5196 5199 
##    1    1    1    1    1    1    1    1    1    0    1    0    1    1    1    1 
## 5205 5207 5212 5213 5214 5216 5218 5222 5226 5230 5237 5242 5245 5248 5252 5255 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 5257 5259 5263 5265 5266 5267 5275 5277 5279 5280 5283 5284 5289 5291 5293 5294 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 5296 5301 5304 5306 5308 5310 5312 5319 5321 5328 5329 5331 5335 5337 5339 5341 
##    0    1    1    1    1    1    0    1    1    1    0    1    1    1    1    1 
## 5342 5343 5352 5356 5358 5360 5361 5364 5365 5366 5371 5374 5375 5376 5377 5379 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5380 5385 5389 5390 5392 5397 5398 5407 5414 5417 5418 5420 5431 5433 5437 5438 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 5442 5445 5449 5450 5456 5464 5466 5472 5479 5483 5491 5493 5495 5496 5498 5500 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5501 5507 5508 5509 5510 5514 5515 5520 5526 5527 5528 5529 5531 5533 5534 5536 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5541 5551 5555 5556 5559 5560 5565 5567 5568 5584 5585 5588 5589 5596 5607 5619 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5620 5621 5626 5630 5632 5633 5634 5636 5637 5639 5640 5641 5643 5645 5647 5663 
##    0    1    1    1    1    0    1    1    1    1    1    1    1    1    1    0 
## 5666 5669 5673 5681 5684 5686 5687 5688 5690 5693 5697 5700 5706 5707 5715 5719 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 5723 5731 5732 5742 5755 5757 5761 5768 5771 5772 5773 5776 5781 5785 5789 5794 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 5801 5810 5815 5817 5819 5830 5833 5842 5844 5847 5859 5868 5880 5884 5887 5888 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 5891 5893 5894 5898 5899 5906 5910 5915 5916 5921 5922 5925 5926 5927 5933 5935 
##    0    1    1    0    1    0    1    1    1    1    1    1    1    1    1    1 
## 5939 5943 5947 5958 5959 5964 5965 5968 5978 5981 5984 5995 5999 6002 6004 6006 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6008 6013 6015 6020 6025 6033 6037 6039 6041 6042 6053 6054 6055 6061 6062 6064 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6067 6069 6077 6080 6089 6092 6094 6097 6098 6100 6106 6110 6111 6116 6120 6121 
##    1    1    1    1    0    1    1    1    1    1    1    0    0    1    1    0 
## 6125 6127 6128 6129 6130 6134 6138 6140 6141 6142 6143 6145 6150 6151 6153 6156 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6164 6171 6172 6178 6181 6188 6191 6197 6200 6203 6210 6214 6215 6216 6221 6224 
##    1    0    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 6231 6235 6236 6237 6238 6240 6243 6246 6247 6250 6262 6266 6270 6272 6275 6276 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6279 6281 6283 6284 6287 6288 6290 6292 6294 6301 6305 6308 6311 6312 6313 6317 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6319 6320 6322 6323 6334 6336 6339 6341 6342 6343 6345 6347 6349 6350 6351 6353 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6354 6359 6362 6366 6367 6368 6375 6377 6384 6386 6387 6388 6395 6396 6406 6407 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6411 6414 6418 6419 6420 6427 6428 6430 6433 6434 6435 6438 6439 6443 6445 6446 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6447 6463 6465 6468 6476 6477 6478 6481 6486 6491 6493 6495 6496 6502 6503 6508 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 6511 6512 6521 6522 6524 6531 6534 6535 6536 6537 6544 6547 6551 6554 6558 6561 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 6562 6566 6569 6570 6571 6572 6573 6574 6578 6579 6585 6590 6591 6592 6597 6605 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6607 6609 6611 6612 6616 6622 6625 6630 6636 6640 6641 6651 6653 6655 6663 6667 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 6673 6674 6676 6677 6678 6679 6680 6687 6689 6696 6697 6698 6700 6703 6709 6711 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6718 6721 6725 6727 6729 6731 6732 6740 6745 6746 6748 6751 6752 6755 6761 6764 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6766 6777 6779 6780 6783 6786 6788 6797 6801 6803 6807 6812 6813 6814 6822 6823 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 6824 6825 6827 6832 6834 6838 6839 6842 6843 6845 6852 6854 6862 6863 6864 6872 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6875 6885 6889 6891 6893 6897 6898 6907 6910 6913 6916 6918 6923 6926 6928 6930 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6936 6937 6939 6945 6949 6950 6951 6952 6954 6957 6959 6960 6961 6962 6966 6968 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6971 6974 6978 6980 6984 6985 6987 6992 6993 6995 6998 6999 7001 7004 7005 7006 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7008 7009 7012 7014 7015 7016 7019 7026 7028 7029 7036 7043 7048 7051 7055 7058 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7065 7066 7069 7073 7077 7079 7082 7083 7088 7091 7094 7100 7103 7106 7109 7110 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7112 7114 7115 7116 7120 7130 7133 7139 7141 7144 7152 7155 7157 7158 7160 7161 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 7166 7167 7168 7178 7179 7181 7182 7186 7188 7191 7192 7196 7197 7202 7203 7207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7209 7210 7221 7222 7226 7228 7229 7237 7238 7241 7247 7248 7250 7270 7273 7275 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7279 7280 7281 7282 7283 7285 7287 7294 7299 7302 7305 7314 7315 7317 7320 7330 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 7332 7337 7338 7339 7341 7342 7344 7346 7350 7355 7360 7364 7365 7366 7371 7373 
##    1    0    1    1    1    1    1    1    0    0    1    1    1    1    1    1 
## 7376 7380 7381 7387 7389 7392 7399 7402 7403 7408 7410 7412 7416 7419 7426 7428 
##    1    0    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 7431 7432 7433 7436 7438 7440 7441 7447 7456 7457 7458 7462 7463 7466 7467 7472 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7475 7484 7485 7487 7488 7490 7497 7498 7502 7507 7511 7519 7520 7523 7525 7526 
##    1    1    0    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 7529 7530 7531 7532 7533 7534 7536 7538 7539 7543 7547 7549 7551 7552 7553 7556 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 7560 7566 7569 7570 7573 7580 7586 7597 7598 7601 7606 7612 7615 7616 7620 7626 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7627 7629 7631 7633 7640 7645 7650 7651 7652 7654 7655 7659 7660 7665 7673 7674 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7676 7677 7678 7685 7692 7697 7700 7704 7709 7712 7720 7721 7729 7730 7736 7739 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7740 7741 7742 7743 7750 7753 7755 7757 7759 7761 7763 7764 7774 7778 7785 7788 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 7791 7793 7796 7797 7802 7805 7807 7811 7813 7814 7815 7826 7831 7837 7838 7842 
##    1    0    1    1    1    1    1    1    1    1    1    0    1    1    1    0 
## 7844 7846 7847 7849 7855 7857 7862 7869 7871 7876 7882 7883 7884 7888 7891 7892 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7894 7896 7898 7910 7911 7921 7923 7926 7927 7928 7929 7933 7936 7937 7939 7949 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 7953 7955 7957 7960 7962 7964 7965 7966 7967 7971 7976 7981 7983 7984 7988 7989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7991 7999 8008 8012 8013 8015 8017 8018 8019 8023 8026 8030 8034 8035 8043 8044 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8049 8054 8065 8066 8067 8076 8083 8089 8090 8104 8108 8110 8111 8113 8118 8125 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8127 8128 8133 8137 8138 8147 8150 8156 8167 8174 8176 8182 8198 8199 8206 8207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8208 8214 8215 8216 8218 8222 8223 8224 8226 8227 8230 8234 8235 8237 8239 8242 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8243 8247 8248 8253 8256 8257 8259 8267 8271 8272 8282 8288 8290 8291 8294 8295 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8302 8303 8306 8308 8319 8321 8322 8325 8326 8328 8337 8340 8344 8345 8352 8359 
##    1    0    0    1    0    1    1    1    1    0    1    1    1    1    0    1 
## 8364 8365 8370 8381 8385 8387 8391 8395 8396 8400 8405 8406 8408 8409 8413 8415 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    0    1    1 
## 8417 8418 8419 8420 8425 8426 8428 8430 8433 8437 8439 8442 8445 8448 8449 8459 
##    1    1    0    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 8460 8464 8466 8468 8471 8474 8475 8476 8477 8486 8488 8490 8496 8497 8498 8501 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8502 8504 8505 8508 8509 8510 8511 8513 8514 8517 8527 8528 8534 8535 8540 8542 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8543 8545 8546 8547 8548 8551 8560 8561 8566 8567 8569 8570 8571 8575 8580 8584 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8587 8600 8603 8607 8623 8626 8627 8629 8630 8635 8637 8646 8649 8651 8652 8656 
##    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8664 8667 8669 8672 8680 8681 8682 8683 8691 8700 8701 8707 8711 8715 8716 8721 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8722 8724 8725 8729 8730 8731 8733 8735 8743 8744 8747 8758 8759 8762 8764 8769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8772 8773 8774 8775 8783 8784 8786 8790 8796 8798 8799 8804 8805 8806 8807 8811 
##    1    1    0    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8817 8818 8819 8820 8826 8830 8832 8835 8836 8845 8847 8850 8851 8854 8860 8861 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8862 8866 8867 8871 8872 8881 8882 8884 8891 8892 8893 8895 8896 8900 8903 8904 
##    1    1    0    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8905 8906 8907 8911 8919 8920 8922 8927 8935 8942 8945 8948 8949 8951 8952 8953 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8955 8959 8961 8965 8967 8970 8971 8973 8978 8982 8984 8985 8986 8990 8992 8998 
##    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
## 9001 9006 9011 9012 9013 9015 9017 9018 9021 9025 9033 9037 9041 9046 9049 9054 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9057 9063 9076 9077 9079 9080 9083 9084 9090 9092 9095 9097 9098 9100 9101 9105 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9108 9109 9117 9119 9127 9130 9133 9136 9139 9151 9153 9156 9158 9162 9163 9166 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    0    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    0    1    1    1    1    1    0    1    1    0    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9404 9405 9409 9413 9414 9418 9419 9425 9430 9431 9434 9435 9436 9437 9439 9442 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9443 9446 9447 9448 9450 9452 9454 9462 9464 9465 9466 9467 9472 9473 9482 9486 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9549 
##    1
pred_class2_2_f <- ifelse(predictions2_f[,2] > 0.1126, 1, 0 )
pred_class2_2 #. If the probability is greater than 0.24, the prediction is a positive class (1), otherwise negative class (0)
##    6   12   14   19   23   24   26   29   33   34   37   38   40   42   43   44 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   46   47   48   50   56   69   70   74   78   80   85   86   87   89   90   91 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   92   93   95   99  102  104  110  111  115  117  118  119  120  123  124  130 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  138  140  141  146  148  157  158  160  166  167  168  169  174  176  177  189 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  190  197  199  202  205  211  212  214  219  220  225  226  228  233  235  239 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  240  241  247  248  254  266  268  280  283  285  289  292  293  301  310  312 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  313  320  322  332  337  347  349  356  357  358  360  363  376  377  378  387 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  388  389  392  395  396  397  399  404  406  409  411  412  416  419  425  430 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  431  439  440  441  443  446  449  450  452  463  465  468  471  475  476  477 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  478  480  483  487  488  493  494  497  499  501  503  507  508  510  514  515 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  516  519  521  524  530  531  533  540  544  545  550  554  556  557  565  566 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
##  571  573  576  579  580  582  585  591  592  593  594  595  596  598  611  622 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
##  626  627  629  635  642  648  650  654  658  661  662  667  670  673  676  679 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  681  687  696  698  699  702  709  717  722  725  726  728  731  732  734  736 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  738  746  747  749  753  757  758  759  760  763  765  766  768  770  771  775 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  776  778  787  791  794  802  803  806  809  811  813  814  815  823  824  833 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  835  837  841  844  846  848  853  857  861  865  868  869  876  877  878  879 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  880  886  888  889  895  900  902  907  909  921  924  928  934  935  937  941 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
##  944  945  951  952  953  955  962  965  968  971  973  975  977  980  983  989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  992  993  994  996  998 1011 1012 1013 1014 1018 1020 1022 1032 1034 1035 1036 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1038 1052 1061 1062 1064 1069 1072 1076 1077 1090 1092 1096 1097 1100 1113 1115 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1116 1117 1118 1121 1122 1124 1125 1127 1130 1131 1134 1136 1141 1144 1145 1148 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1150 1156 1159 1168 1172 1173 1174 1180 1182 1183 1187 1188 1189 1192 1197 1200 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 1208 1210 1218 1220 1221 1229 1231 1237 1242 1244 1247 1250 1253 1254 1255 1257 
##    1    1    1    1    1    1    1    1    0    0    1    1    1    1    1    1 
## 1262 1265 1266 1269 1273 1277 1279 1281 1282 1283 1287 1292 1293 1295 1302 1303 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1305 1310 1311 1317 1320 1321 1326 1329 1332 1336 1343 1346 1348 1353 1355 1357 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1359 1367 1369 1373 1374 1375 1377 1378 1379 1382 1383 1384 1387 1388 1390 1392 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1393 1395 1396 1398 1407 1416 1418 1422 1433 1438 1439 1443 1450 1451 1455 1460 
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## 7695 7697 7698 7706 7713 7715 7721 7724 7732 7738 7739 7745 7749 7754 7755 7758 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7767 7768 7769 7771 7772 7773 7776 7784 7786 7790 7792 7793 7795 7798 7801 7822 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7830 7832 7836 7841 7845 7848 7862 7865 7870 7874 7884 7885 7887 7890 7891 7893 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 7894 7898 7899 7902 7908 7909 7911 7922 7923 7927 7928 7936 7938 7951 7954 7957 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7960 7961 7963 7966 7970 7971 7976 7982 7986 7988 7991 7992 7999 8001 8002 8004 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 8008 8010 8013 8017 8019 8020 8021 8022 8025 8033 8034 8035 8040 8043 8047 8056 
##    0    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 8059 8062 8063 8065 8067 8069 8075 8080 8096 8097 8102 8105 8106 8109 8111 8117 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    0    1    1 
## 8119 8120 8123 8130 8132 8134 8136 8139 8142 8144 8145 8148 8150 8151 8154 8156 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8161 8162 8168 8170 8171 8175 8180 8184 8187 8188 8189 8192 8201 8204 8206 8207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8208 8210 8212 8219 8220 8228 8233 8239 8240 8243 8245 8249 8250 8251 8252 8253 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8254 8256 8257 8258 8267 8273 8274 8278 8282 8285 8286 8288 8289 8292 8295 8302 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8306 8314 8319 8320 8329 8337 8339 8340 8342 8345 8353 8354 8360 8362 8364 8366 
##    0    1    0    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 8367 8369 8378 8380 8381 8383 8386 8391 8396 8397 8398 8415 8417 8418 8424 8425 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8436 8437 8440 8446 8451 8453 8456 8460 8461 8462 8464 8465 8466 8474 8476 8478 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 8483 8484 8498 8499 8504 8505 8506 8511 8515 8522 8524 8534 8545 8547 8556 8559 
##    1    0    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 8560 8561 8563 8565 8567 8573 8574 8575 8576 8581 8582 8585 8586 8589 8592 8595 
##    0    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8600 8602 8604 8605 8607 8609 8612 8617 8618 8619 8622 8625 8626 8627 8632 8647 
##    1    1    1    1    1    0    1    1    1    1    1    0    1    1    1    1 
## 8648 8649 8651 8653 8656 8659 8662 8669 8670 8674 8676 8678 8680 8682 8688 8695 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8696 8697 8699 8700 8705 8711 8713 8715 8725 8731 8733 8735 8740 8742 8745 8746 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8752 8754 8755 8762 8769 8777 8779 8783 8788 8789 8796 8797 8798 8810 8815 8816 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8823 8824 8834 8836 8838 8839 8840 8842 8844 8845 8849 8852 8853 8854 8868 8870 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8875 8877 8880 8887 8889 8890 8895 8902 8906 8907 8911 8916 8917 8918 8921 8922 
##    1    1    1    0    1    1    1    1    1    1    1    1    0    0    1    1 
## 8924 8925 8930 8942 8945 8953 8956 8958 8959 8962 8963 8968 8969 8972 8975 8980 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 8981 8982 8988 8990 8993 8996 9000 9007 9019 9023 9024 9027 9029 9030 9033 9035 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 9037 9038 9040 9043 9047 9049 9054 9070 9072 9073 9085 9086 9089 9090 9092 9093 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9096 9098 9102 9103 9105 9106 9111 9112 9113 9115 9116 9117 9122 9123 9126 9128 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 9132 9141 9143 9144 9150 9151 9152 9156 9159 9163 9164 9176 9183 9185 9186 9190 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9194 9197 9199 9207 9208 9211 9212 9215 9220 9221 9229 9231 9233 9235 9238 9242 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 9245 9248 9253 9263 9268 9272 9275 9277 9281 9282 9286 9292 9294 9299 9302 9303 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 9306 9313 9316 9317 9320 9321 9327 9328 9331 9333 9337 9338 9343 9346 9350 9351 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9354 9356 9361 9364 9365 9367 9374 9378 9380 9381 9383 9385 9387 9389 9393 9395 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9398 9399 9401 9408 9409 9415 9416 9420 9421 9423 9424 9425 9426 9430 9431 9434 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 9437 9441 9442 9447 9455 9457 9459 9461 9473 9476 9480 9481 9482 9487 9490 9494 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9496 9497 9499 9503 9507 9510 9511 9516 9520 9521 9524 9526 9533 9535 9540 9541 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9547 
##    1
#34个0,966个1
view(pred_class2_2_f)

pred_class2_3_f <- ifelse(predictions2_f[,3] > 0.6, 1, 0 )
pred_class2_3_f #. If the probability is greater than 0.75, the prediction is a positive class (1), otherwise negative class (0)
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    1    1    1    1    0    1    1    0    1    1    1    1    1    1 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    1    0    1    1    1    0    1    1    1    1    1    1    1    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    0    1    1    1    0    1    1    1    1    1    1    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
##  588  591  593  595  598  605  606  608  614  619  620  621  622  623  627  628 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  630  632  634  654  658  663  664  666  674  683  686  691  693  696  697  701 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  703  713  714  716  717  721  724  727  735  738  743  744  746  747  751  769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  770  771  772  773  775  778  779  780  781  784  786  788  789  790  793  794 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
##  796  801  808  809  810  811  814  817  819  823  831  840  841  842  848  851 
##    1    1    1    1    1    1    0    1    1    1    1    0    1    1    1    0 
##  853  854  855  856  858  861  868  870  872  873  874  877  882  883  884  885 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  886  887  889  890  893  897  898  900  901  904  908  911  915  917  919  923 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  934  937  942  943  945  949  952  953  957  958  963  964  965  969  970  975 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  982  983  985  986  987  988  990  991  994  995 1003 1004 1011 1012 1014 1016 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1017 1021 1023 1024 1026 1027 1034 1035 1038 1042 1043 1044 1045 1047 1048 1051 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1052 1053 1063 1069 1071 1072 1073 1074 1075 1076 1077 1092 1096 1103 1104 1108 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1109 1110 1116 1119 1125 1126 1127 1131 1132 1143 1147 1150 1151 1160 1162 1168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1169 1170 1171 1173 1177 1178 1180 1181 1182 1196 1198 1199 1205 1206 1216 1218 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1220 1226 1229 1236 1237 1238 1242 1243 1245 1251 1253 1255 1256 1258 1259 1261 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1264 1265 1267 1270 1271 1275 1286 1298 1299 1305 1307 1312 1318 1322 1325 1327 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 1335 1340 1343 1347 1348 1349 1353 1356 1370 1372 1376 1380 1381 1383 1386 1389 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1395 1399 1405 1412 1413 1419 1425 1426 1427 1430 1439 1451 1453 1454 1465 1471 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    0    1    1 
## 1472 1475 1477 1478 1479 1480 1483 1491 1498 1501 1505 1506 1507 1509 1510 1511 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1519 1525 1526 1534 1535 1537 1538 1540 1542 1543 1545 1559 1560 1561 1562 1566 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1568 1573 1582 1593 1603 1604 1610 1614 1622 1623 1625 1627 1633 1635 1637 1645 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1647 1648 1652 1653 1659 1664 1665 1670 1672 1673 1688 1691 1695 1700 1702 1703 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1709 1725 1735 1738 1743 1748 1750 1755 1757 1758 1760 1761 1765 1769 1771 1772 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1777 1781 1787 1789 1790 1798 1803 1804 1807 1808 1809 1811 1820 1821 1828 1829 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1834 1837 1838 1845 1848 1849 1855 1862 1865 1869 1870 1871 1875 1876 1878 1881 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1883 1884 1885 1887 1890 1891 1893 1894 1895 1896 1898 1900 1901 1912 1914 1915 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1917 1918 1919 1923 1924 1926 1929 1931 1933 1936 1937 1939 1940 1942 1948 1956 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1957 1958 1961 1968 1969 1971 1972 1975 1979 1981 1985 1986 1988 1989 1990 1991 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1994 1995 2000 2001 2002 2007 2014 2016 2024 2026 2027 2028 2029 2030 2032 2039 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 2045 2047 2049 2050 2051 2055 2062 2064 2065 2068 2070 2079 2089 2091 2096 2098 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2106 2107 2111 2113 2116 2125 2127 2130 2133 2134 2136 2137 2142 2143 2148 2153 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 2155 2156 2160 2163 2164 2174 2182 2198 2205 2207 2210 2212 2214 2218 2219 2221 
##    1    1    1    1    1    1    0    0    1    1    1    1    1    0    1    1 
## 2223 2231 2233 2239 2246 2248 2250 2252 2255 2258 2259 2261 2264 2266 2269 2275 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2280 2286 2288 2293 2297 2303 2305 2308 2309 2312 2313 2319 2323 2328 2332 2333 
##    1    1    1    1    1    0    1    0    1    1    1    1    1    1    1    1 
## 2334 2337 2339 2343 2344 2346 2352 2355 2359 2368 2371 2374 2375 2376 2381 2382 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    0    1    1 
## 2383 2395 2396 2398 2401 2405 2411 2412 2418 2427 2430 2434 2435 2438 2439 2446 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2454 2456 2458 2459 2462 2466 2472 2475 2476 2478 2481 2484 2491 2495 2496 2498 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 2499 2500 2501 2504 2505 2507 2510 2511 2516 2518 2519 2522 2524 2526 2530 2537 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2546 2553 2564 2566 2567 2568 2573 2576 2587 2588 2589 2590 2591 2594 2595 2597 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2599 2602 2604 2606 2608 2609 2613 2617 2619 2631 2634 2635 2636 2637 2641 2642 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2644 2649 2653 2654 2660 2662 2663 2664 2669 2670 2672 2675 2676 2680 2682 2683 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2684 2685 2688 2698 2699 2704 2709 2710 2713 2717 2719 2730 2735 2740 2748 2749 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2751 2754 2762 2768 2769 2777 2784 2786 2788 2792 2799 2801 2806 2813 2814 2815 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2819 2824 2825 2828 2831 2835 2848 2852 2853 2857 2861 2864 2868 2869 2880 2888 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2889 2890 2892 2894 2900 2909 2916 2920 2927 2930 2932 2939 2942 2947 2948 2952 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2956 2963 2965 2970 2972 2975 2976 2980 2984 2991 2997 3002 3008 3010 3013 3015 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 3021 3023 3024 3026 3032 3038 3041 3046 3047 3055 3062 3063 3072 3074 3084 3091 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 3098 3099 3104 3109 3110 3117 3118 3120 3129 3133 3140 3141 3143 3145 3148 3151 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    0    1 
## 3152 3155 3156 3163 3165 3167 3169 3174 3175 3178 3181 3182 3186 3188 3189 3191 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 3196 3200 3201 3205 3207 3208 3209 3210 3212 3214 3218 3222 3234 3235 3238 3246 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3249 3250 3252 3253 3255 3257 3262 3264 3266 3267 3268 3270 3271 3275 3281 3282 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3283 3287 3288 3289 3295 3298 3300 3314 3316 3319 3320 3327 3329 3331 3340 3341 
##    0    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 3344 3345 3346 3347 3354 3357 3359 3361 3363 3366 3370 3372 3376 3384 3386 3389 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3390 3394 3398 3402 3405 3408 3413 3419 3421 3425 3426 3428 3431 3432 3445 3448 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3451 3456 3457 3458 3463 3469 3471 3475 3476 3481 3482 3486 3489 3492 3494 3498 
##    0    0    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3499 3503 3504 3505 3506 3508 3511 3513 3515 3516 3518 3521 3525 3526 3530 3533 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3535 3539 3540 3543 3544 3547 3549 3550 3553 3556 3561 3567 3573 3577 3581 3586 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3587 3589 3590 3591 3601 3606 3608 3610 3620 3621 3623 3631 3633 3634 3640 3641 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3646 3650 3651 3652 3660 3662 3663 3669 3689 3690 3691 3693 3694 3697 3699 3702 
##    1    0    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 3711 3721 3722 3723 3726 3727 3731 3734 3735 3737 3742 3744 3750 3751 3752 3756 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 3760 3761 3765 3770 3776 3777 3784 3785 3788 3791 3797 3799 3802 3803 3808 3809 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3811 3822 3823 3824 3828 3829 3833 3839 3841 3842 3843 3847 3850 3851 3855 3856 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3858 3860 3862 3863 3873 3876 3877 3886 3889 3891 3894 3898 3900 3902 3903 3907 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3912 3916 3918 3930 3935 3936 3938 3939 3940 3941 3945 3949 3953 3957 3960 3961 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3977 3978 3980 3982 3985 3986 3988 3990 3991 3995 3997 4000 4001 4006 4010 4011 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4012 4014 4023 4025 4029 4038 4040 4044 4045 4051 4052 4054 4070 4071 4074 4077 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4083 4089 4092 4096 4097 4098 4103 4113 4116 4124 4126 4130 4135 4136 4138 4141 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 4142 4146 4152 4154 4156 4157 4159 4160 4170 4173 4175 4178 4180 4184 4191 4193 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4194 4197 4199 4200 4203 4204 4212 4214 4215 4219 4223 4225 4227 4228 4231 4234 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    0    1 
## 4242 4254 4256 4258 4271 4274 4278 4279 4281 4282 4286 4287 4289 4291 4293 4297 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4300 4302 4305 4307 4309 4310 4312 4315 4323 4325 4328 4331 4332 4337 4341 4342 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4344 4345 4346 4350 4354 4360 4364 4367 4370 4376 4378 4386 4387 4389 4395 4401 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    0    1 
## 4404 4407 4411 4412 4413 4414 4418 4420 4422 4442 4444 4450 4451 4457 4462 4467 
##    1    0    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 4475 4477 4479 4487 4499 4500 4503 4506 4515 4520 4525 4534 4536 4541 4542 4544 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4545 4547 4548 4552 4554 4557 4560 4573 4574 4575 4576 4577 4580 4583 4585 4591 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4593 4600 4601 4603 4604 4606 4607 4608 4619 4622 4624 4625 4626 4630 4632 4638 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4639 4640 4641 4643 4646 4649 4650 4652 4660 4673 4674 4675 4680 4683 4687 4689 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 4692 4693 4695 4696 4697 4701 4704 4706 4707 4713 4714 4717 4726 4729 4730 4733 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 4734 4749 4753 4754 4755 4757 4758 4763 4764 4765 4771 4773 4774 4778 4783 4784 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 4785 4786 4787 4798 4799 4800 4806 4812 4815 4816 4818 4822 4826 4827 4833 4834 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4839 4842 4844 4845 4850 4851 4854 4855 4864 4870 4872 4873 4875 4878 4880 4886 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 4892 4895 4898 4900 4902 4906 4907 4909 4915 4916 4918 4919 4922 4923 4926 4937 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 4938 4940 4946 4950 4954 4956 4958 4961 4962 4964 4967 4970 4971 4977 4979 4981 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 4990 4995 4996 5002 5005 5006 5007 5008 5009 5010 5013 5016 5017 5018 5025 5028 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5031 5032 5034 5037 5041 5046 5049 5056 5059 5061 5062 5064 5067 5069 5088 5092 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5093 5094 5100 5101 5104 5110 5112 5116 5119 5120 5121 5125 5131 5144 5146 5151 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5155 5157 5158 5159 5166 5168 5170 5171 5173 5183 5185 5188 5190 5193 5196 5199 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5205 5207 5212 5213 5214 5216 5218 5222 5226 5230 5237 5242 5245 5248 5252 5255 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 5257 5259 5263 5265 5266 5267 5275 5277 5279 5280 5283 5284 5289 5291 5293 5294 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 5296 5301 5304 5306 5308 5310 5312 5319 5321 5328 5329 5331 5335 5337 5339 5341 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5342 5343 5352 5356 5358 5360 5361 5364 5365 5366 5371 5374 5375 5376 5377 5379 
##    0    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 5380 5385 5389 5390 5392 5397 5398 5407 5414 5417 5418 5420 5431 5433 5437 5438 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    0    1    1 
## 5442 5445 5449 5450 5456 5464 5466 5472 5479 5483 5491 5493 5495 5496 5498 5500 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 5501 5507 5508 5509 5510 5514 5515 5520 5526 5527 5528 5529 5531 5533 5534 5536 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 5541 5551 5555 5556 5559 5560 5565 5567 5568 5584 5585 5588 5589 5596 5607 5619 
##    0    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 5620 5621 5626 5630 5632 5633 5634 5636 5637 5639 5640 5641 5643 5645 5647 5663 
##    1    1    1    1    0    1    0    1    1    1    1    1    1    1    1    1 
## 5666 5669 5673 5681 5684 5686 5687 5688 5690 5693 5697 5700 5706 5707 5715 5719 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 5723 5731 5732 5742 5755 5757 5761 5768 5771 5772 5773 5776 5781 5785 5789 5794 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5801 5810 5815 5817 5819 5830 5833 5842 5844 5847 5859 5868 5880 5884 5887 5888 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5891 5893 5894 5898 5899 5906 5910 5915 5916 5921 5922 5925 5926 5927 5933 5935 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 5939 5943 5947 5958 5959 5964 5965 5968 5978 5981 5984 5995 5999 6002 6004 6006 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6008 6013 6015 6020 6025 6033 6037 6039 6041 6042 6053 6054 6055 6061 6062 6064 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 6067 6069 6077 6080 6089 6092 6094 6097 6098 6100 6106 6110 6111 6116 6120 6121 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6125 6127 6128 6129 6130 6134 6138 6140 6141 6142 6143 6145 6150 6151 6153 6156 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6164 6171 6172 6178 6181 6188 6191 6197 6200 6203 6210 6214 6215 6216 6221 6224 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 6231 6235 6236 6237 6238 6240 6243 6246 6247 6250 6262 6266 6270 6272 6275 6276 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 6279 6281 6283 6284 6287 6288 6290 6292 6294 6301 6305 6308 6311 6312 6313 6317 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 6319 6320 6322 6323 6334 6336 6339 6341 6342 6343 6345 6347 6349 6350 6351 6353 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6354 6359 6362 6366 6367 6368 6375 6377 6384 6386 6387 6388 6395 6396 6406 6407 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 6411 6414 6418 6419 6420 6427 6428 6430 6433 6434 6435 6438 6439 6443 6445 6446 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 6447 6463 6465 6468 6476 6477 6478 6481 6486 6491 6493 6495 6496 6502 6503 6508 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6511 6512 6521 6522 6524 6531 6534 6535 6536 6537 6544 6547 6551 6554 6558 6561 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6562 6566 6569 6570 6571 6572 6573 6574 6578 6579 6585 6590 6591 6592 6597 6605 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6607 6609 6611 6612 6616 6622 6625 6630 6636 6640 6641 6651 6653 6655 6663 6667 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6673 6674 6676 6677 6678 6679 6680 6687 6689 6696 6697 6698 6700 6703 6709 6711 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 6718 6721 6725 6727 6729 6731 6732 6740 6745 6746 6748 6751 6752 6755 6761 6764 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6766 6777 6779 6780 6783 6786 6788 6797 6801 6803 6807 6812 6813 6814 6822 6823 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 6824 6825 6827 6832 6834 6838 6839 6842 6843 6845 6852 6854 6862 6863 6864 6872 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6875 6885 6889 6891 6893 6897 6898 6907 6910 6913 6916 6918 6923 6926 6928 6930 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6936 6937 6939 6945 6949 6950 6951 6952 6954 6957 6959 6960 6961 6962 6966 6968 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 6971 6974 6978 6980 6984 6985 6987 6992 6993 6995 6998 6999 7001 7004 7005 7006 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7008 7009 7012 7014 7015 7016 7019 7026 7028 7029 7036 7043 7048 7051 7055 7058 
##    0    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 7065 7066 7069 7073 7077 7079 7082 7083 7088 7091 7094 7100 7103 7106 7109 7110 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7112 7114 7115 7116 7120 7130 7133 7139 7141 7144 7152 7155 7157 7158 7160 7161 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7166 7167 7168 7178 7179 7181 7182 7186 7188 7191 7192 7196 7197 7202 7203 7207 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 7209 7210 7221 7222 7226 7228 7229 7237 7238 7241 7247 7248 7250 7270 7273 7275 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7279 7280 7281 7282 7283 7285 7287 7294 7299 7302 7305 7314 7315 7317 7320 7330 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7332 7337 7338 7339 7341 7342 7344 7346 7350 7355 7360 7364 7365 7366 7371 7373 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7376 7380 7381 7387 7389 7392 7399 7402 7403 7408 7410 7412 7416 7419 7426 7428 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7431 7432 7433 7436 7438 7440 7441 7447 7456 7457 7458 7462 7463 7466 7467 7472 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7475 7484 7485 7487 7488 7490 7497 7498 7502 7507 7511 7519 7520 7523 7525 7526 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7529 7530 7531 7532 7533 7534 7536 7538 7539 7543 7547 7549 7551 7552 7553 7556 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7560 7566 7569 7570 7573 7580 7586 7597 7598 7601 7606 7612 7615 7616 7620 7626 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 7627 7629 7631 7633 7640 7645 7650 7651 7652 7654 7655 7659 7660 7665 7673 7674 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 7676 7677 7678 7685 7692 7697 7700 7704 7709 7712 7720 7721 7729 7730 7736 7739 
##    1    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1 
## 7740 7741 7742 7743 7750 7753 7755 7757 7759 7761 7763 7764 7774 7778 7785 7788 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 7791 7793 7796 7797 7802 7805 7807 7811 7813 7814 7815 7826 7831 7837 7838 7842 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 7844 7846 7847 7849 7855 7857 7862 7869 7871 7876 7882 7883 7884 7888 7891 7892 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 7894 7896 7898 7910 7911 7921 7923 7926 7927 7928 7929 7933 7936 7937 7939 7949 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 7953 7955 7957 7960 7962 7964 7965 7966 7967 7971 7976 7981 7983 7984 7988 7989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7991 7999 8008 8012 8013 8015 8017 8018 8019 8023 8026 8030 8034 8035 8043 8044 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8049 8054 8065 8066 8067 8076 8083 8089 8090 8104 8108 8110 8111 8113 8118 8125 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8127 8128 8133 8137 8138 8147 8150 8156 8167 8174 8176 8182 8198 8199 8206 8207 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8208 8214 8215 8216 8218 8222 8223 8224 8226 8227 8230 8234 8235 8237 8239 8242 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 8243 8247 8248 8253 8256 8257 8259 8267 8271 8272 8282 8288 8290 8291 8294 8295 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 8302 8303 8306 8308 8319 8321 8322 8325 8326 8328 8337 8340 8344 8345 8352 8359 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 8364 8365 8370 8381 8385 8387 8391 8395 8396 8400 8405 8406 8408 8409 8413 8415 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8417 8418 8419 8420 8425 8426 8428 8430 8433 8437 8439 8442 8445 8448 8449 8459 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 8460 8464 8466 8468 8471 8474 8475 8476 8477 8486 8488 8490 8496 8497 8498 8501 
##    1    1    1    1    0    1    1    1    1    1    1    1    0    1    1    1 
## 8502 8504 8505 8508 8509 8510 8511 8513 8514 8517 8527 8528 8534 8535 8540 8542 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8543 8545 8546 8547 8548 8551 8560 8561 8566 8567 8569 8570 8571 8575 8580 8584 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    0 
## 8587 8600 8603 8607 8623 8626 8627 8629 8630 8635 8637 8646 8649 8651 8652 8656 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8664 8667 8669 8672 8680 8681 8682 8683 8691 8700 8701 8707 8711 8715 8716 8721 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 8722 8724 8725 8729 8730 8731 8733 8735 8743 8744 8747 8758 8759 8762 8764 8769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8772 8773 8774 8775 8783 8784 8786 8790 8796 8798 8799 8804 8805 8806 8807 8811 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8817 8818 8819 8820 8826 8830 8832 8835 8836 8845 8847 8850 8851 8854 8860 8861 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8862 8866 8867 8871 8872 8881 8882 8884 8891 8892 8893 8895 8896 8900 8903 8904 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8905 8906 8907 8911 8919 8920 8922 8927 8935 8942 8945 8948 8949 8951 8952 8953 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8955 8959 8961 8965 8967 8970 8971 8973 8978 8982 8984 8985 8986 8990 8992 8998 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9001 9006 9011 9012 9013 9015 9017 9018 9021 9025 9033 9037 9041 9046 9049 9054 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 9057 9063 9076 9077 9079 9080 9083 9084 9090 9092 9095 9097 9098 9100 9101 9105 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 9108 9109 9117 9119 9127 9130 9133 9136 9139 9151 9153 9156 9158 9162 9163 9166 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    1    1    1    1    0    1    1    0    1    1    1 
## 9404 9405 9409 9413 9414 9418 9419 9425 9430 9431 9434 9435 9436 9437 9439 9442 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 9443 9446 9447 9448 9450 9452 9454 9462 9464 9465 9466 9467 9472 9473 9482 9486 
##    1    1    1    0    0    1    1    1    1    1    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1    0 
## 9549 
##    1
#39个0,961个1
view(pred_class2_3_f)

pred_class2_f <- cbind(pred_class2_1_f, pred_class2_2_f,pred_class2_3_f)
pred_class2_f
##      pred_class2_1_f pred_class2_2_f pred_class2_3_f
## 2                  1               1               1
## 4                  1               1               1
## 8                  1               1               1
## 13                 1               1               1
## 16                 1               1               1
## 18                 1               1               1
## 29                 1               1               1
## 30                 1               1               1
## 32                 1               1               1
## 36                 1               1               1
## 39                 1               1               1
## 41                 1               1               1
## 43                 1               1               1
## 48                 1               1               1
## 49                 1               1               1
## 55                 1               1               1
## 58                 1               1               1
## 59                 1               1               1
## 60                 1               1               1
## 62                 1               1               1
## 63                 1               1               1
## 71                 1               1               1
## 73                 0               0               1
## 80                 1               1               1
## 84                 1               1               1
## 86                 1               1               1
## 87                 1               1               1
## 98                 1               1               1
## 102                1               1               1
## 104                1               1               1
## 107                0               0               1
## 109                1               1               1
## 110                1               1               1
## 113                1               1               1
## 123                1               1               1
## 125                1               1               1
## 136                1               1               1
## 137                1               1               1
## 138                1               1               0
## 143                1               1               1
## 145                1               1               1
## 147                1               1               0
## 149                0               1               1
## 151                1               1               1
## 153                1               1               1
## 160                1               1               1
## 162                1               1               1
## 165                0               0               1
## 167                1               1               1
## 168                1               1               1
## 171                1               1               1
## 175                1               1               1
## 177                1               1               1
## 184                1               1               1
## 187                1               1               1
## 188                1               1               1
## 198                1               1               1
## 199                1               1               1
## 205                0               1               1
## 206                1               1               1
## 214                1               1               1
## 217                1               1               1
## 220                1               1               1
## 221                1               1               1
## 225                1               1               1
## 227                1               1               1
## 230                1               1               1
## 231                1               1               1
## 242                0               0               1
## 249                1               1               1
## 251                1               1               1
## 253                1               1               1
## 261                1               1               1
## 262                1               1               1
## 281                1               1               1
## 283                1               1               1
## 284                1               1               1
## 286                1               1               1
## 292                1               1               1
## 294                1               1               1
## 295                1               1               1
## 296                1               1               1
## 300                1               1               0
## 302                1               1               1
## 303                1               1               1
## 306                1               1               1
## 308                1               1               0
## 309                1               1               1
## 314                1               1               1
## 316                1               1               1
## 318                1               1               1
## 321                1               1               1
## 322                1               1               1
## 329                0               1               1
## 332                1               1               1
## 333                1               1               1
## 340                1               1               1
## 350                1               1               1
## 351                1               1               1
## 354                1               1               1
## 366                1               1               1
## 368                1               1               1
## 371                1               1               1
## 374                1               1               1
## 378                1               1               1
## 382                1               1               1
## 387                1               1               1
## 391                1               1               1
## 393                1               1               1
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#15个0,985个1
view(pred_class2_f)


#💙10_1_1 Calculate Accuracy of prediction
accuracy1_f <- mean(pred_class1_f == test_data_f$legacy_collision_severity)
accuracy1_f 
## [1] 0.00954043
print(paste("Accuracy:", accuracy1_f))
## [1] "Accuracy: 0.00954043048283886"
accuracy2_f <- mean(pred_class2_f == test_data_f$legacy_collision_severity)
accuracy2_f 
## [1] 0.009656777
print(paste("Accuracy:", accuracy2_f))
## [1] "Accuracy: 0.00965677719604421"
#💙10_1_2 AUC: compare predicted results with actual categories

#table(Predicted = pred_class1, Actual = test_data$legacy_collision_severity)
library(pROC)
#plot a ROC curve with True Positive Rate (TPR) as the y axis and False Positive Rate (FPR) as x axis.

#MNL best model on train data
roc_curve1_1_f <- roc(test_data_f$legacy_collision_severity==1, predictions1_f[, 1])     #原本没有  ==1
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve1_1_f)

roc_curve1_2_f <- roc(test_data_f$legacy_collision_severity==2, predictions1_f[, 2])  
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve1_2_f)

roc_curve1_3_f <- roc(test_data_f$legacy_collision_severity==3, predictions1_f[, 3])
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve1_3_f)

#P.S. The closer the curve is to the upper left corner, the better the model performance is.
auc(roc_curve1_1_f) ## Area under the curve: 0.9286
## Area under the curve: 0.6215
auc(roc_curve1_2_f)
## Area under the curve: 0.6089
auc(roc_curve1_3_f)
## Area under the curve: 0.6122
#P.S. The AUC value is between 0 and 1. The closer the value is to 1, the better the model performance. 0.5 means the model performance is equivalent to random guessing.
roc_curve2_1_f <- roc(test_data_f$legacy_collision_severity==1, predictions2_f[, 1])  #==1
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve2_1_f)

roc_curve2_2_f <- roc(test_data_f$legacy_collision_severity==2, predictions2_f[, 2])
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve2_2_f)

roc_curve2_3_f <- roc(test_data_f$legacy_collision_severity==3, predictions2_f[, 3])
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve2_3_f)

#P.S. The closer the curve is to the upper left corner, the better the model performance is.
auc(roc_curve2_1_f) ## Area under the curve: 0.9286
## Area under the curve: 0.6318
auc(roc_curve2_2_f)
## Area under the curve: 0.608
auc(roc_curve2_3_f)
## Area under the curve: 0.6122
####




####2: Repeat Predictions for FULL models

#💚10. 

#💙10_1_0 Preparitions: 
#💜10_1_0_1 Divide training set and test set
set.seed(456)
train_index_n <- sample(seq_len(nrow(data4)), size = 0.70 * nrow(data4))   #用70%训练集的数据,来预测30%测试集的结果的正确性
train_data_n <- data4[train_index_n, ]
test_data_n <- data4[-train_index_n, ]
library(fpp3)
view(train_data_n)
view(test_data_n)

#fit MNL and OL FULL models on train data (12, 13 predictors respectively)

library(nnet)
library(MASS)

#make predictions on newdataset
#决定了AUC
shorted_test_n <- multinom(legacy_collision_severity ~ police_force + number_of_vehicles + number_of_casualties + road_type + speed_limit + junction_detail + junction_control + second_road_class + second_road_number + pedestrian_crossing_human_control + pedestrian_crossing_physical_facilities + light_conditions + weather_conditions + road_surface_conditions + special_conditions_at_site + carriageway_hazards + did_police_officer_attend_scene_of_collision , data = train_data_n)
## # weights:  171 (112 variable)
## initial  value 7344.223150 
## iter  10 value 4514.451426
## iter  20 value 4123.097798
## iter  30 value 3970.773694
## iter  40 value 3925.373393
## iter  50 value 3914.033412
## iter  60 value 3909.774238
## iter  70 value 3908.104844
## iter  80 value 3907.702402
## iter  90 value 3907.465656
## iter 100 value 3907.450531
## final  value 3907.450531 
## stopped after 100 iterations
shorted_test2_n <- polr(legacy_collision_severity ~ police_force + number_of_vehicles + number_of_casualties + road_type + speed_limit + junction_detail + junction_control + second_road_class + pedestrian_crossing_human_control + pedestrian_crossing_physical_facilities + light_conditions + weather_conditions + road_surface_conditions + special_conditions_at_site + carriageway_hazards + did_police_officer_attend_scene_of_collision, data = train_data_n, Hess = TRUE)  
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
predictions1_n <- predict(shorted_test_n, newdata = test_data_n, type = "probs")   ##??   
predictions1_n 
##                 1            2         3
## 2    8.459972e-03 2.281924e-01 0.7633477
## 4    5.879358e-03 2.304752e-01 0.7636455
## 8    1.628364e-02 2.201180e-01 0.7635983
## 13   2.613387e-02 1.702157e-01 0.8036505
## 16   9.329920e-04 1.580143e-01 0.8410528
## 18   2.197534e-03 1.774972e-01 0.8203052
## 29   1.180487e-02 2.912248e-01 0.6969703
## 30   4.262910e-02 2.689576e-01 0.6884133
## 32   4.608157e-03 2.189125e-01 0.7764794
## 36   9.306927e-03 3.591301e-01 0.6315630
## 39   2.830591e-03 2.578914e-01 0.7392780
## 41   1.364188e-02 2.370729e-01 0.7492852
## 43   9.650298e-03 2.837600e-01 0.7065897
## 48   6.621240e-03 1.740812e-01 0.8192975
## 49   1.156374e-02 3.093098e-01 0.6791264
## 55   6.714372e-11 2.186975e-01 0.7813025
## 58   7.854927e-03 2.528121e-01 0.7393329
## 59   5.774440e-11 2.918423e-01 0.7081577
## 60   1.222924e-02 2.927713e-01 0.6949994
## 62   8.865836e-03 1.287446e-01 0.8623896
## 63   9.440908e-12 2.345304e-01 0.7654696
## 71   1.581798e-10 2.618246e-01 0.7381754
## 73   5.328431e-11 1.007655e-01 0.8992345
## 80   2.465713e-03 1.252306e-01 0.8723037
## 84   1.949953e-09 2.595027e-01 0.7404973
## 86   4.675540e-03 2.004872e-01 0.7948372
## 87   2.999566e-02 2.057788e-01 0.7642255
## 98   3.841243e-02 2.297722e-01 0.7318153
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## 1127 1.232325e-15 2.821236e-01 0.7178764
## 1131 9.306927e-03 3.591301e-01 0.6315630
## 1132 1.524864e-09 2.491344e-01 0.7508656
## 1143 2.931976e-02 2.961195e-01 0.6745607
## 1147 1.792629e-02 1.963067e-01 0.7857670
## 1150 4.156513e-03 3.089195e-01 0.6869240
## 1151 7.418473e-03 2.101328e-01 0.7824487
## 1160 4.441934e-03 2.667061e-01 0.7288520
## 1162 4.172143e-03 2.437783e-01 0.7520496
## 1168 2.503716e-04 2.619560e-02 0.9735540
## 1169 8.756647e-11 1.724723e-01 0.8275277
## 1170 1.972164e-02 3.070470e-01 0.6732314
## 1171 5.278760e-03 2.592714e-01 0.7354498
## 1173 6.711884e-03 2.813077e-01 0.7119804
## 1177 5.785034e-03 2.724716e-01 0.7217434
## 1178 1.100353e-03 1.206467e-01 0.8782529
## 1180 2.995717e-09 3.251291e-01 0.6748709
## 1181 2.752830e-03 2.350602e-01 0.7621869
## 1182 2.259724e-02 5.795931e-02 0.9194435
## 1196 1.665595e-02 3.538484e-01 0.6294957
## 1198 2.590187e-03 1.413719e-01 0.8560379
## 1199 4.760485e-03 1.688648e-01 0.8263747
## 1205 7.268425e-15 1.076705e-01 0.8923295
## 1206 1.991011e-02 3.391838e-01 0.6409061
## 1216 2.173010e-03 2.870816e-01 0.7107453
## 1218 8.052189e-10 3.339959e-01 0.6660041
## 1220 7.692128e-03 1.682472e-01 0.8240606
## 1226 3.408058e-03 2.529116e-01 0.7436803
## 1229 2.259715e-03 2.409052e-01 0.7568351
## 1236 4.196906e-03 6.963257e-02 0.9261705
## 1237 2.366500e-02 2.184115e-01 0.7579235
## 1238 2.789920e-03 1.985261e-01 0.7986840
## 1242 6.268902e-04 6.258637e-02 0.9367867
## 1243 3.289711e-03 2.948511e-01 0.7018591
## 1245 1.368705e-03 2.046161e-01 0.7940152
## 1251 2.192772e-03 3.183896e-01 0.6794176
## 1253 3.897409e-03 3.535238e-01 0.6425788
## 1255 3.557125e-03 2.576212e-01 0.7388217
## 1256 9.862942e-04 2.227012e-01 0.7763125
## 1258 2.679204e-03 2.182343e-01 0.7790865
## 1259 3.331414e-03 2.676810e-01 0.7289876
## 1261 5.770071e-03 3.423686e-01 0.6518613
## 1264 5.659799e-03 2.249333e-01 0.7694069
## 1265 8.179222e-03 1.104168e-01 0.8814040
## 1267 2.419135e-04 2.843530e-02 0.9713228
## 1270 8.521694e-03 2.422742e-01 0.7492041
## 1271 5.233355e-03 2.287856e-01 0.7659811
## 1275 4.085646e-03 2.355185e-01 0.7603959
## 1286 5.368323e-03 3.017816e-01 0.6928501
## 1298 7.418473e-03 2.101328e-01 0.7824487
## 1299 9.306927e-03 3.591301e-01 0.6315630
## 1305 1.222924e-02 2.927713e-01 0.6949994
## 1307 6.063752e-03 2.456691e-01 0.7482671
## 1312 6.203683e-03 2.245432e-01 0.7692531
## 1318 3.005998e-02 3.082896e-01 0.6616505
## 1322 6.421257e-02 3.578110e-01 0.5779764
## 1325 9.036941e-03 2.911251e-01 0.6998380
## 1327 5.785034e-03 2.724716e-01 0.7217434
## 1335 7.874288e-03 2.654442e-01 0.7266815
## 1340 6.507203e-04 1.985068e-01 0.8008425
## 1343 1.101273e-09 2.603399e-01 0.7396601
## 1347 4.244350e-03 2.051213e-01 0.7906344
## 1348 1.276229e-02 2.797843e-01 0.7074534
## 1349 2.378717e-02 3.610894e-01 0.6151234
## 1353 3.447740e-03 1.413275e-01 0.8552248
## 1356 5.807308e-12 7.151197e-02 0.9284880
## 1370 1.400471e-02 2.874712e-01 0.6985241
## 1372 1.657913e-11 1.990595e-01 0.8009405
## 1376 4.727062e-03 2.600026e-01 0.7352703
## 1380 8.516193e-03 3.053783e-01 0.6861055
## 1381 2.857914e-10 2.318697e-01 0.7681303
## 1383 1.054838e-02 2.847045e-01 0.7047472
## 1386 7.334040e-03 2.432899e-01 0.7493760
## 1389 1.209901e-10 1.451591e-01 0.8548409
## 1395 3.557125e-03 2.576212e-01 0.7388217
## 1399 1.243173e-02 2.790458e-01 0.7085225
## 1405 1.118377e-02 1.793050e-01 0.8095113
## 1412 3.254148e-03 1.091795e-01 0.8875664
## 1413 3.621820e-03 2.870179e-01 0.7093602
## 1419 1.893490e-03 2.576700e-01 0.7404365
## 1425 7.622215e-03 2.506719e-01 0.7417059
## 1426 1.322599e-02 3.693598e-01 0.6174142
## 1427 5.785034e-03 2.724716e-01 0.7217434
## 1430 9.357804e-03 2.391290e-01 0.7515132
## 1439 5.534726e-03 2.577404e-01 0.7367248
## 1451 3.853977e-03 2.381617e-01 0.7579843
## 1453 2.992996e-03 1.597053e-01 0.8373017
## 1454 7.015319e-02 4.333100e-01 0.4965368
## 1465 1.561167e-02 2.201749e-01 0.7642134
## 1471 1.198685e-03 1.556669e-01 0.8431344
## 1472 1.681528e-02 3.002251e-01 0.6829596
## 1475 1.986612e-03 1.004535e-01 0.8975599
## 1477 2.792695e-03 2.218416e-01 0.7753657
## 1478 5.545250e-03 2.676182e-01 0.7268366
## 1479 4.383126e-03 3.348583e-01 0.6607586
## 1480 2.121959e-03 1.875812e-01 0.8102968
## 1483 4.542399e-03 1.978481e-01 0.7976095
## 1491 9.138288e-03 2.517287e-01 0.7391330
## 1498 1.286412e-03 1.982725e-01 0.8004411
## 1501 9.306927e-03 3.591301e-01 0.6315630
## 1505 5.044626e-03 2.319464e-01 0.7630090
## 1506 5.785034e-03 2.724716e-01 0.7217434
## 1507 3.674322e-03 2.799377e-01 0.7163880
## 1509 8.816915e-11 2.517310e-01 0.7482690
## 1510 3.557125e-03 2.576212e-01 0.7388217
## 1511 5.146412e-03 1.681963e-01 0.8266572
## 1519 1.727390e-03 2.589171e-01 0.7393556
## 1525 2.184292e-03 2.112821e-01 0.7865336
## 1526 3.574478e-03 1.603261e-01 0.8360994
## 1534 3.062536e-03 2.012732e-01 0.7956643
## 1535 7.668849e-03 2.646923e-01 0.7276388
## 1537 4.446415e-03 2.023332e-01 0.7932203
## 1538 2.183354e-03 3.178916e-01 0.6799251
## 1540 1.972164e-02 3.070470e-01 0.6732314
## 1542 3.093783e-02 3.946223e-01 0.5744398
## 1543 3.680878e-03 2.428341e-01 0.7534851
## 1545 1.889095e-03 2.434473e-01 0.7546636
## 1559 5.785034e-03 2.724716e-01 0.7217434
## 1560 1.156748e-03 2.065764e-01 0.7922669
## 1561 3.568903e-03 2.245016e-01 0.7719295
## 1562 1.344860e-02 2.818875e-01 0.7046639
## 1566 8.270450e-03 2.819164e-01 0.7098132
## 1568 8.890722e-08 7.589552e-02 0.9241044
## 1573 4.727062e-03 2.600026e-01 0.7352703
## 1582 1.758342e-03 2.046354e-01 0.7936062
## 1593 3.557125e-03 2.576212e-01 0.7388217
## 1603 3.674322e-03 2.799377e-01 0.7163880
## 1604 3.114664e-03 2.614374e-01 0.7354479
## 1610 5.001205e-02 2.193970e-01 0.7305909
## 1614 1.329373e-03 1.594846e-01 0.8391861
## 1622 1.587961e-02 2.841351e-01 0.6999853
## 1623 3.557125e-03 2.576212e-01 0.7388217
## 1625 3.437999e-03 1.488313e-01 0.8477307
## 1627 2.604948e-02 3.080099e-01 0.6659406
## 1633 5.785034e-03 2.724716e-01 0.7217434
## 1635 1.236311e-02 3.495982e-01 0.6380387
## 1637 2.053876e-12 1.251994e-01 0.8748006
## 1645 5.983906e-09 2.477285e-01 0.7522715
## 1647 6.861587e-10 1.584763e-01 0.8415237
## 1648 3.837529e-03 1.231499e-01 0.8730126
## 1652 1.514417e-03 2.393210e-01 0.7591646
## 1653 2.336324e-03 1.916888e-01 0.8059749
## 1659 9.626201e-03 2.102374e-01 0.7801364
## 1664 2.331098e-02 1.618865e-01 0.8148025
## 1665 5.615342e-09 3.056057e-01 0.6943943
## 1670 1.218682e-02 2.507537e-01 0.7370595
## 1672 2.255203e-08 4.051557e-01 0.5948443
## 1673 1.430703e-02 3.005292e-01 0.6851638
## 1688 5.785034e-03 2.724716e-01 0.7217434
## 1691 9.983470e-03 3.295743e-01 0.6604422
## 1695 1.587961e-02 2.841351e-01 0.6999853
## 1700 8.510337e-03 2.731089e-01 0.7183807
## 1702 2.781954e-03 2.568157e-01 0.7404024
## 1703 3.978011e-03 2.853631e-01 0.7106589
## 1709 5.342324e-03 3.012200e-01 0.6934376
## 1725 9.386527e-03 2.259149e-01 0.7646986
## 1735 5.250170e-03 2.153948e-01 0.7793551
## 1738 1.940803e-02 3.806630e-01 0.5999290
## 1743 4.181998e-03 2.107585e-01 0.7850595
## 1748 1.351328e-03 3.231025e-01 0.6755462
## 1750 1.662863e-02 1.733469e-01 0.8100245
## 1755 2.344894e-03 2.170813e-01 0.7805738
## 1757 1.539952e-02 2.209901e-01 0.7636104
## 1758 1.219266e-03 1.866506e-01 0.8121301
## 1760 5.899561e-03 1.981262e-01 0.7959742
## 1761 3.981710e-03 2.402612e-01 0.7557571
## 1765 4.507624e-03 3.089205e-01 0.6865719
## 1769 4.999854e-02 2.940344e-01 0.6559671
## 1771 3.557125e-03 2.576212e-01 0.7388217
## 1772 1.351536e-03 2.379705e-01 0.7606780
## 1777 9.331019e-04 2.813830e-01 0.7176839
## 1781 5.785034e-03 2.724716e-01 0.7217434
## 1787 3.266887e-03 1.919800e-01 0.8047531
## 1789 4.727062e-03 2.600026e-01 0.7352703
## 1790 1.222924e-02 2.927713e-01 0.6949994
## 1798 5.044626e-03 2.319464e-01 0.7630090
## 1803 3.498604e-08 1.419729e-01 0.8580271
## 1804 2.711167e-02 1.833706e-01 0.7895177
## 1807 4.174610e-03 3.341981e-01 0.6616273
## 1808 6.868021e-02 2.314121e-01 0.6999077
## 1809 9.769372e-03 3.001390e-01 0.6900916
## 1811 1.790616e-07 1.661709e-01 0.8338290
## 1820 5.233355e-03 2.287856e-01 0.7659811
## 1821 7.418473e-03 2.101328e-01 0.7824487
## 1828 8.521694e-03 2.422742e-01 0.7492041
## 1829 5.785034e-03 2.724716e-01 0.7217434
## 1834 1.587961e-02 2.841351e-01 0.6999853
## 1837 3.241894e-03 2.231117e-01 0.7736464
## 1838 3.686389e-03 3.398602e-01 0.6564534
## 1845 9.334296e-12 1.243459e-01 0.8756541
## 1848 6.360771e-03 2.517473e-01 0.7418919
## 1849 4.398722e-03 3.392603e-01 0.6563410
## 1855 5.640191e-03 1.492964e-01 0.8450634
## 1862 5.785034e-03 2.724716e-01 0.7217434
## 1865 9.801362e-03 4.704000e-01 0.5197986
## 1869 7.702841e-11 3.238097e-01 0.6761903
## 1870 1.550798e-03 2.999650e-01 0.6984842
## 1871 2.545794e-09 2.579895e-01 0.7420105
## 1875 1.108587e-02 2.478683e-01 0.7410458
## 1876 3.557125e-03 2.576212e-01 0.7388217
## 1878 5.172751e-11 2.848618e-01 0.7151382
## 1881 1.605916e-02 1.901681e-01 0.7937728
## 1883 5.191163e-02 8.861188e-02 0.8594765
## 1884 2.595252e-03 2.686593e-01 0.7287454
## 1885 1.853697e-02 1.526272e-01 0.8288359
## 1887 8.213288e-03 2.455887e-01 0.7461980
## 1890 1.072028e-03 2.156349e-01 0.7832931
## 1891 5.525667e-03 3.071308e-01 0.6873435
## 1893 2.897185e-03 1.575715e-01 0.8395313
## 1894 7.564754e-03 2.699428e-01 0.7224925
## 1895 5.614320e-08 3.832702e-01 0.6167298
## 1896 2.264332e-03 1.979215e-01 0.7998142
## 1898 1.332225e-02 1.669554e-01 0.8197223
## 1900 3.557125e-03 2.576212e-01 0.7388217
## 1901 1.208869e-07 1.286768e-01 0.8713231
## 1912 5.311602e-03 1.447395e-01 0.8499489
## 1914 5.785034e-03 2.724716e-01 0.7217434
## 1915 1.236311e-02 3.495982e-01 0.6380387
## 1917 8.207340e-03 2.525845e-01 0.7392081
## 1918 9.306927e-03 3.591301e-01 0.6315630
## 1919 5.785034e-03 2.724716e-01 0.7217434
## 1923 1.616015e-09 1.390064e-01 0.8609936
## 1924 1.448121e-03 2.193314e-01 0.7792205
## 1926 1.180296e-03 3.852562e-01 0.6135635
## 1929 6.218598e-03 2.665878e-01 0.7271936
## 1931 2.344894e-03 2.170813e-01 0.7805738
## 1933 1.731879e-03 3.270283e-01 0.6712398
## 1936 2.583198e-03 2.283194e-01 0.7690974
## 1937 1.826303e-02 2.192338e-01 0.7625031
## 1939 1.222924e-02 2.927713e-01 0.6949994
## 1940 2.040069e-02 2.264716e-01 0.7531278
## 1942 6.737641e-03 2.297025e-01 0.7635598
## 1948 3.868505e-03 2.694710e-01 0.7266605
## 1956 2.491624e-03 2.861817e-01 0.7113267
## 1957 2.103245e-03 2.463485e-01 0.7515483
## 1958 1.127377e-02 2.145176e-01 0.7742086
## 1961 1.565352e-02 2.223308e-01 0.7620157
## 1968 6.913005e-03 2.993256e-01 0.6937614
## 1969 5.044626e-03 2.319464e-01 0.7630090
## 1971 2.799279e-03 7.104530e-02 0.9261554
## 1972 9.280517e-03 2.201953e-01 0.7705242
## 1975 2.853195e-03 2.042797e-01 0.7928671
## 1979 2.344894e-03 2.170813e-01 0.7805738
## 1981 1.347671e-03 1.868038e-01 0.8118486
## 1985 4.356324e-03 1.678417e-01 0.8278020
## 1986 8.183246e-03 2.544643e-01 0.7373524
## 1988 6.771272e-03 1.749899e-01 0.8182389
## 1989 1.781057e-09 2.050363e-01 0.7949637
## 1990 4.023560e-12 1.156721e-01 0.8843279
## 1991 4.542399e-03 1.978481e-01 0.7976095
## 1994 2.220147e-03 2.640026e-01 0.7337773
## 1995 1.294744e-03 7.686635e-02 0.9218389
## 2000 9.626201e-03 2.102374e-01 0.7801364
## 2001 1.350588e-10 3.081718e-01 0.6918282
## 2002 1.226886e-02 2.458486e-01 0.7418825
## 2007 1.002739e-02 3.521809e-01 0.6377917
## 2014 3.389015e-03 2.981149e-01 0.6984961
## 2016 8.594842e-03 1.742313e-01 0.8171739
## 2024 3.981951e-03 4.296365e-01 0.5663815
## 2026 1.153197e-02 2.563115e-01 0.7321565
## 2027 7.164263e-03 1.661778e-01 0.8266580
## 2028 3.594731e-03 2.700695e-01 0.7263357
## 2029 4.174120e-03 2.652500e-01 0.7305759
## 2030 4.202322e-03 2.984497e-01 0.6973480
## 2032 5.822443e-03 2.590808e-01 0.7350968
## 2039 1.400471e-02 2.874712e-01 0.6985241
## 2045 2.902457e-02 2.727680e-01 0.6982074
## 2047 9.306927e-03 3.591301e-01 0.6315630
## 2049 9.306927e-03 3.591301e-01 0.6315630
## 2050 3.557125e-03 2.576212e-01 0.7388217
## 2051 1.242286e-02 1.512755e-01 0.8363017
## 2055 1.082200e-02 2.166119e-01 0.7725661
## 2062 7.191334e-11 1.641229e-01 0.8358771
## 2064 1.062626e-03 2.000489e-01 0.7988885
## 2065 5.425510e-11 2.893605e-01 0.7106395
## 2068 1.961614e-03 3.582597e-01 0.6397787
## 2070 3.557125e-03 2.576212e-01 0.7388217
## 2079 3.309690e-02 2.212390e-01 0.7456641
## 2089 3.557125e-03 2.576212e-01 0.7388217
## 2091 4.654839e-04 1.047001e-01 0.8948344
## 2096 5.105037e-03 2.957026e-01 0.6991924
## 2098 8.589087e-03 3.076279e-01 0.6837831
## 2106 9.405944e-03 2.179539e-01 0.7726401
## 2107 3.319173e-03 2.628870e-01 0.7337938
## 2111 9.229580e-03 1.845713e-01 0.8061991
## 2113 3.330738e-03 2.050321e-01 0.7916371
## 2116 5.945760e-03 1.930428e-01 0.8010114
## 2125 2.006894e-02 1.914790e-01 0.7884521
## 2127 2.702918e-03 2.868268e-01 0.7104703
## 2130 3.531767e-02 2.412661e-01 0.7234162
## 2133 1.236311e-02 3.495982e-01 0.6380387
## 2134 8.663380e-03 3.655859e-01 0.6257507
## 2136 3.568903e-03 2.245016e-01 0.7719295
## 2137 6.367763e-03 4.081664e-01 0.5854658
## 2142 3.557125e-03 2.576212e-01 0.7388217
## 2143 5.690016e-03 2.009768e-01 0.7933332
## 2148 1.254112e-12 9.077267e-02 0.9092273
## 2153 4.882324e-03 2.622191e-01 0.7328986
## 2155 9.813558e-03 2.700094e-01 0.7201770
## 2156 1.504428e-17 9.527422e-02 0.9047258
## 2160 7.226674e-03 2.063576e-01 0.7864158
## 2163 1.383158e-02 2.557323e-01 0.7304361
## 2164 4.727062e-03 2.600026e-01 0.7352703
## 2174 4.554001e-03 2.634449e-01 0.7320011
## 2182 2.561157e-02 3.815042e-01 0.5928842
## 2198 1.940803e-02 3.806630e-01 0.5999290
## 2205 5.178338e-12 1.802497e-01 0.8197503
## 2207 8.362802e-02 2.735936e-01 0.6427784
## 2210 1.301180e-02 2.718904e-01 0.7150978
## 2212 1.232674e-02 3.612415e-01 0.6264318
## 2214 1.743004e-03 1.918931e-01 0.8063639
## 2218 6.385471e-03 4.480546e-01 0.5455599
## 2219 4.875417e-03 1.240017e-01 0.8711229
## 2221 3.510150e-03 2.816064e-01 0.7148835
## 2223 8.821462e-10 1.627401e-01 0.8372599
## 2231 6.323647e-10 1.634355e-01 0.8365645
## 2233 2.121959e-03 1.875812e-01 0.8102968
## 2239 7.600544e-03 1.506413e-01 0.8417581
## 2246 1.509910e-02 2.227530e-01 0.7621479
## 2248 1.360614e-03 1.465771e-01 0.8520623
## 2250 4.877221e-03 1.763972e-01 0.8187256
## 2252 3.426912e-03 2.610331e-01 0.7355399
## 2255 9.813558e-03 2.700094e-01 0.7201770
## 2258 4.136114e-03 3.046588e-01 0.6912051
## 2259 1.208253e-02 2.296093e-01 0.7583082
## 2261 1.763741e-02 2.023170e-01 0.7800456
## 2264 4.437948e-03 3.016777e-01 0.6938843
## 2266 2.945901e-02 3.270078e-01 0.6435332
## 2269 3.266887e-03 1.919800e-01 0.8047531
## 2275 4.854300e-03 2.326235e-01 0.7625222
## 2280 3.084548e-03 1.991748e-01 0.7977407
## 2286 1.711452e-09 1.954792e-01 0.8045208
## 2288 7.143817e-04 1.946274e-01 0.8046582
## 2293 9.111122e-04 2.021526e-01 0.7969363
## 2297 2.471504e-24 3.596557e-01 0.6403443
## 2303 2.888322e-02 3.419564e-01 0.6291604
## 2305 9.897232e-03 1.874563e-01 0.8026465
## 2308 6.926427e-10 4.127303e-01 0.5872697
## 2309 2.822039e-11 1.551715e-01 0.8448285
## 2312 1.499363e-03 2.319912e-01 0.7665094
## 2313 2.029820e-02 3.646231e-01 0.6150787
## 2319 5.068383e-04 1.147973e-01 0.8846959
## 2323 6.116444e-04 1.868089e-01 0.8125795
## 2328 9.494643e-04 1.631520e-01 0.8358986
## 2332 2.015746e-03 1.801683e-01 0.8178160
## 2333 8.489532e-03 2.413942e-01 0.7501163
## 2334 2.340556e-02 8.118474e-02 0.8954097
## 2337 6.020876e-03 3.271899e-01 0.6667892
## 2339 1.423050e-03 1.167128e-01 0.8818642
## 2343 7.288818e-11 2.306269e-01 0.7693731
## 2344 9.162328e-03 2.484534e-01 0.7423842
## 2346 2.934081e-02 3.017597e-01 0.6688995
## 2352 2.666173e-02 2.831133e-01 0.6902250
## 2355 8.618477e-03 2.544042e-01 0.7369774
## 2359 3.084731e-02 3.935237e-01 0.5756290
## 2368 3.329151e-04 1.178488e-01 0.8818183
## 2371 2.836356e-02 3.105868e-01 0.6610497
## 2374 4.067722e-04 1.450367e-01 0.8545565
## 2375 5.039124e-04 1.454818e-01 0.8540143
## 2376 3.230794e-02 4.689332e-01 0.4987588
## 2381 1.146051e-03 1.389381e-01 0.8599158
## 2382 1.214154e-02 2.498577e-01 0.7380007
## 2383 3.551585e-10 1.046645e-01 0.8953355
## 2395 1.466818e-02 4.512335e-01 0.5340983
## 2396 9.219648e-03 2.408335e-01 0.7499469
## 2398 8.465867e-04 1.238906e-01 0.8752628
## 2401 7.789155e-04 1.434152e-01 0.8558059
## 2405 4.851507e-03 2.246963e-01 0.7704522
## 2411 3.089352e-03 2.563387e-01 0.7405720
## 2412 6.633697e-04 1.575138e-01 0.8418229
## 2418 4.108703e-14 4.472975e-01 0.5527025
## 2427 4.971316e-10 2.404854e-01 0.7595146
## 2430 4.854888e-09 1.493011e-01 0.8506989
## 2434 7.977664e-03 2.613500e-01 0.7306724
## 2435 8.668776e-04 1.555458e-01 0.8435873
## 2438 9.233734e-04 1.558861e-01 0.8431905
## 2439 4.559814e-02 2.610179e-01 0.6933840
## 2446 1.002381e-03 1.990967e-01 0.7999009
## 2454 1.756900e-03 7.446051e-02 0.9237826
## 2456 1.575081e-02 2.207909e-01 0.7634583
## 2458 1.609436e-03 1.181157e-01 0.8802749
## 2459 4.710340e-02 2.548530e-01 0.6980436
## 2462 1.070861e-02 2.130087e-01 0.7762827
## 2466 1.821009e-02 2.467651e-01 0.7350249
## 2472 4.709537e-03 2.590756e-01 0.7362149
## 2475 1.005623e-02 2.442303e-01 0.7457135
## 2476 1.867300e-03 1.417760e-01 0.8563567
## 2478 3.548050e-02 3.919630e-01 0.5725565
## 2481 1.998942e-02 1.907475e-01 0.7892631
## 2484 1.093054e-02 2.830080e-01 0.7060615
## 2491 2.034989e-03 1.991200e-01 0.7988450
## 2495 9.588433e-03 2.094423e-01 0.7809693
## 2496 7.634017e-03 3.163274e-01 0.6760386
## 2498 6.355056e-03 2.771430e-01 0.7165019
## 2499 1.002381e-03 1.990967e-01 0.7999009
## 2500 7.197681e-02 3.766074e-01 0.5514158
## 2501 8.465867e-04 1.238906e-01 0.8752628
## 2504 8.303289e-03 2.458698e-01 0.7458269
## 2505 9.497189e-03 1.918522e-01 0.7986506
## 2507 3.459967e-03 1.989385e-01 0.7976016
## 2510 5.763966e-03 2.715179e-01 0.7227181
## 2511 8.433621e-04 1.479759e-01 0.8511808
## 2516 3.805513e-03 2.387755e-01 0.7574190
## 2518 7.162047e-03 3.537580e-01 0.6390800
## 2519 2.060421e-02 2.119373e-01 0.7674585
## 2522 6.740746e-03 2.683689e-01 0.7248904
## 2524 1.890465e-02 2.754254e-01 0.7056699
## 2526 2.377149e-03 2.593005e-01 0.7383224
## 2530 1.949998e-02 2.119455e-01 0.7685545
## 2537 9.297565e-03 2.738738e-01 0.7168286
## 2546 3.486363e-04 1.128868e-01 0.8867646
## 2553 3.929633e-04 1.221008e-01 0.8775062
## 2564 1.257351e-02 2.997064e-01 0.6877201
## 2566 4.410583e-09 2.991890e-01 0.7008110
## 2567 6.281561e-12 1.461131e-01 0.8538869
## 2568 1.819956e-02 2.684885e-01 0.7133119
## 2573 3.152661e-04 1.426738e-01 0.8570109
## 2576 3.575264e-02 2.796078e-01 0.6846396
## 2587 3.550775e-04 1.323706e-01 0.8672744
## 2588 3.451574e-09 2.856283e-01 0.7143716
## 2589 8.465867e-04 1.238906e-01 0.8752628
## 2590 2.324442e-02 2.510912e-01 0.7256643
## 2591 4.187512e-03 2.974403e-01 0.6983722
## 2594 4.819057e-03 2.773366e-01 0.7178443
## 2595 1.025700e-02 3.811570e-01 0.6085860
## 2597 1.228403e-02 1.802465e-01 0.8074695
## 2599 8.916237e-04 1.643789e-01 0.8347295
## 2602 3.409245e-05 9.696087e-02 0.9030050
## 2604 1.441524e-03 2.072187e-01 0.7913398
## 2606 2.506827e-04 6.876522e-02 0.9309841
## 2608 2.812546e-03 1.888503e-01 0.8083371
## 2609 1.382075e-02 3.219622e-01 0.6642171
## 2613 1.382075e-02 3.219622e-01 0.6642171
## 2617 5.213177e-03 2.279359e-01 0.7668509
## 2619 7.199148e-03 2.481068e-01 0.7446940
## 2631 1.083306e-08 3.405574e-01 0.6594426
## 2634 5.569646e-03 2.488520e-01 0.7455783
## 2635 1.093054e-02 2.830080e-01 0.7060615
## 2636 5.763966e-03 2.715179e-01 0.7227181
## 2637 7.652603e-03 2.737727e-01 0.7185747
## 2641 5.845998e-04 1.417293e-01 0.8576861
## 2642 7.789155e-04 1.434152e-01 0.8558059
## 2644 4.389974e-10 2.456363e-01 0.7543637
## 2649 1.127838e-04 1.028400e-01 0.8970473
## 2653 3.074407e-03 2.174382e-01 0.7794873
## 2654 1.228754e-02 3.601439e-01 0.6275685
## 2660 5.763966e-03 2.715179e-01 0.7227181
## 2662 3.070224e-05 9.266049e-02 0.9073088
## 2663 1.070554e-02 2.173426e-01 0.7719518
## 2664 1.463623e-03 1.754795e-01 0.8230569
## 2669 5.239866e-03 2.147825e-01 0.7799777
## 2670 1.186157e-02 3.268612e-01 0.6612772
## 2672 3.686216e-03 2.445183e-01 0.7517955
## 2675 2.433498e-02 8.092692e-02 0.8947381
## 2676 1.588270e-02 2.867470e-01 0.6973703
## 2680 4.912625e-04 1.134867e-01 0.8860221
## 2682 4.483335e-03 2.342035e-01 0.7613131
## 2683 1.091754e-02 2.826848e-01 0.7063977
## 2684 1.976285e-02 3.635013e-01 0.6167359
## 2685 1.115558e-02 2.324259e-01 0.7564185
## 2688 3.959816e-03 2.390772e-01 0.7569630
## 2698 7.074887e-02 2.511036e-01 0.6781475
## 2699 1.230996e-03 1.536326e-01 0.8451364
## 2704 3.409972e-03 2.597921e-01 0.7367979
## 2709 3.686216e-03 2.445183e-01 0.7517955
## 2710 1.322665e-02 2.702349e-01 0.7165384
## 2713 9.267162e-03 3.576635e-01 0.6330694
## 2717 8.421609e-04 1.477721e-01 0.8513857
## 2719 1.135692e-02 2.016956e-01 0.7869475
## 2730 5.093670e-03 2.319390e-01 0.7629673
## 2735 3.003634e-05 7.129140e-02 0.9286786
## 2740 6.123291e-03 2.121342e-01 0.7817425
## 2748 3.417717e-03 2.485108e-01 0.7480715
## 2749 4.628530e-03 1.497468e-01 0.8456246
## 2751 1.475879e-02 3.302865e-01 0.6549547
## 2754 9.267162e-03 3.576635e-01 0.6330694
## 2762 5.299267e-04 1.062939e-01 0.8931762
## 2768 4.595761e-03 2.006914e-01 0.7947128
## 2769 5.756954e-03 2.712005e-01 0.7230426
## 2777 5.299267e-04 1.062939e-01 0.8931762
## 2784 9.267162e-03 3.576635e-01 0.6330694
## 2786 1.507348e-03 2.086509e-01 0.7898417
## 2788 3.232492e-03 1.926841e-01 0.8040834
## 2792 5.756954e-03 2.712005e-01 0.7230426
## 2799 9.457268e-03 2.107148e-01 0.7798280
## 2801 3.119963e-02 2.557614e-01 0.7130390
## 2806 5.837610e-04 1.415327e-01 0.8578836
## 2813 1.405741e-04 9.079556e-02 0.9090639
## 2814 4.134148e-04 1.018497e-01 0.8977369
## 2815 6.732523e-03 2.680542e-01 0.7252133
## 2819 5.056840e-04 1.221665e-01 0.8773278
## 2824 7.141027e-03 2.083883e-01 0.7844707
## 2825 1.332515e-03 2.010146e-01 0.7976528
## 2828 1.598602e-03 1.869780e-01 0.8114234
## 2831 3.550426e-03 2.233817e-01 0.7730678
## 2835 5.329464e-04 1.622012e-01 0.8372658
## 2848 5.287835e-03 2.360026e-01 0.7587096
## 2852 2.593249e-02 3.066848e-01 0.6673827
## 2853 6.032310e-03 2.185009e-01 0.7754668
## 2857 9.071429e-04 1.707139e-01 0.8283790
## 2861 3.409972e-03 2.597921e-01 0.7367979
## 2864 3.043684e-02 2.786215e-01 0.6909417
## 2868 3.409972e-03 2.597921e-01 0.7367979
## 2869 1.001037e-03 1.988391e-01 0.8001599
## 2880 1.191557e-02 2.889465e-01 0.6991379
## 2888 8.038400e-03 2.129316e-01 0.7790300
## 2889 5.837610e-04 1.415327e-01 0.8578836
## 2890 1.864624e-03 1.415796e-01 0.8565558
## 2892 2.427230e-03 2.937578e-01 0.7038150
## 2894 3.545625e-04 1.321849e-01 0.8674606
## 2900 5.837610e-04 1.415327e-01 0.8578836
## 2909 3.423075e-04 1.342194e-01 0.8654382
## 2916 5.756954e-03 2.712005e-01 0.7230426
## 2920 6.082806e-02 2.544783e-01 0.6846936
## 2927 2.590329e-02 3.063540e-01 0.6677427
## 2930 2.274261e-02 1.861520e-01 0.7911054
## 2932 5.124604e-10 2.279436e-01 0.7720564
## 2939 1.816992e-09 1.497819e-01 0.8502181
## 2942 2.537719e-02 2.932887e-01 0.6813341
## 2947 1.887005e-02 2.632291e-01 0.7179008
## 2948 1.510150e-02 2.008056e-01 0.7840929
## 2952 5.738316e-03 3.405651e-01 0.6536966
## 2956 5.749948e-03 2.708833e-01 0.7233668
## 2963 9.989451e-03 1.658948e-01 0.8241158
## 2965 1.554608e-02 2.913365e-01 0.6931174
## 2970 2.751033e-03 1.674513e-01 0.8297977
## 2972 5.713465e-03 3.089452e-01 0.6853413
## 2975 2.025591e-02 3.638980e-01 0.6158461
## 2976 8.859424e-02 1.886951e-01 0.7227107
## 2980 7.306919e-02 1.853167e-01 0.7416141
## 2984 9.305731e-03 3.172707e-01 0.6734236
## 2991 7.634095e-03 2.731365e-01 0.7192294
## 2997 1.184832e-02 3.265116e-01 0.6616400
## 3002 3.451819e-02 3.273499e-01 0.6381319
## 3008 9.288891e-03 3.236872e-01 0.6670239
## 3010 5.275842e-03 2.532905e-01 0.7414336
## 3013 2.929195e-02 1.705250e-01 0.8001830
## 3015 5.749948e-03 2.708833e-01 0.7233668
## 3021 2.872969e-02 3.402194e-01 0.6310509
## 3023 1.872102e-09 1.767672e-01 0.8232328
## 3024 1.516527e-02 3.010658e-01 0.6837689
## 3026 9.228269e-04 1.516573e-01 0.8474199
## 3032 5.738316e-03 3.405651e-01 0.6536966
## 3038 6.168003e-10 2.583428e-01 0.7416572
## 3041 9.348896e-04 1.051096e-01 0.8939555
## 3046 8.468138e-03 2.408087e-01 0.7507232
## 3047 5.324503e-12 1.162797e-01 0.8837203
## 3055 3.367964e-03 2.316735e-01 0.7649585
## 3062 2.227184e-02 1.929703e-01 0.7847579
## 3063 5.565801e-07 4.972711e-01 0.5027283
## 3072 1.704745e-02 1.911362e-01 0.7918164
## 3074 1.056731e-02 2.235333e-01 0.7658994
## 3084 1.821229e-03 1.614440e-01 0.8367348
## 3091 1.226144e-02 3.594130e-01 0.6283256
## 3098 4.019340e-09 1.697413e-01 0.8302587
## 3099 5.281094e-03 2.357130e-01 0.7590059
## 3104 7.114784e-03 1.650692e-01 0.8278160
## 3109 2.318771e-02 2.505024e-01 0.7263099
## 3110 1.627269e-02 3.495487e-01 0.6341786
## 3117 1.614194e-03 1.885819e-01 0.8098039
## 3118 4.539588e-02 4.667367e-01 0.4878674
## 3120 2.982601e-03 2.518952e-01 0.7451222
## 3129 7.435382e-03 2.561120e-01 0.7364526
## 3133 1.958745e-02 3.050445e-01 0.6753680
## 3140 1.101910e-06 1.238148e-07 0.9999988
## 3141 2.651213e-04 1.044535e-01 0.8952814
## 3143 1.267122e-02 2.778670e-01 0.7094618
## 3145 1.456432e-02 2.297748e-01 0.7556609
## 3148 2.834679e-02 4.096926e-01 0.5619606
## 3151 4.015415e-03 2.685159e-01 0.7274687
## 3152 5.742947e-03 2.705663e-01 0.7236908
## 3155 3.896343e-03 1.560545e-01 0.8400491
## 3156 2.440202e-04 1.344478e-01 0.8653082
## 3163 8.257561e-04 1.362607e-01 0.8629136
## 3165 3.977104e-02 2.616247e-01 0.6986042
## 3167 5.820865e-04 1.411401e-01 0.8582778
## 3169 5.493381e-03 2.913861e-01 0.7031206
## 3174 3.845657e-03 3.198564e-01 0.6762980
## 3175 9.611697e-03 3.062937e-01 0.6840946
## 3178 1.714528e-03 2.570624e-01 0.7412231
## 3181 4.726024e-03 2.300535e-01 0.7652205
## 3182 4.761777e-03 1.886618e-01 0.8065764
## 3186 1.506212e-02 3.001169e-01 0.6848210
## 3188 2.591030e-02 1.085608e-01 0.8655289
## 3189 1.562839e-04 1.107123e-01 0.8891314
## 3191 5.904185e-09 3.871286e-01 0.6128714
## 3196 3.651329e-03 3.000368e-01 0.6963119
## 3200 8.397629e-04 1.473653e-01 0.8517949
## 3201 1.090899e-02 2.932676e-01 0.6958234
## 3205 3.564312e-05 8.908859e-02 0.9108758
## 3207 9.316922e-03 2.854592e-01 0.7052239
## 3208 9.071592e-05 7.713503e-02 0.9227743
## 3209 7.077146e-16 2.139801e-01 0.7860199
## 3210 4.828269e-02 3.277028e-01 0.6240145
## 3212 1.958745e-02 3.050445e-01 0.6753680
## 3214 8.397629e-04 1.473653e-01 0.8517949
## 3218 2.760613e-04 1.302750e-01 0.8694489
## 3222 4.299843e-03 2.847994e-01 0.7109008
## 3234 3.535345e-04 1.318141e-01 0.8678324
## 3235 1.194905e-02 2.220379e-01 0.7660130
## 3238 5.742947e-03 2.705663e-01 0.7236908
## 3246 2.179264e-02 3.209761e-01 0.6572312
## 3249 7.356629e-03 3.033688e-01 0.6892746
## 3250 8.457454e-03 2.405163e-01 0.7510263
## 3252 4.506169e-02 3.209403e-01 0.6339980
## 3253 5.911587e-05 1.153385e-01 0.8846024
## 3255 4.509485e-09 3.202794e-01 0.6797206
## 3257 6.485270e-03 2.976208e-01 0.6958939
## 3262 8.051166e-06 6.193835e-08 0.9999919
## 3264 4.366358e-04 2.444282e-01 0.7551352
## 3266 2.823783e-04 1.417039e-01 0.8580137
## 3267 5.820865e-04 1.411401e-01 0.8582778
## 3268 6.316906e-04 1.766975e-01 0.8226708
## 3270 2.405559e-03 1.963475e-01 0.8012470
## 3271 3.406427e-02 3.468281e-01 0.6191077
## 3275 8.996032e-04 1.794316e-01 0.8196688
## 3281 8.211237e-03 2.799776e-01 0.7118111
## 3282 5.820865e-04 1.411401e-01 0.8582778
## 3283 3.650730e-03 4.277082e-01 0.5686411
## 3287 1.714913e-04 1.323305e-01 0.8674980
## 3288 1.714528e-03 2.570624e-01 0.7412231
## 3289 8.397629e-04 1.473653e-01 0.8517949
## 3295 7.387222e-03 4.072351e-01 0.5853777
## 3298 7.356629e-03 3.033688e-01 0.6892746
## 3300 3.527212e-03 3.221167e-01 0.6743561
## 3314 2.705830e-03 1.957798e-01 0.8015144
## 3316 5.742947e-03 2.705663e-01 0.7236908
## 3319 4.508091e-12 1.496495e-01 0.8503505
## 3320 5.089505e-04 1.279191e-01 0.8715720
## 3327 5.742947e-03 2.705663e-01 0.7236908
## 3329 3.649696e-10 1.998923e-01 0.8001077
## 3331 2.525775e-03 2.090278e-01 0.7884465
## 3340 7.620547e-03 2.040028e-01 0.7883767
## 3341 4.179134e-03 2.036039e-01 0.7922170
## 3344 6.628381e-04 1.439182e-01 0.8554190
## 3345 3.234266e-03 1.805410e-01 0.8162247
## 3346 9.719153e-02 3.231837e-01 0.5796248
## 3347 7.575976e-02 2.705961e-01 0.6536441
## 3354 1.672334e-02 2.785524e-01 0.7047242
## 3357 8.814288e-03 3.704264e-01 0.6207594
## 3359 1.721887e-03 1.896492e-01 0.8086289
## 3361 2.776410e-03 3.410904e-01 0.6561332
## 3363 9.162072e-05 9.141476e-02 0.9084936
## 3366 3.609691e-03 1.642487e-01 0.8321416
## 3370 1.220931e-02 3.579530e-01 0.6298377
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## 3384 7.522570e-03 2.383056e-01 0.7541718
## 3386 1.343035e-03 1.093019e-01 0.8893551
## 3389 2.131536e-03 2.152589e-01 0.7826096
## 3390 6.538676e-04 1.742825e-01 0.8250636
## 3394 4.548614e-02 3.503663e-01 0.6041476
## 3398 1.370183e-09 1.454641e-01 0.8545359
## 3402 1.075600e-02 2.566945e-01 0.7325495
## 3405 2.305185e-04 9.685025e-02 0.9029192
## 3408 1.251113e-03 1.542179e-01 0.8445310
## 3413 6.066597e-04 1.853392e-01 0.8140542
## 3419 3.519973e-04 1.312596e-01 0.8683884
## 3421 9.184585e-18 1.116285e-01 0.8883715
## 3425 2.194121e-04 1.285732e-01 0.8712074
## 3426 3.519973e-04 1.312596e-01 0.8683884
## 3428 3.519973e-04 1.312596e-01 0.8683884
## 3431 4.797004e-04 1.186021e-01 0.8809182
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## 3448 7.900966e-03 2.498288e-01 0.7422702
## 3451 8.287322e-02 3.827578e-01 0.5343690
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## 3463 1.423915e-02 2.933153e-01 0.6924455
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## 3471 7.870370e-03 1.852051e-01 0.8069245
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## 3481 5.715000e-03 2.693007e-01 0.7249843
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## 3492 4.785112e-03 2.564338e-01 0.7387811
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## 3508 2.684884e-03 2.992502e-01 0.6980649
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## 3516 3.513006e-03 2.614957e-01 0.7349913
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## 3540 2.595144e-01 2.508246e-01 0.4896611
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## 3544 1.401578e-03 1.283917e-01 0.8702068
## 3547 5.384409e-03 2.099185e-01 0.7846971
## 3549 2.409648e-02 3.123155e-01 0.6635880
## 3550 1.039007e-02 2.333075e-01 0.7563024
## 3553 5.184360e-03 1.604391e-01 0.8343765
## 3556 3.390460e-03 1.657366e-01 0.8308729
## 3561 5.240781e-03 2.339802e-01 0.7607790
## 3567 5.779180e-04 1.401626e-01 0.8592595
## 3573 7.578745e-03 2.712334e-01 0.7211879
## 3577 4.985074e-03 3.650220e-01 0.6299929
## 3581 2.409648e-02 3.123155e-01 0.6635880
## 3586 5.708027e-03 2.689849e-01 0.7253071
## 3587 2.115143e-06 4.882925e-01 0.5117054
## 3589 3.423075e-03 1.968920e-01 0.7996849
## 3590 1.748701e-02 2.842248e-01 0.6982882
## 3591 2.691460e-02 3.215588e-01 0.6515266
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## 3608 5.708027e-03 2.689849e-01 0.7253071
## 3610 1.703860e-03 2.555235e-01 0.7427727
## 3620 2.697747e-02 1.822842e-01 0.7907384
## 3621 1.225455e-03 2.143222e-01 0.7844524
## 3623 1.893651e-02 2.789297e-01 0.7021338
## 3631 8.961737e-03 1.486892e-01 0.8423491
## 3633 1.093789e-02 2.432463e-01 0.7458158
## 3634 9.903297e-04 1.967870e-01 0.8022227
## 3640 4.542512e-04 2.063081e-01 0.7932377
## 3641 9.465240e-03 1.648151e-01 0.8257197
## 3646 9.250631e-03 2.835088e-01 0.7072406
## 3650 1.248370e-01 3.297135e-01 0.5454495
## 3651 1.717360e-03 1.472418e-01 0.8510409
## 3652 3.057627e-02 3.902327e-01 0.5791911
## 3660 5.356087e-03 2.145404e-01 0.7801036
## 3662 3.649068e-03 2.421461e-01 0.7542049
## 3663 1.200640e-02 2.471822e-01 0.7408114
## 3669 1.094415e-02 2.432995e-01 0.7457564
## 3689 5.960006e-03 3.240204e-01 0.6700196
## 3690 2.834502e-10 1.593652e-01 0.8406348
## 3691 1.786692e-03 3.091223e-01 0.6890910
## 3693 3.657883e-04 1.286424e-01 0.8709918
## 3694 5.880928e-04 1.314023e-01 0.8680096
## 3697 5.202130e-02 3.078648e-01 0.6401139
## 3699 3.332291e-04 1.073891e-01 0.8922777
## 3702 3.649068e-03 2.421461e-01 0.7542049
## 3711 3.518312e-02 2.405596e-01 0.7242573
## 3721 1.583582e-02 2.116730e-01 0.7724911
## 3722 3.900110e-02 3.182273e-01 0.6427716
## 3723 4.101377e-03 3.671607e-01 0.6287379
## 3726 7.254506e-02 2.887751e-01 0.6386798
## 3727 7.140214e-07 4.168154e-01 0.5831838
## 3731 5.603390e-04 1.023389e-01 0.8971008
## 3734 1.107529e-02 2.245792e-01 0.7643455
## 3735 5.770874e-04 1.399677e-01 0.8594552
## 3737 2.723795e-09 3.748562e-01 0.6251438
## 3742 5.694009e-03 3.380478e-01 0.6562582
## 3744 2.752834e-03 1.751194e-01 0.8221277
## 3750 2.861666e-02 2.690876e-01 0.7022957
## 3751 1.981879e-03 2.624855e-01 0.7355326
## 3752 1.412198e-02 3.317197e-01 0.6541584
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## 3761 1.722712e-04 1.761821e-01 0.8236456
## 3765 4.019548e-02 3.896012e-01 0.5702033
## 3770 1.114986e-02 2.197804e-01 0.7690698
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## 3777 2.101026e-01 2.074743e-01 0.5824230
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## 3799 1.109192e-03 1.478675e-01 0.8510233
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## 3803 1.399144e-03 2.174631e-01 0.7811378
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## 3809 5.770874e-04 1.399677e-01 0.8594552
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## 3828 1.020119e-07 3.679498e-01 0.6320501
## 3829 2.197078e-03 2.490145e-01 0.7487885
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## 3843 1.708476e-09 2.492707e-01 0.7507293
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## 3856 2.430495e-08 1.391825e-01 0.8608175
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## 3873 1.075182e-02 3.508501e-01 0.6383981
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## 3936 9.187871e-03 3.547379e-01 0.6360743
## 3938 2.560757e-02 2.735234e-01 0.7008690
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## 3941 8.869627e-04 2.038756e-01 0.7952375
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## 4012 3.054840e-03 2.535833e-01 0.7433619
## 4014 3.052941e-04 1.304291e-01 0.8692656
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## 4052 5.701059e-03 2.686693e-01 0.7256297
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## 4083 5.770874e-04 1.399677e-01 0.8594552
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## 4098 1.800716e-09 1.512668e-01 0.8487332
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## 4156 1.080665e-03 1.007028e-01 0.8982166
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## 4184 5.701059e-03 2.686693e-01 0.7256297
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## 4199 1.963054e-02 3.346273e-01 0.6457421
## 4200 1.777408e-02 1.327337e-01 0.8494922
## 4203 4.665738e-03 2.230369e-01 0.7722973
## 4204 3.616664e-04 1.235231e-01 0.8761152
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## 4228 4.045893e-02 2.753504e-01 0.6841907
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## 4258 3.499566e-04 1.305234e-01 0.8691266
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## 4274 7.389241e-04 8.491696e-02 0.9143441
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## 4279 1.225088e-02 2.851590e-01 0.7025901
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## 4282 8.049791e-03 2.993876e-01 0.6925626
## 4286 3.356179e-03 3.138067e-01 0.6828371
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## 4289 2.219733e-02 2.960830e-01 0.6817196
## 4291 3.496593e-02 1.534032e-01 0.8116309
## 4293 8.967515e-03 2.598806e-01 0.7311519
## 4297 7.413837e-04 1.912582e-01 0.8080005
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## 4302 1.355237e-02 2.143452e-01 0.7721024
## 4305 6.772863e-05 5.832208e-07 0.9999317
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## 4309 3.499566e-04 1.305234e-01 0.8691266
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## 4312 2.756934e-02 3.108363e-01 0.6615943
## 4315 7.560353e-03 2.706008e-01 0.7218389
## 4323 9.656724e-03 1.862527e-01 0.8040906
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## 4331 8.646524e-03 2.137013e-01 0.7776521
## 4332 3.989613e-03 1.939683e-01 0.8020421
## 4337 1.664403e-02 2.772841e-01 0.7060719
## 4341 2.089015e-03 2.643700e-01 0.7335410
## 4342 1.699605e-03 2.549096e-01 0.7433908
## 4344 2.596887e-04 7.039883e-02 0.9293415
## 4345 5.486764e-03 2.311759e-01 0.7633373
## 4346 9.438972e-02 2.437285e-01 0.6618817
## 4350 8.558228e-03 2.663989e-01 0.7250428
## 4354 3.351203e-02 2.524128e-01 0.7140752
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## 4370 1.909093e-09 1.388588e-01 0.8611412
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## 4378 9.177982e-03 3.543729e-01 0.6364492
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## 4387 2.278056e-01 3.941194e-01 0.3780750
## 4389 5.687694e-03 3.376889e-01 0.6566234
## 4395 4.831513e-02 4.010288e-01 0.5506561
## 4401 9.177982e-03 3.543729e-01 0.6364492
## 4404 2.093934e-02 3.208827e-01 0.6581779
## 4407 3.519586e-02 4.774771e-01 0.4873270
## 4411 8.004484e-03 2.167179e-01 0.7752776
## 4412 2.720904e-03 2.206211e-01 0.7766580
## 4413 9.177982e-03 3.543729e-01 0.6364492
## 4414 5.694097e-03 2.683539e-01 0.7259520
## 4418 7.500804e-03 2.877837e-01 0.7047155
## 4420 9.177982e-03 3.543729e-01 0.6364492
## 4422 7.247988e-03 3.528954e-01 0.6398566
## 4442 9.239611e-03 2.831845e-01 0.7075759
## 4444 2.704645e-09 2.573566e-01 0.7426434
## 4450 6.708046e-03 3.100119e-01 0.6832800
## 4451 4.472430e-02 3.186431e-01 0.6366326
## 4457 5.035135e-03 2.293715e-01 0.7655933
## 4462 1.016887e-09 2.471600e-01 0.7528400
## 4467 8.382932e-03 2.384761e-01 0.7531409
## 4475 5.227391e-03 2.334046e-01 0.7613680
## 4477 2.989780e-02 2.830240e-01 0.6870782
## 4479 3.888044e-03 2.064708e-01 0.7896412
## 4487 2.155622e-03 1.746223e-01 0.8232221
## 4499 9.863374e-04 1.960216e-01 0.8029921
## 4500 2.622176e-02 2.513086e-01 0.7224696
## 4503 8.119408e-03 3.006954e-01 0.6911851
## 4506 6.128170e-03 2.067506e-01 0.7871212
## 4515 1.807767e-02 3.113989e-01 0.6705235
## 4520 4.837141e-04 1.042985e-01 0.8952178
## 4525 4.214507e-09 2.845340e-01 0.7154660
## 4534 8.523765e-04 2.028651e-01 0.7962826
## 4536 2.246302e-09 2.866117e-01 0.7133883
## 4541 7.021118e-03 2.115690e-01 0.7814099
## 4542 3.629742e-02 2.283869e-01 0.7353156
## 4544 5.680190e-03 2.677239e-01 0.7265959
## 4545 1.196158e-02 2.462945e-01 0.7417440
## 4547 4.856495e-03 2.495481e-01 0.7455954
## 4548 1.358466e-02 1.700316e-01 0.8163837
## 4552 1.938712e-02 3.020536e-01 0.6785593
## 4554 1.158032e-01 2.253779e-01 0.6588189
## 4557 7.717001e-04 1.497744e-01 0.8494539
## 4560 7.718798e-03 1.490001e-01 0.8432811
## 4573 3.043394e-03 2.526692e-01 0.7442875
## 4574 2.494442e-04 1.350964e-01 0.8646542
## 4575 2.284400e-04 9.600432e-02 0.9037672
## 4576 5.746015e-04 1.393846e-01 0.8600408
## 4577 7.541989e-03 2.699691e-01 0.7224889
## 4580 2.141198e-03 1.498576e-01 0.8480012
## 4583 3.489401e-04 1.301566e-01 0.8694944
## 4585 5.680190e-03 2.677239e-01 0.7265959
## 4591 1.475099e-02 2.334067e-01 0.7518423
## 4593 5.579583e-08 8.014921e-02 0.9198507
## 4600 7.541989e-03 2.699691e-01 0.7224889
## 4601 5.680190e-03 2.677239e-01 0.7265959
## 4603 5.680190e-03 2.677239e-01 0.7265959
## 4604 7.558151e-03 2.267451e-01 0.7656967
## 4606 9.863374e-04 1.960216e-01 0.8029921
## 4607 2.982859e-02 2.823957e-01 0.6877757
## 4608 9.863374e-04 1.960216e-01 0.8029921
## 4619 4.952918e-04 1.169228e-01 0.8825820
## 4622 5.680190e-03 2.677239e-01 0.7265959
## 4624 1.221038e-02 2.742724e-01 0.7135172
## 4625 5.746015e-04 1.393846e-01 0.8600408
## 4626 1.510526e-02 2.169216e-01 0.7679732
## 4630 5.208250e-03 2.271595e-01 0.7676322
## 4632 1.938712e-02 3.020536e-01 0.6785593
## 4638 9.158220e-03 3.536434e-01 0.6371984
## 4639 5.680190e-03 2.677239e-01 0.7265959
## 4640 4.911975e-02 3.961983e-01 0.5546819
## 4641 1.213131e-02 3.557675e-01 0.6321012
## 4643 7.541989e-03 2.699691e-01 0.7224889
## 4646 3.395214e-02 3.185411e-01 0.6475068
## 4649 1.635408e-04 9.979285e-02 0.9000436
## 4650 8.511721e-03 3.704990e-01 0.6209893
## 4652 1.077518e-02 2.791441e-01 0.7100807
## 4660 1.113557e-02 2.176438e-01 0.7712206
## 4673 1.936493e-02 3.017222e-01 0.6789129
## 4674 4.051516e-02 3.110304e-01 0.6484545
## 4675 6.291569e-04 1.316365e-01 0.8677343
## 4680 5.673244e-03 2.674092e-01 0.7269176
## 4683 9.850094e-04 1.957669e-01 0.8032481
## 4687 2.396169e-02 3.106422e-01 0.6653961
## 4689 3.054196e-02 3.886583e-01 0.5807997
## 4692 5.500118e-04 1.966149e-01 0.8028351
## 4693 5.673244e-03 2.674092e-01 0.7269176
## 4695 1.211834e-02 3.554037e-01 0.6324779
## 4696 1.377674e-03 1.840535e-01 0.8145689
## 4697 1.048967e-02 2.493239e-01 0.7401864
## 4701 2.034951e-03 1.631809e-01 0.8347842
## 4704 2.747704e-02 3.098397e-01 0.6626832
## 4706 3.484328e-04 1.299736e-01 0.8696780
## 4707 3.045607e-02 3.887723e-01 0.5807716
## 4713 2.312109e-02 2.880643e-01 0.6888146
## 4714 1.498010e-03 1.811326e-01 0.8173694
## 4717 1.951576e-02 3.591609e-01 0.6213233
## 4726 1.219571e-02 2.739559e-01 0.7138484
## 4729 1.311244e-03 1.979185e-01 0.8007703
## 4730 2.034951e-03 1.631809e-01 0.8347842
## 4733 5.737749e-04 1.391907e-01 0.8602355
## 4734 1.936493e-02 3.017222e-01 0.6789129
## 4749 5.673244e-03 2.674092e-01 0.7269176
## 4753 4.013088e-03 2.081028e-01 0.7878842
## 4754 1.453993e-02 2.679172e-01 0.7175428
## 4755 1.029404e-03 1.348876e-01 0.8640830
## 4757 1.158420e-02 2.859977e-01 0.7024181
## 4758 2.314102e-03 1.660866e-01 0.8315993
## 4763 9.989918e-03 2.519251e-01 0.7380850
## 4764 2.099554e-04 1.160027e-01 0.8837874
## 4765 9.989918e-03 2.519251e-01 0.7380850
## 4771 1.054580e-04 1.146564e-01 0.8852381
## 4773 3.743609e-03 2.614157e-01 0.7348407
## 4774 3.259010e-03 2.604213e-01 0.7363197
## 4778 4.269214e-02 3.944638e-01 0.5628441
## 4783 5.831866e-03 2.892116e-01 0.7049565
## 4784 1.211078e-02 3.427717e-01 0.6451175
## 4785 1.074599e-02 3.406860e-01 0.6485680
## 4786 4.977441e-02 3.146536e-01 0.6355719
## 4787 3.436991e-03 2.258321e-01 0.7707309
## 4798 7.287680e-04 1.362781e-01 0.8629932
## 4799 3.652242e-04 1.777630e-01 0.8218717
## 4800 1.354228e-03 1.572110e-01 0.8414347
## 4806 4.995366e-03 2.291731e-01 0.7658315
## 4812 5.608602e-03 9.570013e-02 0.8986913
## 4815 2.052316e-04 1.311163e-01 0.8686784
## 4816 4.976606e-03 2.610857e-01 0.7339377
## 4818 4.124944e-04 8.985837e-02 0.9097291
## 4822 8.243147e-04 1.447436e-01 0.8544320
## 4826 1.351344e-10 8.728993e-02 0.9127101
## 4827 1.686885e-03 2.530737e-01 0.7452394
## 4833 1.033830e-03 2.071478e-01 0.7918184
## 4834 1.370718e-02 3.100789e-01 0.6762139
## 4839 7.858843e-03 3.253769e-01 0.6667642
## 4842 1.754754e-03 1.369566e-01 0.8612886
## 4844 1.128759e-03 1.589302e-01 0.8399410
## 4845 1.511163e-02 1.717549e-01 0.8131335
## 4850 8.466132e-04 1.374533e-01 0.8617001
## 4851 5.713011e-04 1.386103e-01 0.8608184
## 4854 5.652441e-03 2.664666e-01 0.7278810
## 4855 9.223340e-02 3.387397e-01 0.5690269
## 4864 9.909541e-03 3.311526e-01 0.6589379
## 4870 1.682813e-04 1.299336e-01 0.8698981
## 4872 1.872599e-03 1.838785e-01 0.8142489
## 4873 2.146320e-03 2.308427e-01 0.7670109
## 4875 1.686885e-03 2.530737e-01 0.7452394
## 4878 5.909078e-03 1.643608e-01 0.8297301
## 4880 2.026428e-03 1.625205e-01 0.8354531
## 4886 1.264166e-02 3.888003e-01 0.5985580
## 4892 8.422826e-09 1.994788e-01 0.8005212
## 4895 4.022102e-03 1.271831e-01 0.8687948
## 4898 5.652441e-03 2.664666e-01 0.7278810
## 4900 6.003620e-03 2.081363e-01 0.7858601
## 4902 8.319420e-03 2.367367e-01 0.7549439
## 4906 6.204474e-04 1.736596e-01 0.8257200
## 4907 7.522168e-04 1.477207e-01 0.8515271
## 4909 2.845112e-04 1.235729e-01 0.8761426
## 4915 5.421386e-04 1.072556e-01 0.8922023
## 4916 1.104343e-01 3.108947e-01 0.5786710
## 4918 5.707245e-03 1.666258e-01 0.8276669
## 4919 8.156698e-03 2.805963e-01 0.7112470
## 4922 3.616779e-03 2.400831e-01 0.7563001
## 4923 2.078582e-09 1.582546e-01 0.8417454
## 4926 3.763362e-04 1.352512e-01 0.8643725
## 4937 1.242315e-03 1.436451e-01 0.8551126
## 4938 1.053496e-02 1.777875e-01 0.8116776
## 4940 7.210524e-04 1.312412e-01 0.8680377
## 4946 5.676883e-04 1.784692e-01 0.8209631
## 4950 2.955758e-02 2.545972e-01 0.7158452
## 4954 1.783209e-03 2.619666e-02 0.9720201
## 4956 1.686885e-03 2.530737e-01 0.7452394
## 4958 1.707415e-04 1.083562e-01 0.8914730
## 4961 5.652441e-03 2.664666e-01 0.7278810
## 4962 7.321999e-03 2.007866e-01 0.7918914
## 4964 1.098175e-03 1.464475e-01 0.8524544
## 4967 9.810336e-04 1.950045e-01 0.8040145
## 4970 3.450131e-04 1.492242e-01 0.8504307
## 4971 7.375612e-03 2.826442e-01 0.7099802
## 4977 1.162604e-02 2.544865e-01 0.7338875
## 4979 9.554099e-11 1.077633e-01 0.8922367
## 4981 5.713011e-04 1.386103e-01 0.8608184
## 4990 1.045829e-03 1.090176e-01 0.8899365
## 4995 4.995366e-03 2.291731e-01 0.7658315
## 4996 7.505282e-03 2.868881e-01 0.7056066
## 5002 7.838482e-04 8.582069e-02 0.9133955
## 5005 2.836233e-04 7.796066e-02 0.9217557
## 5006 2.254661e-02 2.328611e-01 0.7445923
## 5007 5.713011e-04 1.386103e-01 0.8608184
## 5008 5.875972e-02 3.395479e-01 0.6016924
## 5009 3.346950e-03 2.551722e-01 0.7414809
## 5010 4.167896e-04 1.385155e-01 0.8610677
## 5013 6.793127e-04 8.271740e-02 0.9166033
## 5016 4.498197e-03 1.876086e-01 0.8078932
## 5017 2.530754e-03 1.429528e-01 0.8545165
## 5018 2.939040e-03 1.392610e-01 0.8578000
## 5025 1.421235e-02 2.796115e-01 0.7061761
## 5028 4.571946e-04 1.203846e-01 0.8791582
## 5031 2.738490e-02 3.088447e-01 0.6637704
## 5032 9.155120e-04 1.029993e-01 0.8960852
## 5034 3.461669e-04 1.243825e-01 0.8752713
## 5037 8.619418e-04 1.373289e-01 0.8618091
## 5041 1.242315e-03 1.436451e-01 0.8551126
## 5046 1.386341e-03 2.155447e-01 0.7830690
## 5049 5.713011e-04 1.386103e-01 0.8608184
## 5056 8.243147e-04 1.447436e-01 0.8544320
## 5059 2.556783e-02 3.016480e-01 0.6727842
## 5061 3.179140e-03 2.053710e-01 0.7914499
## 5062 5.278997e-03 9.594759e-02 0.8987734
## 5064 5.865869e-04 2.239086e-01 0.7755048
## 5067 7.529216e-04 1.204177e-01 0.8788294
## 5069 4.817368e-04 8.939779e-02 0.9101205
## 5088 5.054632e-03 2.991198e-01 0.6958256
## 5092 7.218260e-03 2.622680e-01 0.7305138
## 5093 1.256972e-02 3.036161e-01 0.6838142
## 5094 5.708427e-03 2.828875e-01 0.7114041
## 5100 1.531914e-02 3.504030e-01 0.6342779
## 5101 5.746719e-03 2.964328e-01 0.6978205
## 5104 1.165311e-02 3.468844e-01 0.6414625
## 5110 2.521748e-03 1.724869e-01 0.8249913
## 5112 7.372967e-04 1.709048e-01 0.8283579
## 5116 2.902537e-04 1.836089e-01 0.8161009
## 5119 4.415093e-07 2.221063e-01 0.7778932
## 5120 2.869107e-03 1.932309e-01 0.8039000
## 5121 4.865958e-03 2.026379e-01 0.7924961
## 5125 2.127111e-03 2.015021e-01 0.7963708
## 5131 1.945420e-02 3.580789e-01 0.6224669
## 5144 5.652441e-03 2.664666e-01 0.7278810
## 5146 3.747444e-03 1.737409e-01 0.8225116
## 5151 5.984231e-04 1.829096e-01 0.8164920
## 5155 2.838031e-02 2.669539e-01 0.7046658
## 5157 2.418442e-03 2.625870e-01 0.7349945
## 5158 2.041319e-02 1.275952e-01 0.8519917
## 5159 5.652441e-03 2.664666e-01 0.7278810
## 5166 7.321999e-03 2.007866e-01 0.7918914
## 5168 2.745700e-03 3.374776e-01 0.6597767
## 5170 3.888130e-04 1.621335e-01 0.8374776
## 5171 5.649881e-03 3.355393e-01 0.6588108
## 5173 2.175506e-02 2.952558e-01 0.6829891
## 5183 2.270637e-04 9.544403e-02 0.9043289
## 5185 8.813947e-03 2.941668e-01 0.6970193
## 5188 2.289923e-04 9.662331e-02 0.9031477
## 5190 6.609957e-03 2.633616e-01 0.7300285
## 5193 1.750597e-03 2.192162e-01 0.7790332
## 5196 6.886453e-03 2.512552e-01 0.7418583
## 5199 2.641826e-02 2.715509e-01 0.7020309
## 5205 8.083856e-03 2.758043e-01 0.7161118
## 5207 7.538665e-03 3.243898e-01 0.6680715
## 5212 5.652441e-03 2.664666e-01 0.7278810
## 5213 1.929845e-02 3.007292e-01 0.6799723
## 5214 7.491743e-03 2.588126e-01 0.7336957
## 5216 7.505347e-03 2.687085e-01 0.7237862
## 5218 5.652441e-03 2.664666e-01 0.7278810
## 5222 5.120457e-02 3.259614e-01 0.6228341
## 5226 1.609884e-02 2.746842e-01 0.7092170
## 5230 4.995366e-03 2.291731e-01 0.7658315
## 5237 1.106572e-03 1.194267e-01 0.8794668
## 5242 1.208641e-02 3.084846e-01 0.6794290
## 5245 8.243147e-04 1.447436e-01 0.8544320
## 5248 2.999251e-04 1.114967e-01 0.8882033
## 5252 7.612332e-04 1.402659e-01 0.8589728
## 5255 7.163274e-04 1.744855e-01 0.8247981
## 5257 2.423381e-03 1.217418e-01 0.8758348
## 5259 5.713011e-04 1.386103e-01 0.8608184
## 5263 3.056674e-04 1.095464e-01 0.8901479
## 5265 7.505347e-03 2.687085e-01 0.7237862
## 5266 1.132598e-02 3.211786e-01 0.6674954
## 5267 8.083856e-03 2.758043e-01 0.7161118
## 5275 8.083856e-03 2.758043e-01 0.7161118
## 5277 5.713011e-04 1.386103e-01 0.8608184
## 5279 1.929845e-02 3.007292e-01 0.6799723
## 5280 5.457261e-02 2.827845e-01 0.6626428
## 5283 4.585491e-02 4.144629e-01 0.5396822
## 5284 2.902537e-04 1.836089e-01 0.8161009
## 5289 2.738490e-02 3.088447e-01 0.6637704
## 5291 1.130252e-04 1.342601e-01 0.8656268
## 5293 1.243634e-04 1.447921e-01 0.8550835
## 5294 3.923750e-02 3.318324e-01 0.6289301
## 5296 1.906295e-04 9.129944e-02 0.9085099
## 5301 3.227605e-03 2.889066e-01 0.7078658
## 5304 4.986306e-03 2.401162e-01 0.7548975
## 5306 5.649881e-03 3.355393e-01 0.6588108
## 5308 3.064451e-03 2.213493e-01 0.7755863
## 5310 1.666933e-02 2.928536e-01 0.6904771
## 5312 3.389039e-12 8.246579e-02 0.9175342
## 5319 1.945420e-02 3.580789e-01 0.6224669
## 5321 1.945420e-02 3.580789e-01 0.6224669
## 5328 6.919972e-03 2.911076e-01 0.7019724
## 5329 9.453887e-04 9.676030e-02 0.9022943
## 5331 1.929845e-02 3.007292e-01 0.6799723
## 5335 5.435935e-03 3.395381e-01 0.6550259
## 5337 1.014150e-02 2.666978e-01 0.7231607
## 5339 1.165055e-02 3.212900e-01 0.6670594
## 5341 1.927632e-02 3.003986e-01 0.6803251
## 5342 4.018081e-02 3.582051e-01 0.6016141
## 5343 7.071699e-03 2.094718e-01 0.7834565
## 5352 1.980050e-02 3.155020e-01 0.6646975
## 5356 5.392457e-03 2.635022e-01 0.7311053
## 5358 5.795878e-03 2.932619e-01 0.7009423
## 5360 4.439184e-03 3.144311e-01 0.6811297
## 5361 2.680475e-02 2.086038e-01 0.7645915
## 5364 2.957381e-08 4.537113e-01 0.5462887
## 5365 8.708476e-04 1.541486e-01 0.8449805
## 5366 2.035151e-04 2.000005e-01 0.7997960
## 5371 5.640761e-02 2.426947e-01 0.7008977
## 5374 6.706058e-03 3.494135e-01 0.6438804
## 5375 3.607590e-03 2.394959e-01 0.7568965
## 5376 1.759015e-03 1.295550e-01 0.8686860
## 5377 4.795266e-03 2.417673e-01 0.7534375
## 5379 5.086059e-03 2.558348e-01 0.7390791
## 5380 3.293985e-03 2.071781e-01 0.7895280
## 5385 5.337458e-03 3.036179e-01 0.6910446
## 5389 1.311842e-03 1.966990e-01 0.8019892
## 5390 4.279194e-02 2.809345e-01 0.6762736
## 5392 5.696569e-04 1.382245e-01 0.8612058
## 5397 3.738784e-04 1.022128e-01 0.8974133
## 5398 4.434019e-02 3.160264e-01 0.6396335
## 5407 7.294020e-03 1.909181e-01 0.8017878
## 5414 3.501450e-02 2.740689e-01 0.6909166
## 5417 3.076949e-03 1.804458e-01 0.8164772
## 5418 1.925421e-02 3.000682e-01 0.6806776
## 5420 8.483257e-03 3.104430e-01 0.6810737
## 5431 6.855508e-02 3.922485e-01 0.5391964
## 5433 5.309881e-02 5.059385e-01 0.4409627
## 5437 4.438534e-03 1.210166e-01 0.8745449
## 5438 2.084731e-02 1.782931e-01 0.8008596
## 5442 9.099057e-03 3.514588e-01 0.6394421
## 5445 1.768052e-03 3.060281e-01 0.6922039
## 5449 1.682659e-03 2.524637e-01 0.7458536
## 5450 5.242264e-03 1.993043e-01 0.7954534
## 5456 3.969978e-04 1.367290e-01 0.8628740
## 5464 1.305854e-02 2.897685e-01 0.6971729
## 5466 9.099057e-03 3.514588e-01 0.6394421
## 5472 1.031446e-02 3.080516e-01 0.6816339
## 5479 5.217560e-02 4.011617e-01 0.5466627
## 5483 1.427638e-03 1.713113e-01 0.8272610
## 5491 8.064370e-03 2.751656e-01 0.7167700
## 5493 2.253650e-03 2.507576e-01 0.7469887
## 5495 8.064370e-03 2.751656e-01 0.7167700
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## 5584 1.068518e-02 2.769046e-01 0.7124102
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## 5589 1.212076e-02 2.822506e-01 0.7056287
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## 6591 2.825588e-02 1.838508e-01 0.7878933
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## 7006 1.298495e-02 2.859577e-01 0.7010574
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## 7094 5.501417e-03 2.596178e-01 0.7348808
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## 7210 1.213337e-02 2.665271e-01 0.7213395
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## 7498 1.442635e-02 2.879539e-01 0.6976197
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## 7532 5.518352e-04 1.340400e-01 0.8654082
## 7533 8.883724e-03 3.434996e-01 0.6476166
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## 7551 2.075158e-02 2.603729e-01 0.7188755
## 7552 8.912803e-03 2.735571e-01 0.7175301
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## 7556 1.504981e-02 2.750826e-01 0.7098676
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## 7580 3.043244e-03 1.921702e-01 0.8047866
## 7586 5.487822e-03 2.590007e-01 0.7355114
## 7597 1.636655e-03 2.458178e-01 0.7525455
## 7598 1.392967e-03 2.061543e-01 0.7924527
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## 7606 1.636655e-03 2.458178e-01 0.7525455
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## 7616 6.374421e-03 2.640371e-01 0.7295885
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## 7631 7.852003e-03 2.681991e-01 0.7239489
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## 7640 5.487822e-03 2.590007e-01 0.7355114
## 7645 8.883724e-03 3.434996e-01 0.6476166
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## 7651 1.781298e-03 3.163199e-01 0.6818988
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## 7654 5.160997e-03 2.015141e-01 0.7933249
## 7655 3.566766e-03 2.312650e-01 0.7651683
## 7659 5.487822e-03 2.590007e-01 0.7355114
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## 7665 2.853127e-03 1.675555e-01 0.8295913
## 7673 3.066445e-02 3.023001e-01 0.6670354
## 7674 5.487822e-03 2.590007e-01 0.7355114
## 7676 8.290764e-05 1.070437e-01 0.8928734
## 7677 1.008388e-02 3.163217e-01 0.6735944
## 7678 8.834327e-03 2.448051e-01 0.7463606
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## 7721 1.683597e-02 2.740588e-01 0.7091053
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## 7730 1.339170e-03 1.573221e-01 0.8413387
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## 7742 2.485358e-02 2.754310e-01 0.6997154
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## 7750 2.905528e-02 3.795210e-01 0.5914237
## 7753 1.008388e-02 3.163217e-01 0.6735944
## 7755 5.487822e-03 2.590007e-01 0.7355114
## 7757 5.487822e-03 2.590007e-01 0.7355114
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## 7807 5.481032e-03 2.586926e-01 0.7358264
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## 7862 4.587470e-02 3.241180e-01 0.6300073
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## 7876 2.139912e-02 2.830901e-01 0.6955108
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## 7883 2.123687e-02 3.223599e-01 0.6564032
## 7884 7.964046e-03 2.996921e-01 0.6923438
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## 7892 8.058417e-03 2.295817e-01 0.7623599
## 7894 4.779218e-03 2.690824e-01 0.7261384
## 7896 5.481032e-03 2.586926e-01 0.7358264
## 7898 1.876499e-02 3.169873e-01 0.6642477
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## 7923 1.813339e-03 2.016446e-01 0.7965420
## 7926 5.481032e-03 2.586926e-01 0.7358264
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## 7928 2.754604e-02 2.594139e-01 0.7130401
## 7929 1.484722e-02 2.787549e-01 0.7063979
## 7933 3.988297e-03 2.838414e-01 0.7121703
## 7936 1.120412e-02 2.769817e-01 0.7118142
## 7937 1.309696e-02 2.426559e-01 0.7442472
## 7939 2.321446e-02 3.013550e-01 0.6754305
## 7949 1.683100e-02 2.839514e-01 0.6992176
## 7953 1.562252e-02 2.668734e-01 0.7175041
## 7955 3.973019e-03 1.220460e-01 0.8739809
## 7957 1.209709e-02 2.529007e-01 0.7350022
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## 7962 2.035614e-02 3.363797e-01 0.6432642
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## 7965 8.902037e-03 2.732397e-01 0.7178583
## 7966 1.498658e-11 2.493471e-01 0.7506529
## 7967 3.537199e-03 2.955086e-01 0.7009542
## 7971 1.872777e-02 2.921964e-01 0.6890759
## 7976 3.256979e-03 1.674194e-01 0.8293236
## 7981 5.823279e-02 2.830107e-01 0.6587565
## 7983 6.741091e-09 2.019778e-01 0.7980222
## 7984 4.953491e-02 3.588368e-01 0.5916283
## 7988 8.739728e-03 1.407365e-01 0.8505238
## 7989 8.864275e-03 3.427801e-01 0.6483556
## 7991 3.269652e-03 1.883708e-01 0.8083596
## 7999 7.832877e-03 2.675712e-01 0.7245959
## 8008 4.238057e-10 1.105189e-01 0.8894811
## 8012 8.864275e-03 3.427801e-01 0.6483556
## 8013 4.463515e-02 3.192121e-01 0.6361528
## 8015 3.144587e-02 2.780475e-01 0.6905066
## 8017 9.025668e-09 2.662756e-01 0.7337244
## 8018 5.487566e-03 3.263018e-01 0.6682107
## 8019 4.306174e-03 2.496406e-01 0.7460532
## 8023 3.311028e-02 1.660346e-01 0.8008552
## 8026 8.864275e-03 3.427801e-01 0.6483556
## 8030 7.832877e-03 2.675712e-01 0.7245959
## 8034 1.058701e-09 1.593577e-01 0.8406423
## 8035 3.745077e-09 1.863402e-01 0.8136598
## 8043 1.630834e-02 2.247730e-01 0.7589187
## 8044 1.618629e-09 2.995417e-01 0.7004583
## 8049 1.011863e-02 2.780865e-01 0.7117948
## 8054 2.989310e-03 1.979619e-01 0.7990488
## 8065 6.218170e-03 2.999662e-01 0.6938156
## 8066 1.410530e-09 1.612448e-01 0.8387552
## 8067 1.312848e-02 2.665479e-01 0.7203236
## 8076 1.259035e-02 2.431348e-01 0.7442749
## 8083 1.548073e-02 2.449930e-01 0.7395263
## 8089 2.497351e-02 3.502436e-01 0.6247829
## 8090 1.124163e-02 2.676696e-01 0.7210888
## 8104 1.746556e-02 2.303960e-01 0.7521384
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## 8110 1.048444e-10 2.673769e-01 0.7326231
## 8111 3.904247e-03 2.304379e-01 0.7656579
## 8113 1.681117e-02 2.836303e-01 0.6995585
## 8118 2.958490e-09 1.695166e-01 0.8304834
## 8125 8.048099e-03 2.292986e-01 0.7626533
## 8127 1.058701e-09 1.593577e-01 0.8406423
## 8128 9.164686e-02 3.623220e-01 0.5460311
## 8133 4.941116e-03 2.642822e-01 0.7307767
## 8137 1.358203e-09 2.354477e-01 0.7645523
## 8138 2.318802e-02 3.010260e-01 0.6757860
## 8147 2.655143e-09 1.398187e-01 0.8601813
## 8150 1.058701e-09 1.593577e-01 0.8406423
## 8156 9.947846e-03 2.237381e-01 0.7663141
## 8167 1.179209e-02 2.748968e-01 0.7133111
## 8174 7.269998e-03 2.606036e-01 0.7321264
## 8176 2.629350e-09 3.624253e-01 0.6375747
## 8182 1.058701e-09 1.593577e-01 0.8406423
## 8198 3.059546e-02 3.016486e-01 0.6677560
## 8199 2.318802e-02 3.010260e-01 0.6757860
## 8206 6.090110e-03 2.183871e-01 0.7755228
## 8207 6.608421e-03 1.749290e-01 0.8184626
## 8208 1.269334e-02 2.819855e-01 0.7053211
## 8214 8.864275e-03 3.427801e-01 0.6483556
## 8215 1.017846e-02 1.744032e-01 0.8154183
## 8216 3.284720e-02 3.086132e-01 0.6585396
## 8218 9.462457e-03 2.136028e-01 0.7769348
## 8222 4.319745e-02 3.082324e-01 0.6485701
## 8223 2.751299e-02 2.591149e-01 0.7133721
## 8224 7.859602e-04 2.033119e-01 0.7959021
## 8226 6.460682e-02 2.882905e-01 0.6471027
## 8227 1.420780e-09 1.968940e-01 0.8031060
## 8230 4.818724e-10 1.821413e-01 0.8178587
## 8234 1.329625e-08 3.381792e-01 0.6618208
## 8235 2.832803e-09 1.100434e-01 0.8899566
## 8237 5.610846e-03 2.696910e-01 0.7246981
## 8239 4.408263e-03 4.330161e-01 0.5625756
## 8242 5.474249e-03 2.583847e-01 0.7361411
## 8243 5.474249e-03 2.583847e-01 0.7361411
## 8247 9.162040e-03 1.751999e-01 0.8156381
## 8248 1.009194e-02 2.859454e-01 0.7039627
## 8253 8.891279e-03 2.729224e-01 0.7181863
## 8256 1.525941e-09 1.723601e-01 0.8276399
## 8257 3.535029e-02 3.317277e-01 0.6329220
## 8259 5.010734e-03 2.410311e-01 0.7539582
## 8267 5.121469e-03 2.054737e-01 0.7894048
## 8271 2.871827e-02 3.641936e-01 0.6070882
## 8272 7.382652e-02 1.999073e-01 0.7262661
## 8282 7.254310e-03 1.945397e-01 0.7982060
## 8288 6.344316e-03 1.695307e-01 0.8241250
## 8290 1.374634e-03 1.501378e-01 0.8484876
## 8291 5.010734e-03 2.410311e-01 0.7539582
## 8294 8.296707e-12 1.397873e-01 0.8602127
## 8295 7.307411e-07 3.082850e-01 0.6917142
## 8302 2.747997e-02 2.588162e-01 0.7137038
## 8303 3.203736e-03 4.747801e-02 0.9493183
## 8306 2.983169e-04 9.962513e-02 0.9000766
## 8308 3.107885e-02 2.248609e-01 0.7440603
## 8319 1.073628e-04 1.049549e-01 0.8949378
## 8321 2.316159e-02 3.006971e-01 0.6761413
## 8322 2.316159e-02 3.006971e-01 0.6761413
## 8325 1.316278e-02 3.072604e-01 0.6795768
## 8326 2.955985e-02 3.778694e-01 0.5925707
## 8328 1.659891e-14 1.356792e-01 0.8643208
## 8337 1.332897e-02 2.418431e-01 0.7448279
## 8340 4.963940e-04 1.587170e-01 0.8407866
## 8344 7.863760e-03 2.333303e-01 0.7588059
## 8345 4.460060e-10 1.132983e-01 0.8867017
## 8352 6.932486e-04 1.263422e-01 0.8729645
## 8359 9.059122e-03 1.982845e-01 0.7926564
## 8364 1.951026e-03 1.566738e-01 0.8413752
## 8365 6.488416e-03 2.511023e-01 0.7424093
## 8370 4.794947e-03 2.610949e-01 0.7341101
## 8381 2.043980e-02 1.763760e-01 0.8031842
## 8385 9.212537e-12 1.296407e-01 0.8703593
## 8387 5.009974e-03 2.240472e-01 0.7709428
## 8391 2.033836e-02 2.532356e-01 0.7264260
## 8395 1.069892e-02 2.391419e-01 0.7501592
## 8396 1.389637e-03 1.811384e-01 0.8174720
## 8400 7.823326e-03 2.672576e-01 0.7249190
## 8405 7.427286e-03 2.387855e-01 0.7537872
## 8406 5.467470e-03 2.580770e-01 0.7364555
## 8408 1.506463e-03 2.632902e-01 0.7352033
## 8409 4.818086e-04 1.086412e-01 0.8908770
## 8413 5.843506e-02 3.217240e-01 0.6198410
## 8415 1.870602e-02 2.918708e-01 0.6894232
## 8417 1.992543e-03 1.765256e-01 0.8214819
## 8418 3.376319e-02 2.033014e-01 0.7629355
## 8419 4.985383e-05 7.240919e-02 0.9275410
## 8420 6.590028e-03 3.306687e-01 0.6627413
## 8425 1.293765e-02 2.047578e-01 0.7823045
## 8426 7.492200e-03 3.063160e-01 0.6861918
## 8428 8.686974e-04 1.469550e-01 0.8521763
## 8430 3.821871e-03 2.560587e-01 0.7401194
## 8433 8.532887e-03 2.688543e-01 0.7226128
## 8437 5.494422e-04 1.334777e-01 0.8659728
## 8439 2.182284e-03 2.290417e-01 0.7687761
## 8442 2.122500e-06 5.422708e-01 0.4577271
## 8445 1.898906e-03 1.335383e-01 0.8645628
## 8448 4.037324e-11 1.798092e-01 0.8201908
## 8449 5.494422e-04 1.334777e-01 0.8659728
## 8459 2.278880e-03 1.863609e-01 0.8113602
## 8460 5.467470e-03 2.580770e-01 0.7364555
## 8464 3.265222e-03 1.881245e-01 0.8086103
## 8466 7.261045e-03 2.602950e-01 0.7324439
## 8468 4.586914e-03 2.700037e-01 0.7254094
## 8471 4.768985e-02 3.852308e-01 0.5670793
## 8474 1.191388e-03 1.179746e-01 0.8808340
## 8475 3.186212e-03 2.006374e-01 0.7961764
## 8476 2.768500e-03 2.476629e-01 0.7495686
## 8477 5.348517e-04 1.900352e-01 0.8094299
## 8486 1.278451e-02 1.991675e-01 0.7880480
## 8488 5.481374e-03 3.259490e-01 0.6685696
## 8490 8.854559e-03 3.424207e-01 0.6487248
## 8496 3.101638e-02 3.861318e-01 0.5828518
## 8497 4.590874e-03 2.080966e-01 0.7873125
## 8498 3.357646e-03 2.437053e-01 0.7529370
## 8501 5.494422e-04 1.334777e-01 0.8659728
## 8502 2.223518e-03 2.117475e-01 0.7860290
## 8504 3.857545e-03 2.082715e-01 0.7878710
## 8505 1.426863e-03 1.581416e-01 0.8404315
## 8508 7.321655e-04 1.350828e-01 0.8641851
## 8509 8.927196e-03 2.992500e-01 0.6918228
## 8510 6.020209e-03 4.008835e-01 0.5930962
## 8511 5.494422e-04 1.334777e-01 0.8659728
## 8513 2.556638e-03 2.718965e-01 0.7255469
## 8514 3.468279e-09 2.001021e-01 0.7998979
## 8517 1.757145e-03 1.844091e-01 0.8138338
## 8527 3.357646e-03 2.437053e-01 0.7529370
## 8528 7.823326e-03 2.672576e-01 0.7249190
## 8534 5.467470e-03 2.580770e-01 0.7364555
## 8535 2.958055e-03 2.139380e-01 0.7831040
## 8540 5.467470e-03 2.580770e-01 0.7364555
## 8542 5.467470e-03 2.580770e-01 0.7364555
## 8543 1.592059e-03 1.399840e-01 0.8584239
## 8545 2.160996e-04 1.059145e-01 0.8938694
## 8546 6.088387e-03 2.182007e-01 0.7757109
## 8547 5.467470e-03 2.580770e-01 0.7364555
## 8548 3.304200e-03 2.309266e-01 0.7657692
## 8551 3.140930e-02 2.777373e-01 0.6908534
## 8560 4.195394e-04 1.299287e-01 0.8696517
## 8561 5.467470e-03 2.580770e-01 0.7364555
## 8566 6.998686e-03 1.195812e-01 0.8734202
## 8567 8.880529e-03 2.726054e-01 0.7185141
## 8569 4.461634e-06 5.698698e-01 0.4301257
## 8570 7.077315e-05 1.454349e-01 0.8544943
## 8571 9.798622e-02 1.971046e-01 0.7049092
## 8575 3.711827e-03 1.590776e-01 0.8372106
## 8580 1.424294e-11 1.602226e-01 0.8397774
## 8584 1.220783e-01 3.010714e-01 0.5768503
## 8587 2.649386e-02 2.624403e-01 0.7110658
## 8600 1.437552e-02 2.869800e-01 0.6986445
## 8603 8.890124e-05 6.796257e-02 0.9319485
## 8607 5.467470e-03 2.580770e-01 0.7364555
## 8623 1.263641e-03 1.795231e-01 0.8192132
## 8626 5.467470e-03 2.580770e-01 0.7364555
## 8627 9.943139e-04 2.201333e-01 0.7788724
## 8629 6.398843e-03 6.731522e-02 0.9262859
## 8630 1.992543e-03 1.765256e-01 0.8214819
## 8635 8.037790e-03 2.290158e-01 0.7629464
## 8637 1.952530e-02 2.355128e-01 0.7449619
## 8646 9.458093e-04 1.882437e-01 0.8108105
## 8649 8.809993e-04 1.924760e-01 0.8066430
## 8651 1.356956e-03 1.987153e-01 0.7999278
## 8652 1.598648e-03 2.195940e-01 0.7788074
## 8656 3.063922e-03 2.107025e-01 0.7862336
## 8664 6.310873e-03 2.273177e-01 0.7663715
## 8667 3.431506e-12 1.620810e-01 0.8379190
## 8669 3.254482e-02 3.320342e-01 0.6354210
## 8672 3.530439e-03 1.424103e-01 0.8540593
## 8680 9.419573e-04 1.875037e-01 0.8115543
## 8681 1.319676e-03 1.507700e-01 0.8479103
## 8682 1.977706e-02 2.746132e-01 0.7056097
## 8683 3.123488e-04 1.057236e-01 0.8939641
## 8691 2.994228e-02 3.038705e-01 0.6661872
## 8700 8.825442e-03 3.413432e-01 0.6498313
## 8701 5.715716e-03 2.266006e-01 0.7676837
## 8707 1.902469e-02 2.206611e-01 0.7603142
## 8711 1.124720e-06 2.569262e-01 0.7430727
## 8715 1.534071e-06 5.492208e-01 0.4507776
## 8716 3.251959e-03 1.873870e-01 0.8093610
## 8721 8.006920e-03 2.281687e-01 0.7638244
## 8722 8.743389e-03 3.107599e-01 0.6804968
## 8724 8.825442e-03 3.413432e-01 0.6498313
## 8725 8.825442e-03 3.413432e-01 0.6498313
## 8729 5.470581e-04 1.329175e-01 0.8665355
## 8730 4.284598e-03 2.484369e-01 0.7472785
## 8731 1.381885e-03 2.045724e-01 0.7940457
## 8733 5.470581e-04 1.329175e-01 0.8665355
## 8735 2.308240e-02 2.997117e-01 0.6772059
## 8743 5.466630e-09 3.604487e-01 0.6395513
## 8744 2.947076e-02 3.767842e-01 0.5937450
## 8747 4.491742e-03 2.613519e-01 0.7341564
## 8758 1.034251e-02 2.683677e-01 0.7212898
## 8759 3.192086e-03 3.173264e-01 0.6794815
## 8762 3.618661e-03 2.241404e-01 0.7722410
## 8764 3.347365e-03 2.110557e-01 0.7855969
## 8769 1.239944e-02 1.899504e-01 0.7976502
## 8772 3.347365e-03 2.110557e-01 0.7855969
## 8773 3.146433e-02 3.579385e-01 0.6105972
## 8774 7.912131e-04 1.160401e-01 0.8831687
## 8775 4.611469e-02 3.136272e-01 0.6402581
## 8783 6.706584e-02 3.105234e-01 0.6224108
## 8784 1.480469e-02 2.867820e-01 0.6984133
## 8786 1.884344e-02 3.473312e-01 0.6338254
## 8790 3.391907e-03 1.903328e-01 0.8062753
## 8796 6.805794e-03 2.018730e-01 0.7913213
## 8798 5.742821e-02 2.578048e-01 0.6847670
## 8799 1.261969e-01 6.381197e-02 0.8099911
## 8804 3.270129e-02 3.073007e-01 0.6599980
## 8805 3.360978e-03 1.285923e-01 0.8680468
## 8806 3.045773e-02 3.003476e-01 0.6691947
## 8807 4.300843e-02 3.069419e-01 0.6500497
## 8811 3.532596e-02 3.002015e-01 0.6644725
## 8817 1.669661e-03 3.620446e-01 0.6362857
## 8818 7.069731e-04 1.131256e-01 0.8861674
## 8819 1.531218e-02 3.530693e-01 0.6316185
## 8820 1.886669e-02 3.221562e-01 0.6589771
## 8826 3.511748e-03 2.514384e-01 0.7450498
## 8830 1.311754e-02 3.062480e-01 0.6806345
## 8832 1.941314e-04 6.760606e-02 0.9321998
## 8835 9.910567e-02 3.035095e-01 0.5973848
## 8836 4.674739e-03 1.949520e-01 0.8003733
## 8845 1.173551e-02 2.736297e-01 0.7146348
## 8847 2.269593e-03 1.856278e-01 0.8121026
## 8850 2.038732e-02 2.945954e-01 0.6850173
## 8851 2.990298e-03 2.511017e-01 0.7459080
## 8854 2.308240e-02 2.997117e-01 0.6772059
## 8860 5.447170e-03 2.571553e-01 0.7373975
## 8861 1.741050e-02 2.015148e-01 0.7810747
## 8862 8.825442e-03 3.413432e-01 0.6498313
## 8866 9.645072e-02 3.556765e-01 0.5478728
## 8867 2.158345e-18 7.266764e-02 0.9273324
## 8871 3.223288e-03 2.460941e-01 0.7506826
## 8872 1.146156e-02 2.363796e-01 0.7521589
## 8881 7.912131e-04 1.160401e-01 0.8831687
## 8882 5.713356e-03 3.111567e-01 0.6831300
## 8884 8.006920e-03 2.281687e-01 0.7638244
## 8891 8.006920e-03 2.281687e-01 0.7638244
## 8892 9.023031e-03 1.975226e-01 0.7934544
## 8893 5.447170e-03 2.571553e-01 0.7373975
## 8895 8.848331e-03 2.716556e-01 0.7194961
## 8896 1.255580e-02 3.514594e-01 0.6359848
## 8900 3.388418e-02 2.655740e-01 0.7005418
## 8903 1.625746e-02 3.089835e-01 0.6747590
## 8904 7.135603e-03 2.165705e-01 0.7762939
## 8905 8.848331e-03 2.716556e-01 0.7194961
## 8906 3.964413e-03 2.822086e-01 0.7138270
## 8907 3.251959e-03 1.873870e-01 0.8093610
## 8911 1.048177e-01 2.383143e-01 0.6568680
## 8919 1.168935e-02 2.630177e-01 0.7252930
## 8920 1.494180e-02 2.680024e-01 0.7170558
## 8922 2.148272e-03 2.365408e-01 0.7613109
## 8927 1.550070e-06 3.136277e-01 0.6863707
## 8935 1.091544e-02 2.142699e-01 0.7748146
## 8942 3.477419e-02 3.424948e-01 0.6227310
## 8945 1.038383e-03 1.180568e-01 0.8809048
## 8948 5.782104e-03 2.476342e-01 0.7465837
## 8949 1.603861e-03 2.115421e-01 0.7868541
## 8951 1.127834e-02 2.864853e-01 0.7022364
## 8952 2.016969e-03 2.686908e-01 0.7292922
## 8953 1.736490e-02 2.010060e-01 0.7816291
## 8955 2.302969e-02 2.990557e-01 0.6779146
## 8959 1.691079e-03 2.772856e-01 0.7210233
## 8961 4.726141e-03 1.674072e-01 0.8278667
## 8965 6.333473e-03 2.979208e-01 0.6957457
## 8967 1.719459e-02 3.581051e-01 0.6247003
## 8970 7.668757e-04 9.333436e-02 0.9058988
## 8971 3.135192e-04 1.070123e-01 0.8926742
## 8973 3.338544e-03 2.105196e-01 0.7861419
## 8978 2.696440e-03 3.040786e-01 0.6932250
## 8982 8.826906e-03 2.710236e-01 0.7201495
## 8984 5.433664e-03 2.565421e-01 0.7380242
## 8985 4.245927e-03 2.422536e-01 0.7535005
## 8986 4.297888e-03 2.731124e-01 0.7225897
## 8990 4.285341e-03 1.519205e-01 0.8437941
## 8992 4.105969e-02 2.758158e-01 0.6831245
## 8998 2.979058e-03 2.501934e-01 0.7468275
## 9001 2.214110e-03 2.106599e-01 0.7871260
## 9006 4.564735e-03 2.273292e-01 0.7681060
## 9011 9.188668e-03 2.583672e-01 0.7324441
## 9012 3.846241e-03 2.249826e-01 0.7711712
## 9013 3.946398e-03 1.903166e-01 0.8057370
## 9015 6.018485e-02 3.109048e-01 0.6289104
## 9017 1.870906e-02 2.755425e-01 0.7057484
## 9018 2.397983e-02 4.347891e-01 0.5412311
## 9021 5.060540e-11 2.558270e-01 0.7441730
## 9025 1.017314e-17 1.722304e-01 0.8277696
## 9033 7.976135e-03 2.273238e-01 0.7647001
## 9037 2.043628e-03 2.360201e-01 0.7619363
## 9041 5.249492e-03 2.343634e-01 0.7603871
## 9046 1.153737e-03 1.619265e-01 0.8369197
## 9049 2.272242e-09 1.368692e-01 0.8631308
## 9054 5.605967e-03 2.784444e-01 0.7159496
## 9057 5.426920e-03 2.562358e-01 0.7383373
## 9063 1.817431e-02 2.771877e-01 0.7046380
## 9076 4.440027e-03 1.717131e-01 0.8238469
## 9077 1.572675e-02 2.469184e-01 0.7373549
## 9079 1.464348e-10 2.547296e-01 0.7452704
## 9080 4.461651e-03 1.477169e-01 0.8478214
## 9083 6.207911e-09 2.509681e-01 0.7490319
## 9084 1.238792e-02 2.185224e-01 0.7690897
## 9090 3.586282e-03 2.528598e-01 0.7435539
## 9092 1.586379e-02 2.647875e-01 0.7193487
## 9095 6.012091e-02 3.105892e-01 0.6292899
## 9097 8.424503e-03 2.770004e-01 0.7145751
## 9098 1.201278e-01 3.178933e-01 0.5619789
## 9100 2.430096e-02 3.663188e-01 0.6093803
## 9101 6.076720e-03 1.404240e-01 0.8534993
## 9105 3.305931e-02 3.093085e-01 0.6576322
## 9108 2.935214e-02 3.753388e-01 0.5953091
## 9109 1.070316e-12 2.011098e-01 0.7988902
## 9117 1.295002e-02 2.400358e-01 0.7470142
## 9119 2.763581e-02 2.441218e-01 0.7282424
## 9127 3.193699e-04 7.234339e-02 0.9273372
## 9130 5.420181e-03 2.559298e-01 0.7386500
## 9133 1.620532e-02 2.285599e-01 0.7552348
## 9136 5.729824e-03 2.499094e-01 0.7443608
## 9139 5.716369e-02 2.566659e-01 0.6861704
## 9151 5.222238e-03 2.593426e-01 0.7354351
## 9153 6.961106e-03 2.876991e-01 0.7053398
## 9156 1.001307e-02 3.035550e-01 0.6864320
## 9158 9.666919e-03 2.802796e-01 0.7100535
## 9162 9.178493e-03 2.838390e-01 0.7069825
## 9163 3.187731e-02 2.988602e-01 0.6692625
## 9166 9.938834e-03 2.972840e-01 0.6927771
## 9170 2.477728e-02 3.469152e-01 0.6283075
## 9180 8.786694e-03 3.399091e-01 0.6513043
## 9182 5.438931e-04 1.321735e-01 0.8672826
## 9186 3.016760e-03 1.124522e-01 0.8845311
## 9187 2.970033e-02 3.033449e-01 0.6669548
## 9192 1.219437e-02 2.579914e-01 0.7298142
## 9194 3.327983e-03 2.416325e-01 0.7550395
## 9197 6.961106e-03 2.876991e-01 0.7053398
## 9199 4.281982e-02 3.056538e-01 0.6515264
## 9201 4.477722e-03 2.876413e-01 0.7078810
## 9202 5.438136e-03 3.234853e-01 0.6710766
## 9203 4.780243e-03 2.196578e-01 0.7755619
## 9205 2.297705e-02 2.984004e-01 0.6786225
## 9208 1.848532e-02 2.479753e-01 0.7335394
## 9209 1.435244e-02 1.071662e-01 0.8784813
## 9214 3.925824e-02 2.920202e-01 0.6687215
## 9216 3.569814e-03 2.067472e-01 0.7896830
## 9217 1.876269e-02 3.459083e-01 0.6353290
## 9219 5.420181e-03 2.559298e-01 0.7386500
## 9220 9.823008e-04 1.087315e-01 0.8902862
## 9224 1.668737e-03 2.296886e-01 0.7686427
## 9229 4.800614e-09 2.103248e-01 0.7896752
## 9234 2.917454e-02 3.731739e-01 0.5976516
## 9235 2.325207e-02 3.468991e-01 0.6298488
## 9237 6.024820e-03 1.392642e-01 0.8547109
## 9238 1.146424e-03 5.407706e-02 0.9447765
## 9246 2.570706e-02 3.667114e-01 0.6075815
## 9249 3.603513e-03 1.642237e-01 0.8321728
## 9252 8.998951e-11 1.016944e-01 0.8983056
## 9253 7.699846e-03 2.632016e-01 0.7290985
## 9254 8.728736e-03 3.377631e-01 0.6535082
## 9257 1.864187e-02 3.437787e-01 0.6375795
## 9262 2.281954e-02 2.964392e-01 0.6807413
## 9266 4.504257e-04 2.118716e-01 0.7876780
## 9267 6.940599e-03 1.906892e-01 0.8023702
## 9271 5.776966e-03 3.156961e-01 0.6785269
## 9272 5.379867e-03 2.540985e-01 0.7405216
## 9274 6.430319e-12 1.518784e-01 0.8481216
## 9277 6.307811e-03 2.175222e-01 0.7761700
## 9279 3.564197e-03 4.211065e-01 0.5753293
## 9280 6.911565e-03 2.857329e-01 0.7073556
## 9281 2.777684e-02 1.491503e-01 0.8230729
## 9282 1.603752e-03 2.410587e-01 0.7573375
## 9283 3.245644e-02 2.430685e-01 0.7244751
## 9288 8.215597e-03 1.909093e-01 0.8008751
## 9290 7.145014e-03 1.969609e-01 0.7958941
## 9294 8.510511e-03 1.343801e-01 0.8571094
## 9305 3.267318e-04 1.221332e-01 0.8775400
## 9318 8.159970e-03 2.779042e-01 0.7139358
## 9319 1.885498e-02 2.787308e-01 0.7024143
## 9323 1.925163e-03 1.447988e-01 0.8532760
## 9325 8.251374e-03 2.860474e-01 0.7057012
## 9328 5.373167e-03 2.537942e-01 0.7408327
## 9329 3.846329e-03 1.946603e-01 0.8014934
## 9330 9.279382e-04 1.848095e-01 0.8142625
## 9336 3.299066e-03 2.081190e-01 0.7885819
## 9338 1.239929e-02 4.249288e-01 0.5626719
## 9344 2.517468e-01 8.361863e-02 0.6646345
## 9345 8.329687e-03 2.244503e-01 0.7672200
## 9346 1.092219e-02 2.929361e-01 0.6961417
## 9351 4.713854e-03 2.258824e-01 0.7694037
## 9352 2.917015e-03 2.271560e-01 0.7699270
## 9353 1.735378e-03 2.490663e-01 0.7491984
## 9360 1.716681e-10 1.090367e-01 0.8909633
## 9362 1.565775e-02 2.803682e-01 0.7039740
## 9363 1.087755e-02 2.265811e-01 0.7625413
## 9366 9.179467e-02 2.866594e-01 0.6215460
## 9369 7.249739e-03 1.622489e-01 0.8305013
## 9373 8.709460e-03 3.370492e-01 0.6542414
## 9377 1.510297e-03 2.121627e-01 0.7863270
## 9378 2.763641e-07 2.277371e-01 0.7722626
## 9383 1.784742e-02 3.319535e-01 0.6501991
## 9384 4.379317e-03 2.415736e-01 0.7540471
## 9386 8.684091e-02 3.215073e-01 0.5916518
## 9387 5.596285e-03 2.062426e-01 0.7881611
## 9388 2.276717e-02 2.957869e-01 0.6814459
## 9390 6.093627e-03 4.129964e-01 0.5809099
## 9393 5.212692e-03 2.363337e-01 0.7584536
## 9401 8.226571e-03 2.090712e-01 0.7827023
## 9402 8.098392e-03 2.969218e-01 0.6949798
## 9404 5.366474e-03 2.534900e-01 0.7411435
## 9405 1.161283e-09 2.997095e-01 0.7002905
## 9409 8.098392e-03 2.969218e-01 0.6949798
## 9413 7.680963e-03 2.625810e-01 0.7297380
## 9414 3.427268e-03 2.279570e-01 0.7686157
## 9418 3.983682e-03 2.661420e-01 0.7298743
## 9419 5.388951e-03 3.206812e-01 0.6739298
## 9425 1.172026e-03 1.822898e-01 0.8165382
## 9430 2.689505e-02 3.859602e-01 0.5871447
## 9431 2.266515e-03 2.750497e-01 0.7226838
## 9434 8.709460e-03 3.370492e-01 0.6542414
## 9435 6.274657e-03 2.505007e-01 0.7432247
## 9436 3.294307e-03 2.392782e-01 0.7574274
## 9437 5.636329e-03 3.308126e-01 0.6635511
## 9439 8.709460e-03 3.370492e-01 0.6542414
## 9442 2.020757e-03 2.334372e-01 0.7645421
## 9443 8.709460e-03 3.370492e-01 0.6542414
## 9446 5.366474e-03 2.534900e-01 0.7411435
## 9447 3.294307e-03 2.392782e-01 0.7574274
## 9448 1.824078e-02 3.773143e-01 0.6044450
## 9450 3.511646e-02 3.545254e-01 0.6103581
## 9452 2.101255e-03 2.500237e-01 0.7478751
## 9454 1.821874e-02 3.583721e-01 0.6234092
## 9462 2.232742e-03 1.827178e-01 0.8150495
## 9464 5.366474e-03 2.534900e-01 0.7411435
## 9465 2.349910e-03 3.597181e-02 0.9616783
## 9466 6.656813e-03 3.070616e-01 0.6862816
## 9467 6.288380e-03 2.180519e-01 0.7756597
## 9472 1.991042e-02 2.771946e-01 0.7028950
## 9473 4.987837e-03 2.812182e-01 0.7137939
## 9482 3.222945e-02 3.030535e-01 0.6647170
## 9486 1.655226e-02 2.156827e-01 0.7677650
## 9491 3.653168e-03 2.051768e-01 0.7911700
## 9492 2.274101e-02 2.954611e-01 0.6817979
## 9497 6.803033e-02 3.569556e-01 0.5750141
## 9504 3.409442e-03 2.525370e-01 0.7440535
## 9505 1.889141e-03 2.043439e-01 0.7937669
## 9506 2.274101e-02 2.954611e-01 0.6817979
## 9510 5.622812e-02 2.329807e-01 0.7107911
## 9516 4.869323e-02 3.530240e-01 0.5982827
## 9517 2.198034e-02 2.202617e-01 0.7577579
## 9519 2.229692e-03 1.824769e-01 0.8152934
## 9521 2.881061e-03 1.969510e-01 0.8001680
## 9530 8.113551e-02 2.130791e-01 0.7057854
## 9534 2.874200e-03 1.764691e-01 0.8206567
## 9541 5.827450e-03 3.065716e-01 0.6876009
## 9545 9.834657e-03 2.942935e-01 0.6958718
## 9548 9.335334e-09 3.862422e-01 0.6137578
## 9549 1.998783e-02 2.535126e-01 0.7264995
view(predictions1_n)

predictions2_n <- predict(shorted_test2_n, newdata = test_data_n, type = "probs")
predictions2_n
##                 1            2         3
## 2    9.755200e-03 2.294170e-01 0.7608278
## 4    8.747643e-03 2.109797e-01 0.7802727
## 8    1.125571e-02 2.552095e-01 0.7335348
## 13   8.135728e-03 1.993098e-01 0.7925545
## 16   6.331161e-03 1.626322e-01 0.8310366
## 18   6.847652e-03 1.734918e-01 0.8196606
## 29   1.395714e-02 2.971861e-01 0.6888567
## 30   1.401936e-02 2.980915e-01 0.6878891
## 32   1.035190e-02 2.399035e-01 0.7497446
## 36   1.785522e-02 3.492829e-01 0.6328619
## 39   1.148278e-02 2.589498e-01 0.7295675
## 41   1.105435e-02 2.518579e-01 0.7370877
## 43   1.311726e-02 2.847042e-01 0.7021786
## 48   7.131746e-03 1.793381e-01 0.8135301
## 49   1.634393e-02 3.301490e-01 0.6535071
## 55   8.840076e-03 2.127107e-01 0.7784492
## 58   1.165899e-02 2.618241e-01 0.7265169
## 59   1.246545e-02 2.746732e-01 0.7128613
## 60   1.368653e-02 2.932175e-01 0.6930959
## 62   5.770687e-03 1.504992e-01 0.8437301
## 63   8.017799e-03 1.970180e-01 0.7949642
## 71   1.096912e-02 2.504294e-01 0.7386015
## 73   3.575228e-03 9.915815e-02 0.8972666
## 80   5.363661e-03 1.414515e-01 0.8531848
## 84   1.234894e-02 2.728473e-01 0.7148038
## 86   9.444326e-03 2.238283e-01 0.7667273
## 87   1.017536e-02 2.368333e-01 0.7529913
## 98   1.137409e-02 2.571645e-01 0.7314614
## 102  7.040243e-03 1.774647e-01 0.8154950
## 104  7.441535e-03 1.856135e-01 0.8069450
## 107  3.247144e-03 9.091872e-02 0.9058341
## 109  7.533915e-03 1.874650e-01 0.8050010
## 110  1.110478e-02 2.527004e-01 0.7361948
## 113  9.137978e-03 2.182345e-01 0.7726275
## 123  7.853259e-03 1.937967e-01 0.7983500
## 125  1.159636e-02 2.608054e-01 0.7275982
## 136  1.417404e-02 3.003314e-01 0.6854946
## 137  1.232838e-02 2.725240e-01 0.7151476
## 138  2.246083e-02 4.005717e-01 0.5769675
## 143  1.134984e-02 2.567650e-01 0.7318852
## 145  1.124924e-02 2.551023e-01 0.7336484
## 147  2.228417e-02 3.987782e-01 0.5789377
## 149  4.972886e-03 1.325710e-01 0.8624561
## 151  1.342543e-02 2.893408e-01 0.6972338
## 153  1.612007e-02 3.272053e-01 0.6566747
## 160  1.785522e-02 3.492829e-01 0.6328619
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## 1182 3.458367e-03 9.624132e-02 0.9003003
## 1196 1.881606e-02 3.608135e-01 0.6203704
## 1198 5.869813e-03 1.526722e-01 0.8414580
## 1199 7.074781e-03 1.781729e-01 0.8147523
## 1205 3.486268e-03 9.693953e-02 0.8995742
## 1206 1.767314e-02 3.470437e-01 0.6352831
## 1216 1.283273e-02 2.803634e-01 0.7068039
## 1218 1.789410e-02 3.497587e-01 0.6323472
## 1220 7.229577e-03 1.813310e-01 0.8114394
## 1226 1.101644e-02 2.512231e-01 0.7377605
## 1229 9.649075e-03 2.275190e-01 0.7628319
## 1236 2.627982e-03 7.493141e-02 0.9224406
## 1237 1.015554e-02 2.364869e-01 0.7533575
## 1238 8.670453e-03 2.095278e-01 0.7818018
## 1242 2.367729e-03 6.803464e-02 0.9295976
## 1243 1.468663e-02 3.076414e-01 0.6776720
## 1245 8.077914e-03 1.981880e-01 0.7937341
## 1251 1.574023e-02 3.221431e-01 0.6621167
## 1253 1.383375e-02 2.953826e-01 0.6907836
## 1255 1.066452e-02 2.452748e-01 0.7440607
## 1256 9.360201e-03 2.223009e-01 0.7683389
## 1258 9.933126e-03 2.325766e-01 0.7574902
## 1259 1.201576e-02 2.675697e-01 0.7204145
## 1261 1.612007e-02 3.272053e-01 0.6566747
## 1264 1.003592e-02 2.343894e-01 0.7555747
## 1265 4.993242e-03 1.330384e-01 0.8619683
## 1267 1.022810e-03 3.061512e-02 0.9683621
## 1270 1.055894e-02 2.434700e-01 0.7459710
## 1271 9.525957e-03 2.253043e-01 0.7651697
## 1275 1.064025e-02 2.448607e-01 0.7444991
## 1286 1.357594e-02 2.915812e-01 0.6948429
## 1298 8.853991e-03 2.129706e-01 0.7781754
## 1299 1.785522e-02 3.492829e-01 0.6328619
## 1305 1.368653e-02 2.932175e-01 0.6930959
## 1307 1.133944e-02 2.565934e-01 0.7320671
## 1312 9.704598e-03 2.285133e-01 0.7617821
## 1318 1.619876e-02 3.282433e-01 0.6555579
## 1322 2.221021e-02 3.980236e-01 0.5797662
## 1325 1.335945e-02 2.883537e-01 0.6982868
## 1327 1.181950e-02 2.644212e-01 0.7237593
## 1335 1.171987e-02 2.628117e-01 0.7254685
## 1340 7.990287e-03 1.964813e-01 0.7955284
## 1343 1.041821e-02 2.410497e-01 0.7485321
## 1347 9.611569e-03 2.268458e-01 0.7635427
## 1348 1.298765e-02 2.827339e-01 0.7042784
## 1349 2.001793e-02 3.745915e-01 0.6053906
## 1353 5.299673e-03 1.400105e-01 0.8546898
## 1356 2.477663e-03 7.096097e-02 0.9265614
## 1370 1.417404e-02 3.003314e-01 0.6854946
## 1372 7.441336e-03 1.856095e-01 0.8069492
## 1376 1.110478e-02 2.527004e-01 0.7361948
## 1380 1.461307e-02 3.066028e-01 0.6787841
## 1381 1.014264e-02 2.362613e-01 0.7535961
## 1383 1.360413e-02 2.919991e-01 0.6943968
## 1386 1.060238e-02 2.442137e-01 0.7451840
## 1389 5.797391e-03 1.510857e-01 0.8431169
## 1395 1.066452e-02 2.452748e-01 0.7440607
## 1399 1.286253e-02 2.808207e-01 0.7063168
## 1405 7.767487e-03 1.921065e-01 0.8001260
## 1412 4.119918e-03 1.124970e-01 0.8833831
## 1413 1.243873e-02 2.742553e-01 0.7133060
## 1419 8.762729e-03 2.112627e-01 0.7799745
## 1425 1.100914e-02 2.511008e-01 0.7378901
## 1426 1.939338e-02 3.675187e-01 0.6130879
## 1427 1.181950e-02 2.644212e-01 0.7237593
## 1430 1.133090e-02 2.564526e-01 0.7322165
## 1439 1.151453e-02 2.594696e-01 0.7290159
## 1451 9.743871e-03 2.292149e-01 0.7610412
## 1453 6.904270e-03 1.746640e-01 0.8184318
## 1454 3.065879e-02 4.716490e-01 0.4976922
## 1465 9.836554e-03 2.308652e-01 0.7592982
## 1471 6.296356e-03 1.618895e-01 0.8318141
## 1472 1.516469e-02 3.143068e-01 0.6705285
## 1475 4.104979e-03 1.121367e-01 0.8837584
## 1477 9.933126e-03 2.325766e-01 0.7574902
## 1478 1.220905e-02 2.706417e-01 0.7171493
## 1479 1.610006e-02 3.269408e-01 0.6569592
## 1480 7.042091e-03 1.775027e-01 0.8154552
## 1483 7.986456e-03 1.964065e-01 0.7956071
## 1491 1.259732e-02 2.767276e-01 0.7106751
## 1498 8.346112e-03 2.033637e-01 0.7882902
## 1501 1.785522e-02 3.492829e-01 0.6328619
## 1505 9.716880e-03 2.287329e-01 0.7615503
## 1506 1.181950e-02 2.644212e-01 0.7237593
## 1507 1.213661e-02 2.694937e-01 0.7183697
## 1509 1.014087e-02 2.362304e-01 0.7536287
## 1510 1.066452e-02 2.452748e-01 0.7440607
## 1511 6.625180e-03 1.688511e-01 0.8245237
## 1519 1.047876e-02 2.420931e-01 0.7474281
## 1525 8.218659e-03 2.009131e-01 0.7908682
## 1526 6.186938e-03 1.595454e-01 0.8342677
## 1534 8.095724e-03 1.985340e-01 0.7933703
## 1535 1.160683e-02 2.609759e-01 0.7274173
## 1537 8.151368e-03 1.996127e-01 0.7922359
## 1538 1.574023e-02 3.221431e-01 0.6621167
## 1540 1.516378e-02 3.142943e-01 0.6705419
## 1542 2.286777e-02 4.046551e-01 0.5724771
## 1543 1.071673e-02 2.461637e-01 0.7431196
## 1545 8.760609e-03 2.112230e-01 0.7800164
## 1559 1.181950e-02 2.644212e-01 0.7237593
## 1560 8.250370e-03 2.015243e-01 0.7902253
## 1561 9.111186e-03 2.177411e-01 0.7731477
## 1562 1.329024e-02 2.873151e-01 0.6993947
## 1566 1.284450e-02 2.805441e-01 0.7066114
## 1568 2.687387e-03 7.649076e-02 0.9208219
## 1573 1.110478e-02 2.527004e-01 0.7361948
## 1582 7.638563e-03 1.895516e-01 0.8028098
## 1593 1.066452e-02 2.452748e-01 0.7440607
## 1603 1.213661e-02 2.694937e-01 0.7183697
## 1604 1.163230e-02 2.613904e-01 0.7269773
## 1610 1.106815e-02 2.520886e-01 0.7368432
## 1614 6.138201e-03 1.584968e-01 0.8353650
## 1622 1.347363e-02 2.900599e-01 0.6964664
## 1623 1.066452e-02 2.452748e-01 0.7440607
## 1625 5.629516e-03 1.473841e-01 0.8469864
## 1627 1.578682e-02 3.227686e-01 0.6614446
## 1633 1.181950e-02 2.644212e-01 0.7237593
## 1635 1.753588e-02 3.453440e-01 0.6371201
## 1637 4.226042e-03 1.150477e-01 0.8807263
## 1645 1.105397e-02 2.518515e-01 0.7370946
## 1647 5.457900e-03 1.435644e-01 0.8509777
## 1648 4.703592e-03 1.263374e-01 0.8689590
## 1652 9.735942e-03 2.290734e-01 0.7611907
## 1653 8.021796e-03 1.970959e-01 0.7948823
## 1659 8.905612e-03 2.139331e-01 0.7771613
## 1664 7.267194e-03 1.820946e-01 0.8106383
## 1665 1.352000e-02 2.907504e-01 0.6957296
## 1670 1.147590e-02 2.588371e-01 0.7296870
## 1672 2.298307e-02 4.058001e-01 0.5712168
## 1673 1.504363e-02 3.126326e-01 0.6723238
## 1688 1.181950e-02 2.644212e-01 0.7237593
## 1691 1.659020e-02 3.333538e-01 0.6500560
## 1695 1.347363e-02 2.900599e-01 0.6964664
## 1700 1.326058e-02 2.868689e-01 0.6998705
## 1702 1.225597e-02 2.713831e-01 0.7163610
## 1703 9.523232e-03 2.252551e-01 0.7652216
## 1709 1.435187e-02 3.028869e-01 0.6827612
## 1725 1.050175e-02 2.424885e-01 0.7470098
## 1735 8.896096e-03 2.137559e-01 0.7773480
## 1738 2.065575e-02 3.816274e-01 0.5977169
## 1743 9.193070e-03 2.192469e-01 0.7715601
## 1748 1.408991e-02 2.991151e-01 0.6867950
## 1750 8.718194e-03 2.104264e-01 0.7808554
## 1755 8.902007e-03 2.138660e-01 0.7772320
## 1757 1.004329e-02 2.345189e-01 0.7554378
## 1758 7.794766e-03 1.926449e-01 0.7995604
## 1760 8.033060e-03 1.973154e-01 0.7946516
## 1761 1.050650e-02 2.425701e-01 0.7469234
## 1765 1.374577e-02 2.940906e-01 0.6921637
## 1769 1.670391e-02 3.348220e-01 0.6484741
## 1771 1.066452e-02 2.452748e-01 0.7440607
## 1772 1.041187e-02 2.409403e-01 0.7486478
## 1777 1.159371e-02 2.607622e-01 0.7276441
## 1781 1.181950e-02 2.644212e-01 0.7237593
## 1787 7.922718e-03 1.951599e-01 0.7969174
## 1789 1.110478e-02 2.527004e-01 0.7361948
## 1790 1.368653e-02 2.932175e-01 0.6930959
## 1798 9.716880e-03 2.287329e-01 0.7615503
## 1803 5.636920e-03 1.475481e-01 0.8468150
## 1804 8.490995e-03 2.061299e-01 0.7853791
## 1807 1.599246e-02 3.255142e-01 0.6584934
## 1808 1.442072e-02 3.038707e-01 0.6817086
## 1809 1.525945e-02 3.156111e-01 0.6691295
## 1811 6.265894e-03 1.612383e-01 0.8324958
## 1820 9.525957e-03 2.253043e-01 0.7651697
## 1821 8.853991e-03 2.129706e-01 0.7781754
## 1828 1.055894e-02 2.434700e-01 0.7459710
## 1829 1.181950e-02 2.644212e-01 0.7237593
## 1834 1.347363e-02 2.900599e-01 0.6964664
## 1837 9.488969e-03 2.246363e-01 0.7658747
## 1838 1.743522e-02 3.440912e-01 0.6384736
## 1845 4.378485e-03 1.186848e-01 0.8769367
## 1848 1.206979e-02 2.684312e-01 0.7194990
## 1849 1.723565e-02 3.415909e-01 0.6411735
## 1855 5.855898e-03 1.523678e-01 0.8417763
## 1862 1.181950e-02 2.644212e-01 0.7237593
## 1865 2.741657e-02 4.461382e-01 0.5264452
## 1869 1.462840e-02 3.068195e-01 0.6785521
## 1870 1.284801e-02 2.805979e-01 0.7065541
## 1871 1.087170e-02 2.487891e-01 0.7403392
## 1875 1.213286e-02 2.694342e-01 0.7184330
## 1876 1.066452e-02 2.452748e-01 0.7440607
## 1878 1.144819e-02 2.583827e-01 0.7301691
## 1881 8.360297e-03 2.036354e-01 0.7880043
## 1883 4.962793e-03 1.323391e-01 0.8626981
## 1884 1.156627e-02 2.603148e-01 0.7281189
## 1885 6.592410e-03 1.681629e-01 0.8252447
## 1887 1.077034e-02 2.470743e-01 0.7421554
## 1890 9.071479e-03 2.170087e-01 0.7739198
## 1891 1.474057e-02 3.084008e-01 0.6768587
## 1893 6.904270e-03 1.746640e-01 0.8184318
## 1894 1.208875e-02 2.687330e-01 0.7191782
## 1895 1.766883e-02 3.469905e-01 0.6353407
## 1896 8.071530e-03 1.980639e-01 0.7938645
## 1898 8.219227e-03 2.009240e-01 0.7908567
## 1900 1.066452e-02 2.452748e-01 0.7440607
## 1901 4.682823e-03 1.258527e-01 0.8694644
## 1912 5.963716e-03 1.547198e-01 0.8393165
## 1914 1.181950e-02 2.644212e-01 0.7237593
## 1915 1.753588e-02 3.453440e-01 0.6371201
## 1917 1.128473e-02 2.556898e-01 0.7330254
## 1918 1.785522e-02 3.492829e-01 0.6328619
## 1919 1.181950e-02 2.644212e-01 0.7237593
## 1923 4.990288e-03 1.329706e-01 0.8620391
## 1924 8.760609e-03 2.112230e-01 0.7800164
## 1926 1.713436e-02 3.403136e-01 0.6425520
## 1929 1.162112e-02 2.612085e-01 0.7271704
## 1931 8.902007e-03 2.138660e-01 0.7772320
## 1933 1.429856e-02 3.021229e-01 0.6835785
## 1936 1.035271e-02 2.399175e-01 0.7497298
## 1937 1.008045e-02 2.351716e-01 0.7547480
## 1939 1.368653e-02 2.932175e-01 0.6930959
## 1940 1.031717e-02 2.393016e-01 0.7503812
## 1942 1.119690e-02 2.542340e-01 0.7345691
## 1948 1.198963e-02 2.671521e-01 0.7208582
## 1956 1.197190e-02 2.668686e-01 0.7211595
## 1957 9.814123e-03 2.304665e-01 0.7597194
## 1958 9.758197e-03 2.294705e-01 0.7607713
## 1961 9.871998e-03 2.314943e-01 0.7586337
## 1968 1.561076e-02 3.203978e-01 0.6639914
## 1969 9.716880e-03 2.287329e-01 0.7615503
## 1971 2.966705e-03 8.374967e-02 0.9132836
## 1972 1.093599e-02 2.498724e-01 0.7391916
## 1975 8.352707e-03 2.034901e-01 0.7881572
## 1979 8.902007e-03 2.138660e-01 0.7772320
## 1981 7.077402e-03 1.782266e-01 0.8146960
## 1985 6.959872e-03 1.758117e-01 0.8172284
## 1986 1.107937e-02 2.522761e-01 0.7366445
## 1988 7.716761e-03 1.911033e-01 0.8011799
## 1989 7.723425e-03 1.912353e-01 0.8010413
## 1990 3.858518e-03 1.061477e-01 0.8899938
## 1991 7.986456e-03 1.964065e-01 0.7956071
## 1994 1.081639e-02 2.478544e-01 0.7413292
## 1995 2.989088e-03 8.432620e-02 0.9126847
## 2000 8.905612e-03 2.139331e-01 0.7771613
## 2001 1.346484e-02 2.899290e-01 0.6966061
## 2002 1.165750e-02 2.618000e-01 0.7265425
## 2007 1.755734e-02 3.456105e-01 0.6368322
## 2014 1.468663e-02 3.076414e-01 0.6776720
## 2016 7.173399e-03 1.801879e-01 0.8126387
## 2024 2.194906e-02 3.953408e-01 0.5827101
## 2026 1.267777e-02 2.779746e-01 0.7093476
## 2027 6.620710e-03 1.687573e-01 0.8246220
## 2028 1.163298e-02 2.614014e-01 0.7269656
## 2029 1.172553e-02 2.629032e-01 0.7253712
## 2030 1.300681e-02 2.830261e-01 0.7039671
## 2032 1.119078e-02 2.541323e-01 0.7346769
## 2039 1.417404e-02 3.003314e-01 0.6854946
## 2045 1.355145e-02 2.912177e-01 0.6952308
## 2047 1.785522e-02 3.492829e-01 0.6328619
## 2049 1.785522e-02 3.492829e-01 0.6328619
## 2050 1.066452e-02 2.452748e-01 0.7440607
## 2051 6.687811e-03 1.701632e-01 0.8231490
## 2055 1.015352e-02 2.364517e-01 0.7533947
## 2062 6.077649e-03 1.571901e-01 0.8367322
## 2064 7.726808e-03 1.913022e-01 0.8009710
## 2065 1.062782e-02 2.446485e-01 0.7447237
## 2068 1.881148e-02 3.607597e-01 0.6204288
## 2070 1.066452e-02 2.452748e-01 0.7440607
## 2079 1.155240e-02 2.600883e-01 0.7283593
## 2089 1.066452e-02 2.452748e-01 0.7440607
## 2091 3.631204e-03 1.005483e-01 0.8958205
## 2096 1.326267e-02 2.869004e-01 0.6998370
## 2098 1.440754e-02 3.036826e-01 0.6819098
## 2106 1.068321e-02 2.455933e-01 0.7437235
## 2107 1.090695e-02 2.493835e-01 0.7397096
## 2111 8.302435e-03 2.025257e-01 0.7891719
## 2113 8.152202e-03 1.996288e-01 0.7922189
## 2116 8.023104e-03 1.971214e-01 0.7948555
## 2125 8.645982e-03 2.090663e-01 0.7822877
## 2127 1.248446e-02 2.749700e-01 0.7125455
## 2130 1.189223e-02 2.655914e-01 0.7225164
## 2133 1.753588e-02 3.453440e-01 0.6371201
## 2134 1.825809e-02 3.541754e-01 0.6275665
## 2136 9.111186e-03 2.177411e-01 0.7731477
## 2137 2.121107e-02 3.876045e-01 0.5911845
## 2142 1.066452e-02 2.452748e-01 0.7440607
## 2143 8.194309e-03 2.004431e-01 0.7913626
## 2148 3.241441e-03 9.077411e-02 0.9059844
## 2153 1.197264e-02 2.668805e-01 0.7211469
## 2155 1.215900e-02 2.698489e-01 0.7179921
## 2156 3.085640e-03 8.680449e-02 0.9101099
## 2160 8.521040e-03 2.067010e-01 0.7847780
## 2163 1.170262e-02 2.625321e-01 0.7257653
## 2164 1.110478e-02 2.527004e-01 0.7361948
## 2174 1.132699e-02 2.563880e-01 0.7322850
## 2182 2.149951e-02 3.906558e-01 0.5878447
## 2198 2.065575e-02 3.816274e-01 0.5977169
## 2205 6.521095e-03 1.666609e-01 0.8268181
## 2207 1.624569e-02 3.288608e-01 0.6548935
## 2210 1.266017e-02 2.777022e-01 0.7096377
## 2212 1.858676e-02 3.581046e-01 0.6233086
## 2214 7.533915e-03 1.874650e-01 0.8050010
## 2218 2.429615e-02 4.184776e-01 0.5572263
## 2219 5.558676e-03 1.458118e-01 0.8486295
## 2221 1.374577e-02 2.940906e-01 0.6921637
## 2223 5.798834e-03 1.511174e-01 0.8430838
## 2231 6.984489e-03 1.763188e-01 0.8166967
## 2233 7.042091e-03 1.775027e-01 0.8154552
## 2239 6.371945e-03 1.635008e-01 0.8301273
## 2246 1.059608e-02 2.441059e-01 0.7452981
## 2248 6.029112e-03 1.561396e-01 0.8378313
## 2250 6.989477e-03 1.764214e-01 0.8165891
## 2252 1.087801e-02 2.488956e-01 0.7402264
## 2255 1.215900e-02 2.698489e-01 0.7179921
## 2258 1.565127e-02 3.209449e-01 0.6634038
## 2259 1.002857e-02 2.342600e-01 0.7557114
## 2261 8.957290e-03 2.148942e-01 0.7761486
## 2264 1.560992e-02 3.203865e-01 0.6640036
## 2266 1.736347e-02 3.431947e-01 0.6394418
## 2269 7.922718e-03 1.951599e-01 0.7969174
## 2275 9.741001e-03 2.291637e-01 0.7610953
## 2280 8.248634e-03 2.014909e-01 0.7902605
## 2286 7.387152e-03 1.845193e-01 0.8080935
## 2288 8.060793e-03 1.978552e-01 0.7940841
## 2293 8.412493e-03 2.046337e-01 0.7869538
## 2297 1.439704e-02 3.035327e-01 0.6820702
## 2303 1.847042e-02 3.567200e-01 0.6248096
## 2305 9.302771e-03 2.212544e-01 0.7694429
## 2308 2.342025e-02 4.100941e-01 0.5664857
## 2309 5.377018e-03 1.417516e-01 0.8528713
## 2312 9.831597e-03 2.307771e-01 0.7593913
## 2313 1.951582e-02 3.689198e-01 0.6115643
## 2319 4.593030e-03 1.237507e-01 0.8716563
## 2323 6.986714e-03 1.763646e-01 0.8166487
## 2328 6.380722e-03 1.636874e-01 0.8299318
## 2332 5.309015e-03 1.402212e-01 0.8544697
## 2333 1.050881e-02 2.426099e-01 0.7468813
## 2334 4.190603e-03 1.141976e-01 0.8816118
## 2337 1.522656e-02 3.151590e-01 0.6696145
## 2339 4.473749e-03 1.209418e-01 0.8745844
## 2343 9.069820e-03 2.169781e-01 0.7739521
## 2344 1.141891e-02 2.579018e-01 0.7306792
## 2346 1.572367e-02 3.219203e-01 0.6623560
## 2352 1.431589e-02 3.023716e-01 0.6833125
## 2355 1.132589e-02 2.563699e-01 0.7323042
## 2359 2.276055e-02 4.035857e-01 0.5736538
## 2368 4.125587e-03 1.126336e-01 0.8832408
## 2371 1.633733e-02 3.300626e-01 0.6536000
## 2374 3.728752e-03 1.029602e-01 0.8933111
## 2375 5.776051e-03 1.506171e-01 0.8436069
## 2376 2.240400e-02 3.999961e-01 0.5775999
## 2381 5.956765e-03 1.545686e-01 0.8394747
## 2382 1.142147e-02 2.579439e-01 0.7306346
## 2383 3.569419e-03 9.901361e-02 0.8974170
## 2395 1.820819e-02 3.535739e-01 0.6282179
## 2396 1.129075e-02 2.557894e-01 0.7329198
## 2398 4.561818e-03 1.230175e-01 0.8724207
## 2401 5.322312e-03 1.405209e-01 0.8541568
## 2405 9.378736e-03 2.226380e-01 0.7679833
## 2411 1.051628e-02 2.427381e-01 0.7467456
## 2412 5.958331e-03 1.546026e-01 0.8394390
## 2418 1.763247e-02 3.465412e-01 0.6358263
## 2427 7.009619e-03 1.768357e-01 0.8161547
## 2430 5.248311e-03 1.388502e-01 0.8559015
## 2434 1.162220e-02 2.612261e-01 0.7271517
## 2435 6.275950e-03 1.614534e-01 0.8322707
## 2438 5.917489e-03 1.537131e-01 0.8403694
## 2439 1.032081e-02 2.393647e-01 0.7503144
## 2446 7.746500e-03 1.916918e-01 0.8005617
## 2454 2.841673e-03 8.051513e-02 0.9166432
## 2456 1.009310e-02 2.353936e-01 0.7545133
## 2458 4.623403e-03 1.244629e-01 0.8709137
## 2459 1.335709e-02 2.883184e-01 0.6983245
## 2462 9.569540e-03 2.260899e-01 0.7643406
## 2466 1.143752e-02 2.582076e-01 0.7303549
## 2472 1.105209e-02 2.518201e-01 0.7371278
## 2475 1.093862e-02 2.499166e-01 0.7391448
## 2476 5.523477e-03 1.450282e-01 0.8494483
## 2478 1.745390e-02 3.443241e-01 0.6382220
## 2481 8.604856e-03 2.082894e-01 0.7831058
## 2484 1.331023e-02 2.876154e-01 0.6990743
## 2491 8.781168e-03 2.116085e-01 0.7796104
## 2495 8.863263e-03 2.131437e-01 0.7779931
## 2496 1.494835e-02 3.113084e-01 0.6737432
## 2498 8.313328e-03 2.027349e-01 0.7889518
## 2499 7.746500e-03 1.916918e-01 0.8005617
## 2500 2.491045e-02 4.241881e-01 0.5509014
## 2501 4.561818e-03 1.230175e-01 0.8724207
## 2504 1.092508e-02 2.496887e-01 0.7393862
## 2505 9.351544e-03 2.221433e-01 0.7685052
## 2507 7.770681e-03 1.921696e-01 0.8000598
## 2510 1.176346e-02 2.635167e-01 0.7247198
## 2511 5.556547e-03 1.457644e-01 0.8486790
## 2516 1.135096e-02 2.567835e-01 0.7318655
## 2518 1.157714e-02 2.604920e-01 0.7279308
## 2519 1.124446e-02 2.550231e-01 0.7337324
## 2522 1.201136e-02 2.674994e-01 0.7204893
## 2524 1.360513e-02 2.920139e-01 0.6943810
## 2526 1.148508e-02 2.589874e-01 0.7295275
## 2530 6.975520e-03 1.761341e-01 0.8168904
## 2537 9.695042e-03 2.283424e-01 0.7619626
## 2546 3.933070e-03 1.079682e-01 0.8880987
## 2553 4.296473e-03 1.167320e-01 0.8789715
## 2564 1.054827e-02 2.432871e-01 0.7461646
## 2566 1.502731e-02 3.124061e-01 0.6725666
## 2567 5.018412e-03 1.336156e-01 0.8613660
## 2568 1.270813e-02 2.784440e-01 0.7088479
## 2573 5.863413e-03 1.525322e-01 0.8416044
## 2576 1.430147e-02 3.021648e-01 0.6835338
## 2587 4.607711e-03 1.240951e-01 0.8712972
## 2588 1.235297e-02 2.729107e-01 0.7147364
## 2589 4.561818e-03 1.230175e-01 0.8724207
## 2590 1.198174e-02 2.670260e-01 0.7209923
## 2591 1.294522e-02 2.820864e-01 0.7049684
## 2594 1.356307e-02 2.913903e-01 0.6950467
## 2595 1.337537e-02 2.885922e-01 0.6980325
## 2597 7.761541e-03 1.919890e-01 0.8002494
## 2599 6.238324e-03 1.606480e-01 0.8331137
## 2602 3.187219e-03 8.939671e-02 0.9074161
## 2604 8.421299e-03 2.048018e-01 0.7867769
## 2606 2.310783e-03 6.651124e-02 0.9311780
## 2608 7.298987e-03 1.827387e-01 0.8099623
## 2609 1.588599e-02 3.240957e-01 0.6600183
## 2613 1.588599e-02 3.240957e-01 0.6600183
## 2617 9.480686e-03 2.244865e-01 0.7660328
## 2619 1.211884e-02 2.692115e-01 0.7186697
## 2631 1.791721e-02 3.500412e-01 0.6320415
## 2634 1.059428e-02 2.440751e-01 0.7453307
## 2635 1.331023e-02 2.876154e-01 0.6990743
## 2636 1.176346e-02 2.635167e-01 0.7247198
## 2637 1.224852e-02 2.712655e-01 0.7164860
## 2641 5.110118e-03 1.357117e-01 0.8591782
## 2642 5.322312e-03 1.405209e-01 0.8541568
## 2644 9.090583e-03 2.173613e-01 0.7735481
## 2649 3.857203e-03 1.061155e-01 0.8900273
## 2653 9.973205e-03 2.332845e-01 0.7567423
## 2654 1.849923e-02 3.570636e-01 0.6244372
## 2660 1.176346e-02 2.635167e-01 0.7247198
## 2662 3.187219e-03 8.939671e-02 0.9074161
## 2663 9.571280e-03 2.261212e-01 0.7643075
## 2664 6.917291e-03 1.749331e-01 0.8181496
## 2669 8.795655e-03 2.118798e-01 0.7793245
## 2670 1.617073e-02 3.278739e-01 0.6559553
## 2672 1.005434e-02 2.347131e-01 0.7552326
## 2675 4.151757e-03 1.132638e-01 0.8825844
## 2676 1.091988e-02 2.496012e-01 0.7394789
## 2680 2.948738e-03 8.328633e-02 0.9137649
## 2682 9.886670e-03 2.317544e-01 0.7583589
## 2683 1.328920e-02 2.872993e-01 0.6994115
## 2684 1.929868e-02 3.664300e-01 0.6142714
## 2685 1.018996e-02 2.370883e-01 0.7527217
## 2688 9.885291e-03 2.317300e-01 0.7583848
## 2698 1.390660e-02 2.964487e-01 0.6896447
## 2699 5.907460e-03 1.534943e-01 0.8405982
## 2704 1.080923e-02 2.477332e-01 0.7414576
## 2709 1.005434e-02 2.347131e-01 0.7552326
## 2710 1.242934e-02 2.741083e-01 0.7134624
## 2713 1.774311e-02 3.479063e-01 0.6343506
## 2717 5.547696e-03 1.455675e-01 0.8488848
## 2719 8.700628e-03 2.100960e-01 0.7812034
## 2730 9.840995e-03 2.309441e-01 0.7592149
## 2735 2.330848e-03 6.704860e-02 0.9306206
## 2740 8.981582e-03 2.153450e-01 0.7756734
## 2748 1.028119e-02 2.386770e-01 0.7510419
## 2749 7.540166e-03 1.875900e-01 0.8048698
## 2751 1.199285e-02 2.672036e-01 0.7208035
## 2754 1.774311e-02 3.479063e-01 0.6343506
## 2762 3.739022e-03 1.032133e-01 0.8930476
## 2768 8.079596e-03 1.982207e-01 0.7936997
## 2769 1.174483e-02 2.632156e-01 0.7250395
## 2777 3.739022e-03 1.032133e-01 0.8930476
## 2784 1.774311e-02 3.479063e-01 0.6343506
## 2786 8.787597e-03 2.117289e-01 0.7794835
## 2788 7.615986e-03 1.891024e-01 0.8032816
## 2792 1.174483e-02 2.632156e-01 0.7250395
## 2799 9.082071e-03 2.172042e-01 0.7737137
## 2801 9.426211e-03 2.235000e-01 0.7670738
## 2806 5.101974e-03 1.355260e-01 0.8593720
## 2813 2.948238e-03 8.327344e-02 0.9137783
## 2814 3.582000e-03 9.932655e-02 0.8970914
## 2815 1.199235e-02 2.671956e-01 0.7208120
## 2819 4.375609e-03 1.186165e-01 0.8770079
## 2824 6.838684e-03 1.733058e-01 0.8198556
## 2825 8.054462e-03 1.977320e-01 0.7942135
## 2828 8.066060e-03 1.979576e-01 0.7939764
## 2831 9.053474e-03 2.166761e-01 0.7742704
## 2835 5.984093e-03 1.551627e-01 0.8388532
## 2848 9.884281e-03 2.317121e-01 0.7584037
## 2852 1.568749e-02 3.214334e-01 0.6628791
## 2853 1.035757e-02 2.400017e-01 0.7496407
## 2857 6.504798e-03 1.663168e-01 0.8271784
## 2861 1.080923e-02 2.477332e-01 0.7414576
## 2864 1.428233e-02 3.018900e-01 0.6838277
## 2868 1.080923e-02 2.477332e-01 0.7414576
## 2869 7.734187e-03 1.914482e-01 0.8008176
## 2880 1.358476e-02 2.917120e-01 0.6947032
## 2888 6.466510e-03 1.655073e-01 0.8280262
## 2889 5.101974e-03 1.355260e-01 0.8593720
## 2890 5.514678e-03 1.448321e-01 0.8496532
## 2892 1.237445e-02 2.732480e-01 0.7143776
## 2894 4.600364e-03 1.239228e-01 0.8714769
## 2900 5.101974e-03 1.355260e-01 0.8593720
## 2909 4.693034e-03 1.260911e-01 0.8692159
## 2916 1.174483e-02 2.632156e-01 0.7250395
## 2920 1.100995e-02 2.511144e-01 0.7378757
## 2927 1.566276e-02 3.211000e-01 0.6632373
## 2930 6.192247e-03 1.596595e-01 0.8341483
## 2932 1.239237e-02 2.735291e-01 0.7140785
## 2939 5.527656e-03 1.451214e-01 0.8493510
## 2942 1.475791e-02 3.086444e-01 0.6765976
## 2947 1.264860e-02 2.775229e-01 0.7098285
## 2948 9.059582e-03 2.167890e-01 0.7741514
## 2952 1.599343e-02 3.255270e-01 0.6584796
## 2956 1.172624e-02 2.629147e-01 0.7253590
## 2963 7.174684e-03 1.802141e-01 0.8126112
## 2965 1.441700e-02 3.038176e-01 0.6817654
## 2970 6.819217e-03 1.729017e-01 0.8202791
## 2972 1.546269e-02 3.183895e-01 0.6661478
## 2975 1.945456e-02 3.682197e-01 0.6123257
## 2976 8.032745e-03 1.973092e-01 0.7946580
## 2980 1.008805e-02 2.353051e-01 0.7546069
## 2984 1.552705e-02 3.192640e-01 0.6652089
## 2991 1.220979e-02 2.706534e-01 0.7171368
## 2997 1.614524e-02 3.275377e-01 0.6563170
## 3002 1.792683e-02 3.501587e-01 0.6319144
## 3008 1.557329e-02 3.198908e-01 0.6645359
## 3010 1.091065e-02 2.494457e-01 0.7396436
## 3013 7.809058e-03 1.929266e-01 0.7992643
## 3015 1.172624e-02 2.629147e-01 0.7253590
## 3021 1.832566e-02 3.549876e-01 0.6266868
## 3023 7.614246e-03 1.890678e-01 0.8033180
## 3024 1.055775e-02 2.434496e-01 0.7459927
## 3026 5.663035e-03 1.481259e-01 0.8462110
## 3032 1.599343e-02 3.255270e-01 0.6584796
## 3038 1.173645e-02 2.630800e-01 0.7251836
## 3041 3.831618e-03 1.054889e-01 0.8906795
## 3046 1.047553e-02 2.420375e-01 0.7474870
## 3047 3.986992e-03 1.092801e-01 0.8867329
## 3055 9.479173e-03 2.244592e-01 0.7660617
## 3062 8.899469e-03 2.138187e-01 0.7772818
## 3063 3.062563e-02 4.714031e-01 0.4979713
## 3072 8.369710e-03 2.038157e-01 0.7878146
## 3074 9.756218e-03 2.294352e-01 0.7608086
## 3084 6.603283e-03 1.683914e-01 0.8250054
## 3091 1.844111e-02 3.563701e-01 0.6251888
## 3098 4.847226e-03 1.296740e-01 0.8654788
## 3099 9.868604e-03 2.314341e-01 0.7586973
## 3104 6.568200e-03 1.676536e-01 0.8257782
## 3109 1.194384e-02 2.664193e-01 0.7216368
## 3110 1.811148e-02 3.524046e-01 0.6294839
## 3117 8.072015e-03 1.980733e-01 0.7938546
## 3118 2.434466e-02 4.189335e-01 0.5567219
## 3120 1.132048e-02 2.562805e-01 0.7323990
## 3129 1.234888e-02 2.728463e-01 0.7148048
## 3133 1.502080e-02 3.123158e-01 0.6726634
## 3140 1.281041e-08 3.959732e-07 0.9999996
## 3141 3.751880e-03 1.035300e-01 0.8927181
## 3143 1.286492e-02 2.808573e-01 0.7062778
## 3145 1.079741e-02 2.475330e-01 0.7416695
## 3148 1.765939e-02 3.468739e-01 0.6354667
## 3151 1.138906e-02 2.574110e-01 0.7311999
## 3152 1.170768e-02 2.626141e-01 0.7256783
## 3155 6.223606e-03 1.603325e-01 0.8334439
## 3156 3.345621e-03 9.340840e-02 0.9032460
## 3163 5.385081e-03 1.419327e-01 0.8526822
## 3165 1.526664e-02 3.157098e-01 0.6690236
## 3167 5.085725e-03 1.351552e-01 0.8597591
## 3169 9.508699e-03 2.249928e-01 0.7654985
## 3174 1.466167e-02 3.072894e-01 0.6780489
## 3175 1.586045e-02 3.237545e-01 0.6603851
## 3178 1.037949e-02 2.403809e-01 0.7492397
## 3181 1.057237e-02 2.437001e-01 0.7457275
## 3182 7.604745e-03 1.888786e-01 0.8035167
## 3186 1.437562e-02 3.032266e-01 0.6823977
## 3188 5.660347e-03 1.480665e-01 0.8462732
## 3189 4.007000e-03 1.097659e-01 0.8862271
## 3191 1.980278e-02 3.721758e-01 0.6080214
## 3196 1.451223e-02 3.051735e-01 0.6803142
## 3200 5.530035e-03 1.451743e-01 0.8492956
## 3201 1.426163e-02 3.015927e-01 0.6841457
## 3205 2.948862e-03 8.328955e-02 0.9137616
## 3207 1.297415e-02 2.825280e-01 0.7044978
## 3208 2.715596e-03 7.722930e-02 0.9200551
## 3209 7.806876e-03 1.928836e-01 0.7993095
## 3210 1.879227e-02 3.605337e-01 0.6206740
## 3212 1.502080e-02 3.123158e-01 0.6726634
## 3214 5.530035e-03 1.451743e-01 0.8492956
## 3218 3.207793e-03 8.991986e-02 0.9068723
## 3222 1.365519e-02 2.927546e-01 0.6935902
## 3234 4.585705e-03 1.235787e-01 0.8718355
## 3235 9.985094e-03 2.334942e-01 0.7565207
## 3238 1.170768e-02 2.626141e-01 0.7256783
## 3246 1.214405e-02 2.696117e-01 0.7182442
## 3249 1.412614e-02 2.996395e-01 0.6862343
## 3250 1.045892e-02 2.417516e-01 0.7477895
## 3252 1.801019e-02 3.511748e-01 0.6308150
## 3253 4.027488e-03 1.102628e-01 0.8857098
## 3255 1.479974e-02 3.092315e-01 0.6759687
## 3257 1.385313e-02 2.956666e-01 0.6904803
## 3262 4.373045e-09 1.351721e-07 0.9999999
## 3264 8.830926e-03 2.125397e-01 0.7786293
## 3266 4.996647e-03 1.331165e-01 0.8618868
## 3267 5.085725e-03 1.351552e-01 0.8597591
## 3268 6.596058e-03 1.682395e-01 0.8251644
## 3270 7.522395e-03 1.872346e-01 0.8052430
## 3271 1.958191e-02 3.696732e-01 0.6107449
## 3275 7.343633e-03 1.836414e-01 0.8090150
## 3281 1.272311e-02 2.786753e-01 0.7086016
## 3282 5.085725e-03 1.351552e-01 0.8597591
## 3283 1.685868e-02 3.368084e-01 0.6463329
## 3287 4.505346e-03 1.216877e-01 0.8738069
## 3288 1.037949e-02 2.403809e-01 0.7492397
## 3289 5.530035e-03 1.451743e-01 0.8492956
## 3295 1.670696e-02 3.348613e-01 0.6484318
## 3298 1.412614e-02 2.996395e-01 0.6862343
## 3300 1.505646e-02 3.128105e-01 0.6721331
## 3314 8.738511e-03 2.108082e-01 0.7804533
## 3316 1.170768e-02 2.626141e-01 0.7256783
## 3319 3.760712e-03 1.037475e-01 0.8924918
## 3320 4.543589e-03 1.225887e-01 0.8728677
## 3327 1.170768e-02 2.626141e-01 0.7256783
## 3329 7.305004e-03 1.828605e-01 0.8098345
## 3331 8.097260e-03 1.985638e-01 0.7933390
## 3340 8.461055e-03 2.055600e-01 0.7859790
## 3341 8.369404e-03 2.038098e-01 0.7878208
## 3344 5.241930e-03 1.387058e-01 0.8560523
## 3345 7.532423e-03 1.874352e-01 0.8050324
## 3346 2.158444e-02 3.915474e-01 0.5868681
## 3347 1.522631e-02 3.151555e-01 0.6696182
## 3354 1.333138e-02 2.879328e-01 0.6987358
## 3357 1.891499e-02 3.619743e-01 0.6191107
## 3359 7.426796e-03 1.853172e-01 0.8072560
## 3361 1.561743e-02 3.204880e-01 0.6638946
## 3363 2.894474e-03 8.188400e-02 0.9152215
## 3366 7.293812e-03 1.826339e-01 0.8100723
## 3370 1.832539e-02 3.549844e-01 0.6266902
## 3372 3.191885e-03 8.951541e-02 0.9072927
## 3376 2.812638e-03 7.976060e-02 0.9174268
## 3384 1.028703e-02 2.387785e-01 0.7509344
## 3386 4.140299e-03 1.129880e-01 0.8828717
## 3389 8.890839e-03 2.136579e-01 0.7774512
## 3390 7.250288e-03 1.817516e-01 0.8109981
## 3394 2.016622e-02 3.762440e-01 0.6035898
## 3398 5.327886e-03 1.406465e-01 0.8540256
## 3402 1.158603e-02 2.606370e-01 0.7277770
## 3405 3.244273e-03 9.084592e-02 0.9059098
## 3408 5.867305e-03 1.526173e-01 0.8415154
## 3413 6.920295e-03 1.749951e-01 0.8180846
## 3419 4.563804e-03 1.230642e-01 0.8723720
## 3421 3.507862e-03 9.747912e-02 0.8990130
## 3425 4.940876e-03 1.318350e-01 0.8632241
## 3426 4.563804e-03 1.230642e-01 0.8723720
## 3428 4.563804e-03 1.230642e-01 0.8723720
## 3431 4.417972e-03 1.196218e-01 0.8759602
## 3432 2.898474e-03 8.198752e-02 0.9151140
## 3445 1.726490e-02 3.419587e-01 0.6407764
## 3448 1.085691e-02 2.485394e-01 0.7406037
## 3451 2.551111e-02 4.296421e-01 0.5448468
## 3456 2.189512e-02 3.947832e-01 0.5833217
## 3457 2.860214e-02 4.558214e-01 0.5155765
## 3458 1.144942e-02 2.584029e-01 0.7301476
## 3463 9.536143e-03 2.254881e-01 0.7649758
## 3469 8.447616e-03 2.053039e-01 0.7862485
## 3471 7.627254e-03 1.893267e-01 0.8030461
## 3475 1.362932e-02 2.923721e-01 0.6939986
## 3476 1.378762e-02 2.947058e-01 0.6915066
## 3481 1.163371e-02 2.614133e-01 0.7269530
## 3482 1.504812e-02 3.126949e-01 0.6722570
## 3486 1.264281e-02 2.774333e-01 0.7099239
## 3489 1.239626e-02 2.735901e-01 0.7140137
## 3492 1.246177e-02 2.746156e-01 0.7129226
## 3494 6.248680e-03 1.608698e-01 0.8328815
## 3498 6.543741e-03 1.671384e-01 0.8263178
## 3499 5.045327e-03 1.342319e-01 0.8607228
## 3503 1.134038e-02 2.566089e-01 0.7320507
## 3504 1.209433e-02 2.688217e-01 0.7190840
## 3505 1.650898e-02 3.323007e-01 0.6511903
## 3506 1.066177e-02 2.452279e-01 0.7441103
## 3508 1.296504e-02 2.823890e-01 0.7046459
## 3511 6.176487e-03 1.593208e-01 0.8345027
## 3513 1.174560e-02 2.632281e-01 0.7250263
## 3515 1.012659e-02 2.359805e-01 0.7538929
## 3516 1.108017e-02 2.522895e-01 0.7366304
## 3518 1.580090e-02 3.229574e-01 0.6612417
## 3521 7.672417e-03 1.902242e-01 0.8021034
## 3525 1.202412e-02 2.677030e-01 0.7202728
## 3526 2.125881e-02 3.881119e-01 0.5906293
## 3530 1.046068e-02 2.417819e-01 0.7477574
## 3533 1.754859e-02 3.455018e-01 0.6369496
## 3535 1.532856e-02 3.165587e-01 0.6681128
## 3539 8.684728e-03 2.097967e-01 0.7815186
## 3540 2.209237e-02 3.968165e-01 0.5810911
## 3543 1.650898e-02 3.323007e-01 0.6511903
## 3544 5.973755e-03 1.549381e-01 0.8390882
## 3547 8.527273e-03 2.068193e-01 0.7846534
## 3549 1.580090e-02 3.229574e-01 0.6612417
## 3550 1.016742e-02 2.366947e-01 0.7531379
## 3553 6.239490e-03 1.606730e-01 0.8330875
## 3556 6.755510e-03 1.715764e-01 0.8216681
## 3561 9.775058e-03 2.297711e-01 0.7604539
## 3567 5.045327e-03 1.342319e-01 0.8607228
## 3573 1.209433e-02 2.688217e-01 0.7190840
## 3577 1.845947e-02 3.565894e-01 0.6249511
## 3581 1.580090e-02 3.229574e-01 0.6612417
## 3586 1.161529e-02 2.611136e-01 0.7272711
## 3587 2.963640e-02 4.639292e-01 0.5064344
## 3589 7.672417e-03 1.902242e-01 0.8021034
## 3590 1.373575e-02 2.939431e-01 0.6923212
## 3591 1.895246e-02 3.624126e-01 0.6186350
## 3601 7.462787e-03 1.860402e-01 0.8064970
## 3606 1.223805e-02 2.711001e-01 0.7166618
## 3608 1.161529e-02 2.611136e-01 0.7272711
## 3610 1.029748e-02 2.389599e-01 0.7507426
## 3620 8.342488e-03 2.032942e-01 0.7883633
## 3621 8.858969e-03 2.130636e-01 0.7780775
## 3623 1.367219e-02 2.930058e-01 0.6933220
## 3631 7.253392e-03 1.818146e-01 0.8109320
## 3633 1.208058e-02 2.686031e-01 0.7193164
## 3634 7.636381e-03 1.895082e-01 0.8028554
## 3640 8.776910e-03 2.115287e-01 0.7796944
## 3641 6.932313e-03 1.752433e-01 0.8178244
## 3646 1.285154e-02 2.806521e-01 0.7064963
## 3650 2.509066e-02 4.258378e-01 0.5490716
## 3651 5.768785e-03 1.504574e-01 0.8437738
## 3652 2.244183e-02 4.003794e-01 0.5771788
## 3660 8.866904e-03 2.132116e-01 0.7779215
## 3662 9.927485e-03 2.324769e-01 0.7575956
## 3663 1.125970e-02 2.552756e-01 0.7334647
## 3669 1.208058e-02 2.686031e-01 0.7193164
## 3689 1.501172e-02 3.121897e-01 0.6727986
## 3690 5.752591e-03 1.501012e-01 0.8441462
## 3691 1.331375e-02 2.876682e-01 0.6990181
## 3693 5.163999e-03 1.369382e-01 0.8578978
## 3694 4.476385e-03 1.210041e-01 0.8745195
## 3697 1.695413e-02 3.380268e-01 0.6450191
## 3699 4.053529e-03 1.108934e-01 0.8850531
## 3702 9.927485e-03 2.324769e-01 0.7575956
## 3711 1.280419e-02 2.799247e-01 0.7072712
## 3721 9.698321e-03 2.284010e-01 0.7619007
## 3722 1.756033e-02 3.456475e-01 0.6367922
## 3723 1.739966e-02 3.436473e-01 0.6389530
## 3726 1.735236e-02 3.430557e-01 0.6395920
## 3727 2.157344e-02 3.914322e-01 0.5869944
## 3731 3.629091e-03 1.004959e-01 0.8958750
## 3734 1.010058e-02 2.355248e-01 0.7543746
## 3735 5.037285e-03 1.340479e-01 0.8609149
## 3737 1.803618e-02 3.514910e-01 0.6304729
## 3742 1.581778e-02 3.231835e-01 0.6609987
## 3744 7.279501e-03 1.823440e-01 0.8103765
## 3750 1.329667e-02 2.874117e-01 0.6992916
## 3751 7.133887e-03 1.793819e-01 0.8134843
## 3752 1.636873e-02 3.304733e-01 0.6531580
## 3756 1.146565e-02 2.586691e-01 0.7298652
## 3760 1.924164e-02 3.657721e-01 0.6149863
## 3761 6.225349e-03 1.603699e-01 0.8334048
## 3765 2.335681e-02 4.094756e-01 0.5671675
## 3770 9.659217e-03 2.277008e-01 0.7626400
## 3776 1.164487e-02 2.615947e-01 0.7267604
## 3777 1.513046e-02 3.138343e-01 0.6710352
## 3784 1.159690e-02 2.608142e-01 0.7275889
## 3785 4.980674e-03 1.327499e-01 0.8622694
## 3788 1.581778e-02 3.231835e-01 0.6609987
## 3791 1.871053e-02 3.595701e-01 0.6217193
## 3797 1.322029e-02 2.862618e-01 0.7005179
## 3799 5.704744e-03 1.490471e-01 0.8452482
## 3802 1.133506e-02 2.565213e-01 0.7321437
## 3803 8.234697e-03 2.012223e-01 0.7905430
## 3808 8.327567e-03 2.030081e-01 0.7886643
## 3809 5.037285e-03 1.340479e-01 0.8609149
## 3811 6.307476e-03 1.621270e-01 0.8315656
## 3822 3.172895e-02 4.794307e-01 0.4888403
## 3823 2.786506e-03 7.908037e-02 0.9181331
## 3824 9.024388e-03 2.161382e-01 0.7748374
## 3828 1.712316e-02 3.401720e-01 0.6427048
## 3829 1.111542e-02 2.528778e-01 0.7360068
## 3833 9.629928e-03 2.271755e-01 0.7631946
## 3839 1.298762e-02 2.827335e-01 0.7042788
## 3841 1.036720e-02 2.401683e-01 0.7494645
## 3842 7.147213e-03 1.796539e-01 0.8131989
## 3843 1.020283e-02 2.373128e-01 0.7524844
## 3847 8.225176e-03 2.010388e-01 0.7907360
## 3850 5.618500e-03 1.471400e-01 0.8472415
## 3851 9.927485e-03 2.324769e-01 0.7575956
## 3855 6.669563e-03 1.697813e-01 0.8235491
## 3856 5.311761e-03 1.402831e-01 0.8544051
## 3858 1.235430e-02 2.729315e-01 0.7147141
## 3860 4.917287e-03 1.312917e-01 0.8637910
## 3862 8.046111e-03 1.975695e-01 0.7943844
## 3863 1.657922e-03 4.866782e-02 0.9496743
## 3873 1.788801e-02 3.496842e-01 0.6324278
## 3876 7.636381e-03 1.895082e-01 0.8028554
## 3877 1.149913e-02 2.592176e-01 0.7292833
## 3886 2.007141e-02 3.751886e-01 0.6047400
## 3889 9.961599e-03 2.330797e-01 0.7569587
## 3891 1.471533e-02 3.080456e-01 0.6772391
## 3894 6.973759e-03 1.760978e-01 0.8169284
## 3898 1.035984e-02 2.400409e-01 0.7495993
## 3900 1.207810e-02 2.685635e-01 0.7193584
## 3902 1.369485e-02 2.933402e-01 0.6929649
## 3903 1.554366e-02 3.194894e-01 0.6649669
## 3907 9.301269e-03 2.212269e-01 0.7694718
## 3912 1.247365e-02 2.748013e-01 0.7127251
## 3916 5.242719e-03 1.387236e-01 0.8560336
## 3918 1.487915e-02 3.103431e-01 0.6747778
## 3930 6.320403e-03 1.624028e-01 0.8312768
## 3935 1.147790e-02 2.588698e-01 0.7296523
## 3936 1.752097e-02 3.451588e-01 0.6373202
## 3938 1.361400e-02 2.921454e-01 0.6942406
## 3939 4.491960e-03 1.213719e-01 0.8741362
## 3940 1.487915e-02 3.103431e-01 0.6747778
## 3941 7.962971e-03 1.959477e-01 0.7960894
## 3945 1.209081e-02 2.687658e-01 0.7191434
## 3949 1.159690e-02 2.608142e-01 0.7275889
## 3953 4.956967e-03 1.322051e-01 0.8628379
## 3957 5.187348e-03 1.374686e-01 0.8573440
## 3960 1.487915e-02 3.103431e-01 0.6747778
## 3961 1.046345e-02 2.418295e-01 0.7477070
## 3977 1.159690e-02 2.608142e-01 0.7275889
## 3978 1.047971e-02 2.421094e-01 0.7474109
## 3980 1.035984e-02 2.400409e-01 0.7495993
## 3982 9.346147e-03 2.220450e-01 0.7686088
## 3985 4.060593e-03 1.110643e-01 0.8848751
## 3986 5.309256e-03 1.402267e-01 0.8544641
## 3988 1.204758e-02 2.680773e-01 0.7198751
## 3990 1.159690e-02 2.608142e-01 0.7275889
## 3991 4.496765e-03 1.214853e-01 0.8740180
## 3995 5.964127e-03 1.547287e-01 0.8393072
## 3997 5.477387e-03 1.440000e-01 0.8505226
## 4000 4.542006e-03 1.225515e-01 0.8729065
## 4001 1.371405e-02 2.936234e-01 0.6926626
## 4006 5.858356e-03 1.524216e-01 0.8417200
## 4010 8.443189e-03 2.052195e-01 0.7863374
## 4011 4.630800e-03 1.246362e-01 0.8707330
## 4012 1.036720e-02 2.401683e-01 0.7494645
## 4014 4.499979e-03 1.215611e-01 0.8739389
## 4023 5.037285e-03 1.340479e-01 0.8609149
## 4025 6.030947e-03 1.561794e-01 0.8377897
## 4029 1.159690e-02 2.608142e-01 0.7275889
## 4038 4.496765e-03 1.214853e-01 0.8740180
## 4040 2.279172e-03 6.566333e-02 0.9320575
## 4044 8.737408e-03 2.107875e-01 0.7804751
## 4045 1.086700e-02 2.487097e-01 0.7404233
## 4051 1.752097e-02 3.451588e-01 0.6373202
## 4052 1.159690e-02 2.608142e-01 0.7275889
## 4054 9.346147e-03 2.220450e-01 0.7686088
## 4070 1.276215e-02 2.792774e-01 0.7079604
## 4071 1.260285e-02 2.768134e-01 0.7105837
## 4074 1.756033e-02 3.456475e-01 0.6367922
## 4077 6.612741e-03 1.685900e-01 0.8247972
## 4083 5.037285e-03 1.340479e-01 0.8609149
## 4089 1.228082e-02 2.717751e-01 0.7159441
## 4092 3.691551e-03 1.020420e-01 0.8942665
## 4096 7.660221e-03 1.899820e-01 0.8023578
## 4097 1.069516e-02 2.457967e-01 0.7435082
## 4098 6.652199e-03 1.694177e-01 0.8239301
## 4103 8.737408e-03 2.107875e-01 0.7804751
## 4113 7.273845e-03 1.822294e-01 0.8104967
## 4116 1.252837e-02 2.756550e-01 0.7118166
## 4124 1.381363e-02 2.950876e-01 0.6910987
## 4126 2.415528e-02 4.171486e-01 0.5586961
## 4130 1.159690e-02 2.608142e-01 0.7275889
## 4135 4.085985e-03 1.116781e-01 0.8842359
## 4136 1.413690e-02 2.997951e-01 0.6860680
## 4138 1.125970e-02 2.552756e-01 0.7334647
## 4141 9.308838e-03 2.213651e-01 0.7693261
## 4142 1.061509e-02 2.444310e-01 0.7449540
## 4146 4.496765e-03 1.214853e-01 0.8740180
## 4152 1.221059e-02 2.706660e-01 0.7171234
## 4154 7.423938e-03 1.852598e-01 0.8073163
## 4156 3.768695e-03 1.039439e-01 0.8922874
## 4157 9.352795e-03 2.221661e-01 0.7684811
## 4159 1.159690e-02 2.608142e-01 0.7275889
## 4160 8.169727e-03 1.999679e-01 0.7918624
## 4170 1.823907e-02 3.539462e-01 0.6278147
## 4173 4.730722e-03 1.269697e-01 0.8682996
## 4175 1.566199e-02 3.210896e-01 0.6632484
## 4178 6.725714e-03 1.709551e-01 0.8223192
## 4180 1.452599e-02 3.053690e-01 0.6801050
## 4184 1.159690e-02 2.608142e-01 0.7275889
## 4191 5.037285e-03 1.340479e-01 0.8609149
## 4193 1.260285e-02 2.768134e-01 0.7105837
## 4194 1.612343e-02 3.272497e-01 0.6566268
## 4197 1.161314e-02 2.610786e-01 0.7273082
## 4199 1.731494e-02 3.425869e-01 0.6400982
## 4200 6.051792e-03 1.566308e-01 0.8373174
## 4203 9.294065e-03 2.210955e-01 0.7696105
## 4204 4.301163e-03 1.168439e-01 0.8788549
## 4212 1.322918e-02 2.863958e-01 0.7003751
## 4214 2.703954e-02 4.429679e-01 0.5299926
## 4215 1.749340e-02 3.448159e-01 0.6376907
## 4219 1.091568e-02 2.495306e-01 0.7395537
## 4223 1.157854e-02 2.605149e-01 0.7279066
## 4225 1.865659e-03 5.442207e-02 0.9437123
## 4227 1.045854e-02 2.417450e-01 0.7477965
## 4228 1.442510e-02 3.039332e-01 0.6816417
## 4231 2.043736e-02 3.792391e-01 0.6003235
## 4234 1.089588e-02 2.491969e-01 0.7399072
## 4242 3.747373e-03 1.034190e-01 0.8928336
## 4254 1.394273e-02 2.969760e-01 0.6890813
## 4256 1.613968e-02 3.274643e-01 0.6563960
## 4258 4.534764e-03 1.223810e-01 0.8730843
## 4271 9.088585e-03 2.173244e-01 0.7735870
## 4274 3.037585e-03 8.557278e-02 0.9113896
## 4278 1.066843e-02 2.453415e-01 0.7439901
## 4279 1.335972e-02 2.883578e-01 0.6982825
## 4281 1.034341e-02 2.397565e-01 0.7499001
## 4282 1.533221e-02 3.166087e-01 0.6680591
## 4286 9.863792e-03 2.313488e-01 0.7587875
## 4287 1.579284e-02 3.228493e-01 0.6613579
## 4289 1.537329e-02 3.171705e-01 0.6674562
## 4291 7.171275e-03 1.801446e-01 0.8126841
## 4293 1.178840e-02 2.639196e-01 0.7242920
## 4297 4.949066e-03 1.320234e-01 0.8630275
## 4300 5.271998e-03 1.393857e-01 0.8553423
## 4302 9.482630e-03 2.245217e-01 0.7659957
## 4305 6.571259e-08 2.031191e-06 0.9999979
## 4307 7.301245e-03 1.827844e-01 0.8099143
## 4309 4.534764e-03 1.223810e-01 0.8730843
## 4310 1.193242e-02 2.662363e-01 0.7218313
## 4312 1.613968e-02 3.274643e-01 0.6563960
## 4315 1.205608e-02 2.682127e-01 0.7197312
## 4323 7.882749e-03 1.943761e-01 0.7977412
## 4325 7.648044e-03 1.897401e-01 0.8026119
## 4328 5.030479e-03 1.338920e-01 0.8610775
## 4331 9.066018e-03 2.169079e-01 0.7740261
## 4332 7.809903e-03 1.929433e-01 0.7992468
## 4337 1.324729e-02 2.866688e-01 0.7000839
## 4341 1.178609e-02 2.638823e-01 0.7243316
## 4342 1.026485e-02 2.383930e-01 0.7513421
## 4344 2.581261e-03 7.370116e-02 0.9237176
## 4345 6.710371e-03 1.706347e-01 0.8226549
## 4346 1.404531e-02 2.984685e-01 0.6874862
## 4350 1.206485e-02 2.683526e-01 0.7195825
## 4354 1.325767e-02 2.868250e-01 0.6999173
## 4360 3.838932e-03 1.056681e-01 0.8904929
## 4364 1.749340e-02 3.448159e-01 0.6376907
## 4367 1.157854e-02 2.605149e-01 0.7279066
## 4370 5.028298e-03 1.338421e-01 0.8611296
## 4376 1.752369e-03 5.129296e-02 0.9469547
## 4378 1.749340e-02 3.448159e-01 0.6376907
## 4386 1.017936e-02 2.369031e-01 0.7529175
## 4387 2.644229e-02 4.378526e-01 0.5357051
## 4389 1.579284e-02 3.228493e-01 0.6613579
## 4395 2.480147e-02 4.231850e-01 0.5520136
## 4401 1.749340e-02 3.448159e-01 0.6376907
## 4404 1.779915e-02 3.485952e-01 0.6336057
## 4407 2.205555e-02 3.964382e-01 0.5815063
## 4411 9.217159e-03 2.196887e-01 0.7710942
## 4412 1.013986e-02 2.362127e-01 0.7536475
## 4413 1.749340e-02 3.448159e-01 0.6376907
## 4414 1.157854e-02 2.605149e-01 0.7279066
## 4418 1.494558e-02 3.112698e-01 0.6737847
## 4420 1.749340e-02 3.448159e-01 0.6376907
## 4422 1.139512e-02 2.575107e-01 0.7310942
## 4442 1.283122e-02 2.803401e-01 0.7068287
## 4444 7.523851e-03 1.872638e-01 0.8052124
## 4450 1.411872e-02 2.995322e-01 0.6863491
## 4451 1.781279e-02 3.487626e-01 0.6334246
## 4457 9.701393e-03 2.284560e-01 0.7618426
## 4462 9.286508e-03 2.209575e-01 0.7697560
## 4467 1.034341e-02 2.397565e-01 0.7499001
## 4475 9.744071e-03 2.292185e-01 0.7610375
## 4477 1.438072e-02 3.032996e-01 0.6823197
## 4479 8.221460e-03 2.009671e-01 0.7908114
## 4487 6.522507e-03 1.666907e-01 0.8267868
## 4499 7.600021e-03 1.887844e-01 0.8036155
## 4500 1.231458e-02 2.723069e-01 0.7153785
## 4503 1.420590e-02 3.007909e-01 0.6850032
## 4506 1.046134e-02 2.417933e-01 0.7477454
## 4515 1.542749e-02 3.179101e-01 0.6666624
## 4520 4.213058e-03 1.147364e-01 0.8810505
## 4525 1.309767e-02 2.844072e-01 0.7024952
## 4534 7.968717e-03 1.960600e-01 0.7959713
## 4536 1.237338e-02 2.732311e-01 0.7143955
## 4541 9.009480e-03 2.158621e-01 0.7751284
## 4542 1.162773e-02 2.613160e-01 0.7270563
## 4544 1.154190e-02 2.599170e-01 0.7285411
## 4545 1.120628e-02 2.543898e-01 0.7344039
## 4547 1.052532e-02 2.428934e-01 0.7465813
## 4548 7.173145e-03 1.801827e-01 0.8126441
## 4552 1.480882e-02 3.093588e-01 0.6758323
## 4554 1.481218e-02 3.094059e-01 0.6757819
## 4557 6.290970e-03 1.617744e-01 0.8319346
## 4560 6.410013e-03 1.643098e-01 0.8292802
## 4573 1.031797e-02 2.393155e-01 0.7503665
## 4574 4.893810e-03 1.307503e-01 0.8643559
## 4575 3.213316e-03 9.006018e-02 0.9067265
## 4576 5.013238e-03 1.334970e-01 0.8614897
## 4577 1.201795e-02 2.676046e-01 0.7203775
## 4580 5.957732e-03 1.545896e-01 0.8394527
## 4583 4.520313e-03 1.220406e-01 0.8734391
## 4585 1.154190e-02 2.599170e-01 0.7285411
## 4591 1.038611e-02 2.404953e-01 0.7491186
## 4593 2.547427e-03 7.280808e-02 0.9246445
## 4600 1.201795e-02 2.676046e-01 0.7203775
## 4601 1.154190e-02 2.599170e-01 0.7285411
## 4603 1.154190e-02 2.599170e-01 0.7285411
## 4604 9.684254e-03 2.281493e-01 0.7621665
## 4606 7.600021e-03 1.887844e-01 0.8036155
## 4607 1.433535e-02 3.026504e-01 0.6830143
## 4608 7.600021e-03 1.887844e-01 0.8036155
## 4619 4.132410e-03 1.127980e-01 0.8830696
## 4622 1.154190e-02 2.599170e-01 0.7285411
## 4624 1.256075e-02 2.761591e-01 0.7112801
## 4625 5.013238e-03 1.334970e-01 0.8614897
## 4626 9.806999e-03 2.303398e-01 0.7598532
## 4630 1.010842e-02 2.356622e-01 0.7542294
## 4632 1.480882e-02 3.093588e-01 0.6758323
## 4638 1.743837e-02 3.441305e-01 0.6384312
## 4639 1.154190e-02 2.599170e-01 0.7285411
## 4640 2.463598e-02 4.216535e-01 0.5537105
## 4641 1.815315e-02 3.529090e-01 0.6289378
## 4643 1.201795e-02 2.676046e-01 0.7203775
## 4646 1.705734e-02 3.393385e-01 0.6436041
## 4649 3.479198e-03 9.676270e-02 0.8997581
## 4650 1.880659e-02 3.607022e-01 0.6204913
## 4652 1.305993e-02 2.838343e-01 0.7031058
## 4660 9.408642e-03 2.231812e-01 0.7674101
## 4673 1.478545e-02 3.090311e-01 0.6761835
## 4674 1.750442e-02 3.449531e-01 0.6375425
## 4675 4.744203e-03 1.272835e-01 0.8679723
## 4680 1.152363e-02 2.596183e-01 0.7288581
## 4683 7.587939e-03 1.885436e-01 0.8038684
## 4687 1.567673e-02 3.212884e-01 0.6630349
## 4689 2.274285e-02 4.034087e-01 0.5738485
## 4692 7.830943e-03 1.933577e-01 0.7988114
## 4693 1.152363e-02 2.596183e-01 0.7288581
## 4695 1.812460e-02 3.525635e-01 0.6293119
## 4696 7.294384e-03 1.826455e-01 0.8100601
## 4697 1.100303e-02 2.509984e-01 0.7379986
## 4701 6.434018e-03 1.648190e-01 0.8287470
## 4704 1.606348e-02 3.264566e-01 0.6574800
## 4706 4.513105e-03 1.218707e-01 0.8736162
## 4707 2.230158e-02 3.989555e-01 0.5787430
## 4713 1.446701e-02 3.045303e-01 0.6810027
## 4714 7.084219e-03 1.783662e-01 0.8145496
## 4717 1.893793e-02 3.622426e-01 0.6188195
## 4726 1.254088e-02 2.758499e-01 0.7116092
## 4729 7.902206e-03 1.947578e-01 0.7973399
## 4730 6.434018e-03 1.648190e-01 0.8287470
## 4733 5.005248e-03 1.333138e-01 0.8616809
## 4734 1.478545e-02 3.090311e-01 0.6761835
## 4749 1.152363e-02 2.596183e-01 0.7288581
## 4753 8.851926e-03 2.129321e-01 0.7782160
## 4754 1.334681e-02 2.881643e-01 0.6984889
## 4755 5.337058e-03 1.408530e-01 0.8538099
## 4757 1.360850e-02 2.920639e-01 0.6943276
## 4758 6.146637e-03 1.586785e-01 0.8351749
## 4763 1.119495e-02 2.542016e-01 0.7346034
## 4764 3.918432e-03 1.076114e-01 0.8884702
## 4765 1.119495e-02 2.542016e-01 0.7346034
## 4771 3.773640e-03 1.040655e-01 0.8921609
## 4773 1.117432e-02 2.538587e-01 0.7349670
## 4774 8.699836e-03 2.100811e-01 0.7812191
## 4778 2.409996e-02 4.166247e-01 0.5592753
## 4783 1.305064e-02 2.836930e-01 0.7032564
## 4784 1.701875e-02 3.388487e-01 0.6441325
## 4785 1.333237e-02 2.879476e-01 0.6987200
## 4786 1.434243e-02 3.027517e-01 0.6829058
## 4787 9.700418e-03 2.284385e-01 0.7618611
## 4798 4.989612e-03 1.329551e-01 0.8620553
## 4799 7.372352e-03 1.842210e-01 0.8084067
## 4800 5.627463e-03 1.473386e-01 0.8470339
## 4806 9.464658e-03 2.241965e-01 0.7663388
## 4812 3.164443e-03 8.881681e-02 0.9080187
## 4815 3.759889e-03 1.037272e-01 0.8925129
## 4816 1.124673e-02 2.550607e-01 0.7336926
## 4818 3.126575e-03 8.785097e-02 0.9090225
## 4822 5.416594e-03 1.426397e-01 0.8519437
## 4826 2.930906e-03 8.282600e-02 0.9142431
## 4827 1.016759e-02 2.366976e-01 0.7531349
## 4833 7.834792e-03 1.934334e-01 0.7987318
## 4834 1.517355e-02 3.144290e-01 0.6703974
## 4839 1.295278e-02 2.822019e-01 0.7048453
## 4842 5.279571e-03 1.395568e-01 0.8551636
## 4844 4.888835e-03 1.306355e-01 0.8644757
## 4845 7.395532e-03 1.846881e-01 0.8079164
## 4850 5.078057e-03 1.349801e-01 0.8599418
## 4851 4.981353e-03 1.327655e-01 0.8622532
## 4854 1.146897e-02 2.587235e-01 0.7298075
## 4855 2.158825e-02 3.915874e-01 0.5868244
## 4864 1.827659e-02 3.543979e-01 0.6273255
## 4870 4.412832e-03 1.195000e-01 0.8760872
## 4872 7.347440e-03 1.837183e-01 0.8089343
## 4873 7.912002e-03 1.949499e-01 0.7971381
## 4875 1.016759e-02 2.366976e-01 0.7531349
## 4878 6.615459e-03 1.686471e-01 0.8247375
## 4880 6.403346e-03 1.641682e-01 0.8294285
## 4886 1.736458e-02 3.432086e-01 0.6394268
## 4892 8.215293e-03 2.008481e-01 0.7909366
## 4895 5.111901e-03 1.357523e-01 0.8591358
## 4898 1.146897e-02 2.587235e-01 0.7298075
## 4900 8.770048e-03 2.114000e-01 0.7798300
## 4902 1.024541e-02 2.380548e-01 0.7516997
## 4906 6.460891e-03 1.653884e-01 0.8281507
## 4907 6.251009e-03 1.609197e-01 0.8328293
## 4909 4.398968e-03 1.191711e-01 0.8764299
## 4915 3.851450e-03 1.059747e-01 0.8901738
## 4916 2.051659e-02 3.801081e-01 0.5993753
## 4918 6.655907e-03 1.694954e-01 0.8238487
## 4919 1.277328e-02 2.794489e-01 0.7077778
## 4922 9.817789e-03 2.305317e-01 0.7596505
## 4923 5.128304e-03 1.361261e-01 0.8587456
## 4926 4.852557e-03 1.297973e-01 0.8653501
## 4937 5.424254e-03 1.428113e-01 0.8517644
## 4938 7.609829e-03 1.889798e-01 0.8034103
## 4940 4.839360e-03 1.294919e-01 0.8656687
## 4946 5.283826e-03 1.396529e-01 0.8550633
## 4950 1.247839e-02 2.748753e-01 0.7126463
## 4954 1.554928e-03 4.578782e-02 0.9526573
## 4956 1.016759e-02 2.366976e-01 0.7531349
## 4958 4.088845e-03 1.117472e-01 0.8841640
## 4961 1.146897e-02 2.587235e-01 0.7298075
## 4962 8.247015e-03 2.014597e-01 0.7902933
## 4964 5.641443e-03 1.476482e-01 0.8467104
## 4967 7.551808e-03 1.878226e-01 0.8046256
## 4970 4.192185e-03 1.142356e-01 0.8815722
## 4971 1.020447e-02 2.373415e-01 0.7524540
## 4977 1.157834e-02 2.605117e-01 0.7279100
## 4979 3.556301e-03 9.868707e-02 0.8977566
## 4981 4.981353e-03 1.327655e-01 0.8622532
## 4990 4.063651e-03 1.111383e-01 0.8847981
## 4995 9.464658e-03 2.241965e-01 0.7663388
## 4996 1.151036e-02 2.594014e-01 0.7290882
## 5002 3.087875e-03 8.686170e-02 0.9100504
## 5005 2.641455e-03 7.528555e-02 0.9220730
## 5006 1.128477e-02 2.556905e-01 0.7330247
## 5007 4.981353e-03 1.327655e-01 0.8622532
## 5008 2.066453e-02 3.817229e-01 0.5976125
## 5009 1.055511e-02 2.434044e-01 0.7460405
## 5010 3.961698e-03 1.086652e-01 0.8873731
## 5013 2.976033e-03 8.399003e-02 0.9130339
## 5016 7.502660e-03 1.868396e-01 0.8056577
## 5017 5.740718e-03 1.498399e-01 0.8444194
## 5018 6.736253e-03 1.711750e-01 0.8220888
## 5025 1.419340e-02 3.006106e-01 0.6851960
## 5028 4.267233e-03 1.160336e-01 0.8796992
## 5031 1.598765e-02 3.254501e-01 0.6585622
## 5032 3.746898e-03 1.034073e-01 0.8928458
## 5034 4.346011e-03 1.179127e-01 0.8777413
## 5037 5.274599e-03 1.394445e-01 0.8552809
## 5041 5.424254e-03 1.428113e-01 0.8517644
## 5046 8.143552e-03 1.994613e-01 0.7923951
## 5049 4.981353e-03 1.327655e-01 0.8622532
## 5056 5.416594e-03 1.426397e-01 0.8519437
## 5059 1.562581e-02 3.206013e-01 0.6637729
## 5061 8.099670e-03 1.986106e-01 0.7932898
## 5062 3.365652e-03 9.391307e-02 0.9027213
## 5064 9.094653e-03 2.174363e-01 0.7734690
## 5067 3.779451e-03 1.042084e-01 0.8920122
## 5069 3.159801e-03 8.869855e-02 0.9081417
## 5088 1.343706e-02 2.895145e-01 0.6970484
## 5092 1.148786e-02 2.590331e-01 0.7294791
## 5093 1.484394e-02 3.098507e-01 0.6753053
## 5094 1.044473e-02 2.415071e-01 0.7480482
## 5100 1.477562e-02 3.088932e-01 0.6763312
## 5101 1.337521e-02 2.885897e-01 0.6980351
## 5104 1.735721e-02 3.431164e-01 0.6395264
## 5110 6.770067e-03 1.718797e-01 0.8213503
## 5112 5.105515e-03 1.356067e-01 0.8592877
## 5116 6.691894e-03 1.702486e-01 0.8230595
## 5119 9.503637e-03 2.249013e-01 0.7655950
## 5120 7.577221e-03 1.883299e-01 0.8040929
## 5121 8.235403e-03 2.012359e-01 0.7905286
## 5125 8.221364e-03 2.009653e-01 0.7908134
## 5131 1.884878e-02 3.611980e-01 0.6199533
## 5144 1.146897e-02 2.587235e-01 0.7298075
## 5146 7.396152e-03 1.847006e-01 0.8079033
## 5151 6.810987e-03 1.727307e-01 0.8204583
## 5155 1.315024e-02 2.852036e-01 0.7016461
## 5157 1.105094e-02 2.518008e-01 0.7371483
## 5158 5.568125e-03 1.460219e-01 0.8484100
## 5159 1.146897e-02 2.587235e-01 0.7298075
## 5166 8.247015e-03 2.014597e-01 0.7902933
## 5168 1.537287e-02 3.171648e-01 0.6674624
## 5170 4.862680e-03 1.300314e-01 0.8651060
## 5171 1.564402e-02 3.208472e-01 0.6635088
## 5173 1.532138e-02 3.164603e-01 0.6682183
## 5183 3.192842e-03 8.953974e-02 0.9072674
## 5185 1.366159e-02 2.928492e-01 0.6934893
## 5188 3.712536e-03 1.025602e-01 0.8937273
## 5190 1.171074e-02 2.626637e-01 0.7256255
## 5193 8.680639e-03 2.097197e-01 0.7815997
## 5196 1.111161e-02 2.528143e-01 0.7360741
## 5199 1.371450e-02 2.936300e-01 0.6926555
## 5205 1.246396e-02 2.746499e-01 0.7128861
## 5207 1.226669e-02 2.715522e-01 0.7161811
## 5212 1.146897e-02 2.587235e-01 0.7298075
## 5213 1.471555e-02 3.080488e-01 0.6772357
## 5214 1.126254e-02 2.553225e-01 0.7334149
## 5216 1.194204e-02 2.663906e-01 0.7216674
## 5218 1.146897e-02 2.587235e-01 0.7298075
## 5222 1.916989e-02 3.649424e-01 0.6158877
## 5226 1.299575e-02 2.828575e-01 0.7041468
## 5230 9.464658e-03 2.241965e-01 0.7663388
## 5237 4.535968e-03 1.224093e-01 0.8730547
## 5242 1.201374e-02 2.675374e-01 0.7204489
## 5245 5.416594e-03 1.426397e-01 0.8519437
## 5248 3.851753e-03 1.059821e-01 0.8901661
## 5252 5.188228e-03 1.374886e-01 0.8573232
## 5255 7.316914e-03 1.831014e-01 0.8095817
## 5257 3.837960e-03 1.056443e-01 0.8905177
## 5259 4.981353e-03 1.327655e-01 0.8622532
## 5263 4.340814e-03 1.177890e-01 0.8778702
## 5265 1.194204e-02 2.663906e-01 0.7216674
## 5266 1.228391e-02 2.718238e-01 0.7158922
## 5267 1.246396e-02 2.746499e-01 0.7128861
## 5275 1.246396e-02 2.746499e-01 0.7128861
## 5277 4.981353e-03 1.327655e-01 0.8622532
## 5279 1.471555e-02 3.080488e-01 0.6772357
## 5280 1.583402e-02 3.234009e-01 0.6607651
## 5283 2.638577e-02 4.373626e-01 0.5362517
## 5284 6.691894e-03 1.702486e-01 0.8230595
## 5289 1.598765e-02 3.254501e-01 0.6585622
## 5291 3.377941e-03 9.422239e-02 0.9023997
## 5293 4.859778e-03 1.299643e-01 0.8651759
## 5294 1.866818e-02 3.590695e-01 0.6222623
## 5296 3.019346e-03 8.510437e-02 0.9118763
## 5301 1.425230e-02 3.014586e-01 0.6842891
## 5304 8.513397e-03 2.065558e-01 0.7849308
## 5306 1.564402e-02 3.208472e-01 0.6635088
## 5308 8.881334e-03 2.134808e-01 0.7776379
## 5310 1.462704e-02 3.068004e-01 0.6785726
## 5312 2.873334e-03 8.133644e-02 0.9157902
## 5319 1.884878e-02 3.611980e-01 0.6199533
## 5321 1.884878e-02 3.611980e-01 0.6199533
## 5328 1.542464e-02 3.178713e-01 0.6667041
## 5329 3.270861e-03 9.151965e-02 0.9052095
## 5331 1.471555e-02 3.080488e-01 0.6772357
## 5335 1.595559e-02 3.250237e-01 0.6590207
## 5337 9.702982e-03 2.284844e-01 0.7618126
## 5339 1.576767e-02 3.225117e-01 0.6617207
## 5341 1.469233e-02 3.077217e-01 0.6775860
## 5342 2.065754e-02 3.816469e-01 0.5976956
## 5343 8.754004e-03 2.110990e-01 0.7801470
## 5352 1.795067e-02 3.504497e-01 0.6315996
## 5356 9.226693e-03 2.198633e-01 0.7709100
## 5358 9.483431e-03 2.245361e-01 0.7659804
## 5360 1.641839e-02 3.311217e-01 0.6524599
## 5361 9.642810e-03 2.274066e-01 0.7629506
## 5364 2.169216e-02 3.926740e-01 0.5856338
## 5365 5.611068e-03 1.469752e-01 0.8474137
## 5366 5.467267e-03 1.437739e-01 0.8507589
## 5371 1.616002e-02 3.277328e-01 0.6561072
## 5374 1.397989e-02 2.975174e-01 0.6885027
## 5375 9.786669e-03 2.299779e-01 0.7602354
## 5376 5.611737e-03 1.469901e-01 0.8473982
## 5377 1.019106e-02 2.371075e-01 0.7527014
## 5379 1.222177e-02 2.708428e-01 0.7169354
## 5380 8.233733e-03 2.012038e-01 0.7905625
## 5385 1.005878e-02 2.347911e-01 0.7551501
## 5389 8.072038e-03 1.980738e-01 0.7938542
## 5390 1.539546e-02 3.174733e-01 0.6671313
## 5392 4.965486e-03 1.324010e-01 0.8626335
## 5397 3.530229e-03 9.803731e-02 0.8984325
## 5398 1.758978e-02 3.460127e-01 0.6363975
## 5407 7.818234e-03 1.931074e-01 0.7990743
## 5414 1.390033e-02 2.963571e-01 0.6897426
## 5417 7.024038e-03 1.771320e-01 0.8158439
## 5418 1.466914e-02 3.073948e-01 0.6779361
## 5420 1.455072e-02 3.057198e-01 0.6797295
## 5431 1.962104e-02 3.701183e-01 0.6102607
## 5433 3.733295e-02 5.157407e-01 0.4469264
## 5437 4.565450e-03 1.231029e-01 0.8723316
## 5438 8.198071e-03 2.005157e-01 0.7912862
## 5442 1.727432e-02 3.420771e-01 0.6406486
## 5445 1.312554e-02 2.848296e-01 0.7020449
## 5449 1.013537e-02 2.361341e-01 0.7537305
## 5450 8.074508e-03 1.981218e-01 0.7938037
## 5456 4.829456e-03 1.292627e-01 0.8659079
## 5464 1.376750e-02 2.944101e-01 0.6918224
## 5466 1.727432e-02 3.420771e-01 0.6406486
## 5472 1.498887e-02 3.118722e-01 0.6731390
## 5479 2.545851e-02 4.291695e-01 0.5453720
## 5483 6.721857e-03 1.708745e-01 0.8224036
## 5491 1.242456e-02 2.740335e-01 0.7135419
## 5493 1.116204e-02 2.536544e-01 0.7351836
## 5495 1.242456e-02 2.740335e-01 0.7135419
## 5496 1.642660e-02 3.312287e-01 0.6523447
## 5498 1.090183e-02 2.492972e-01 0.7398010
## 5500 1.254321e-02 2.758861e-01 0.7115707
## 5501 7.610113e-03 1.889855e-01 0.8034044
## 5507 5.656876e-03 1.479897e-01 0.8463534
## 5508 8.358687e-03 2.036046e-01 0.7880367
## 5509 1.522929e-02 3.151965e-01 0.6695742
## 5510 1.379517e-02 2.948166e-01 0.6913882
## 5514 1.841328e-02 3.560376e-01 0.6255491
## 5515 1.401667e-02 2.980525e-01 0.6879308
## 5520 6.928792e-03 1.751706e-01 0.8179006
## 5526 1.252476e-02 2.755987e-01 0.7118765
## 5527 1.129742e-02 2.558996e-01 0.7328030
## 5528 1.684119e-02 3.365846e-01 0.6465742
## 5529 4.957571e-03 1.322190e-01 0.8628234
## 5531 1.101962e-02 2.512765e-01 0.7377039
## 5533 8.161391e-03 1.998067e-01 0.7920319
## 5534 1.448044e-02 3.047216e-01 0.6807980
## 5536 1.756210e-02 3.456695e-01 0.6367684
## 5541 2.196091e-02 3.954631e-01 0.5825760
## 5551 1.031736e-02 2.393049e-01 0.7503778
## 5555 1.359693e-02 2.918925e-01 0.6945106
## 5556 1.687020e-02 3.369557e-01 0.6461741
## 5559 1.724713e-02 3.417353e-01 0.6410176
## 5560 1.258433e-02 2.765257e-01 0.7108900
## 5565 1.141457e-02 2.578306e-01 0.7307548
## 5567 2.284907e-02 4.044689e-01 0.5726820
## 5568 1.522929e-02 3.151965e-01 0.6695742
## 5584 1.291608e-02 2.816409e-01 0.7054430
## 5585 1.552899e-02 3.192905e-01 0.6651806
## 5588 1.464598e-02 3.070680e-01 0.6782860
## 5589 1.317087e-02 2.855156e-01 0.7013136
## 5596 2.245712e-02 4.005341e-01 0.5770088
## 5607 6.947416e-03 1.755549e-01 0.8174977
## 5619 5.407644e-03 1.424390e-01 0.8521533
## 5620 2.630179e-03 7.498918e-02 0.9223806
## 5621 6.070846e-03 1.570430e-01 0.8368861
## 5626 1.187080e-02 2.652470e-01 0.7228822
## 5630 1.251035e-02 2.753740e-01 0.7121156
## 5632 3.395151e-02 4.946791e-01 0.4713694
## 5633 4.150012e-03 1.132219e-01 0.8826281
## 5634 2.167968e-02 3.925437e-01 0.5857766
## 5636 3.839051e-03 1.056711e-01 0.8904899
## 5637 1.414305e-02 2.998839e-01 0.6859730
## 5639 1.389985e-02 2.963500e-01 0.6897502
## 5640 1.064220e-02 2.448939e-01 0.7444639
## 5641 1.461402e-02 3.066163e-01 0.6787697
## 5643 4.902520e-03 1.309513e-01 0.8641462
## 5645 9.547618e-03 2.256950e-01 0.7647574
## 5647 7.912637e-03 1.949624e-01 0.7971250
## 5663 3.495994e-03 9.718265e-02 0.8993214
## 5666 6.279282e-03 1.615246e-01 0.8321961
## 5669 4.902520e-03 1.309513e-01 0.8641462
## 5673 1.117275e-02 2.538327e-01 0.7349946
## 5681 5.330910e-03 1.407146e-01 0.8539545
## 5684 1.240497e-02 2.737267e-01 0.7138684
## 5686 8.324963e-03 2.029582e-01 0.7887169
## 5687 1.119884e-02 2.542662e-01 0.7345350
## 5688 1.427554e-02 3.017925e-01 0.6839319
## 5690 4.902520e-03 1.309513e-01 0.8641462
## 5693 4.192696e-03 1.142479e-01 0.8815594
## 5697 1.873056e-02 3.598066e-01 0.6214628
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## 5707 6.907052e-03 1.747215e-01 0.8183715
## 5715 5.191149e-03 1.375549e-01 0.8572539
## 5719 4.518529e-03 1.219985e-01 0.8734829
## 5723 4.902520e-03 1.309513e-01 0.8641462
## 5731 4.342957e-03 1.178400e-01 0.8778171
## 5732 1.128863e-02 2.557543e-01 0.7329570
## 5742 5.117262e-03 1.358745e-01 0.8590082
## 5755 1.608002e-02 3.266755e-01 0.6572445
## 5757 1.294459e-02 2.820767e-01 0.7049787
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## 5771 9.348853e-03 2.220943e-01 0.7685568
## 5772 7.432599e-03 1.854339e-01 0.8071335
## 5773 1.128863e-02 2.557543e-01 0.7329570
## 5776 1.777541e-02 3.483035e-01 0.6339211
## 5781 7.856821e-03 1.938667e-01 0.7982764
## 5785 8.856385e-03 2.130153e-01 0.7781283
## 5789 2.714415e-03 7.719841e-02 0.9200872
## 5794 1.376206e-02 2.943301e-01 0.6919078
## 5801 1.335027e-02 2.882161e-01 0.6984337
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## 5815 4.902520e-03 1.309513e-01 0.8641462
## 5817 3.644603e-03 1.008804e-01 0.8954750
## 5819 1.353505e-02 2.909742e-01 0.6954908
## 5830 3.400001e-03 9.477710e-02 0.9018229
## 5833 8.243729e-03 2.013964e-01 0.7903599
## 5842 1.238535e-02 2.734189e-01 0.7141957
## 5844 9.851591e-03 2.311322e-01 0.7590162
## 5847 6.029268e-03 1.561430e-01 0.8378278
## 5859 1.043580e-02 2.413532e-01 0.7482110
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## 5880 7.237761e-03 1.814973e-01 0.8112650
## 5884 1.345506e-02 2.897832e-01 0.6967617
## 5887 4.894705e-03 1.307710e-01 0.8643343
## 5888 8.251572e-03 2.015475e-01 0.7902010
## 5891 1.835972e-03 5.360418e-02 0.9445599
## 5893 6.191917e-03 1.596524e-01 0.8341557
## 5894 1.360020e-02 2.919410e-01 0.6944588
## 5898 4.369417e-03 1.184693e-01 0.8771612
## 5899 1.284908e-02 2.806144e-01 0.7065365
## 5906 4.369417e-03 1.184693e-01 0.8771612
## 5910 1.115251e-02 2.534958e-01 0.7353517
## 5915 1.348606e-02 2.902453e-01 0.6962687
## 5916 1.019166e-02 2.371180e-01 0.7526903
## 5921 1.038334e-02 2.404473e-01 0.7491693
## 5922 1.438233e-02 3.033226e-01 0.6822951
## 5925 1.480489e-02 3.093037e-01 0.6758914
## 5926 1.870456e-02 3.594996e-01 0.6217958
## 5927 7.420781e-03 1.851963e-01 0.8073829
## 5933 7.944462e-03 1.955857e-01 0.7964699
## 5935 1.084080e-02 2.482672e-01 0.7408920
## 5939 3.450259e-03 9.603822e-02 0.9005115
## 5943 1.004655e-02 2.345761e-01 0.7553773
## 5947 1.370394e-02 2.934743e-01 0.6928217
## 5958 1.434527e-02 3.027924e-01 0.6828623
## 5959 1.711360e-02 3.400512e-01 0.6428352
## 5964 8.273566e-03 2.019708e-01 0.7897556
## 5965 5.329943e-03 1.406928e-01 0.8539772
## 5968 1.434527e-02 3.027924e-01 0.6828623
## 5978 1.847465e-02 3.567705e-01 0.6247549
## 5981 5.863215e-03 1.525279e-01 0.8416089
## 5984 1.127075e-02 2.554585e-01 0.7332707
## 5995 1.127075e-02 2.554585e-01 0.7332707
## 5999 1.384053e-02 2.954820e-01 0.6906775
## 6002 1.571257e-02 3.217711e-01 0.6625163
## 6004 7.244416e-03 1.816324e-01 0.8111232
## 6006 5.329943e-03 1.406928e-01 0.8539772
## 6008 1.327092e-02 2.870245e-01 0.6997046
## 6013 1.504812e-02 3.126948e-01 0.6722571
## 6015 1.394751e-02 2.970457e-01 0.6890068
## 6020 1.444413e-02 3.042045e-01 0.6813514
## 6025 1.102926e-02 2.514379e-01 0.7375328
## 6033 2.049417e-02 3.798625e-01 0.5996434
## 6037 1.568750e-02 3.214334e-01 0.6628791
## 6039 1.456792e-02 3.059636e-01 0.6794684
## 6041 1.503294e-02 3.124843e-01 0.6724828
## 6042 9.024744e-03 2.161448e-01 0.7748305
## 6053 7.056468e-03 1.777976e-01 0.8151459
## 6054 5.914246e-03 1.536424e-01 0.8404434
## 6055 1.125290e-02 2.551630e-01 0.7335841
## 6061 1.611692e-02 3.271637e-01 0.6567194
## 6062 1.617465e-02 3.279257e-01 0.6558996
## 6064 2.045989e-02 3.794865e-01 0.6000536
## 6067 7.600455e-03 1.887931e-01 0.8036064
## 6069 1.662057e-02 3.337467e-01 0.6496327
## 6077 6.614765e-03 1.686325e-01 0.8247527
## 6080 9.202482e-03 2.194196e-01 0.7713780
## 6089 3.418798e-03 9.524920e-02 0.9013320
## 6092 1.098647e-02 2.507206e-01 0.7382929
## 6094 8.477503e-03 2.058732e-01 0.7856493
## 6097 1.550761e-02 3.190002e-01 0.6654922
## 6098 2.085373e-02 3.837740e-01 0.5953723
## 6100 1.518866e-02 3.146373e-01 0.6701741
## 6106 9.280799e-03 2.208532e-01 0.7698660
## 6110 4.770469e-03 1.278943e-01 0.8673352
## 6111 3.331358e-03 9.304869e-02 0.9036200
## 6116 1.125290e-02 2.551630e-01 0.7335841
## 6120 1.568750e-02 3.214334e-01 0.6628791
## 6121 3.596001e-03 9.967456e-02 0.8967294
## 6125 1.125290e-02 2.551630e-01 0.7335841
## 6127 3.581199e-03 9.930664e-02 0.8971122
## 6128 1.213220e-02 2.694236e-01 0.7184442
## 6129 1.508438e-02 3.131971e-01 0.6717185
## 6130 4.886902e-03 1.305909e-01 0.8645222
## 6134 2.178707e-02 3.936625e-01 0.5845504
## 6138 1.489587e-02 3.105765e-01 0.6745276
## 6140 1.125290e-02 2.551630e-01 0.7335841
## 6141 1.717799e-02 3.408645e-01 0.6419575
## 6142 1.494891e-02 3.113162e-01 0.6737349
## 6143 8.079754e-03 1.982238e-01 0.7936965
## 6145 1.125290e-02 2.551630e-01 0.7335841
## 6150 1.581271e-02 3.231156e-01 0.6610717
## 6151 1.125290e-02 2.551630e-01 0.7335841
## 6153 1.091794e-02 2.495686e-01 0.7395135
## 6156 1.069746e-02 2.458359e-01 0.7434667
## 6164 1.700427e-02 3.386648e-01 0.6443309
## 6171 3.120137e-03 8.768656e-02 0.9091933
## 6172 7.408982e-03 1.849589e-01 0.8076321
## 6178 1.808259e-02 3.520544e-01 0.6298630
## 6181 3.683072e-02 5.127636e-01 0.4504057
## 6188 9.529298e-03 2.253646e-01 0.7651061
## 6191 1.686979e-02 3.369505e-01 0.6461798
## 6197 1.847050e-02 3.567210e-01 0.6248085
## 6200 3.158158e-03 8.865665e-02 0.9081852
## 6203 1.838029e-02 3.556427e-01 0.6259770
## 6210 8.524161e-03 2.067602e-01 0.7847156
## 6214 1.227175e-02 2.716321e-01 0.7160962
## 6215 7.397202e-03 1.847217e-01 0.8078811
## 6216 8.726282e-03 2.105784e-01 0.7806953
## 6221 1.835250e-02 3.553096e-01 0.6263379
## 6224 1.697749e-02 3.383243e-01 0.6446982
## 6231 1.500922e-02 3.121550e-01 0.6728358
## 6235 1.234619e-02 2.728041e-01 0.7148497
## 6236 1.169862e-02 2.624672e-01 0.7258342
## 6237 9.197993e-03 2.193372e-01 0.7714648
## 6238 1.278491e-02 2.796280e-01 0.7075871
## 6240 8.354031e-03 2.035154e-01 0.7881305
## 6243 9.959967e-03 2.330508e-01 0.7569892
## 6246 7.230772e-03 1.813553e-01 0.8114139
## 6247 6.775798e-03 1.719990e-01 0.8212252
## 6250 1.441642e-02 3.038093e-01 0.6817743
## 6262 1.050803e-02 2.425963e-01 0.7468957
## 6266 1.775818e-02 3.480917e-01 0.6341501
## 6270 8.839600e-03 2.127018e-01 0.7784586
## 6272 5.567412e-03 1.460060e-01 0.8484266
## 6275 1.566306e-02 3.211041e-01 0.6632329
## 6276 5.951317e-03 1.544500e-01 0.8395987
## 6279 2.386475e-03 6.853501e-02 0.9290785
## 6281 6.575263e-03 1.678022e-01 0.8256225
## 6283 6.554777e-03 1.673710e-01 0.8260743
## 6284 8.863646e-03 2.131508e-01 0.7779855
## 6287 2.042130e-02 3.790627e-01 0.6005160
## 6288 1.430001e-02 3.021437e-01 0.6835563
## 6290 1.123508e-02 2.548676e-01 0.7338973
## 6292 8.414955e-03 2.046807e-01 0.7869044
## 6294 1.156426e-02 2.602819e-01 0.7281538
## 6301 1.441642e-02 3.038093e-01 0.6817743
## 6305 9.509698e-03 2.250108e-01 0.7654795
## 6308 1.492532e-02 3.109875e-01 0.6740872
## 6311 5.518570e-03 1.449189e-01 0.8495625
## 6312 1.002918e-02 2.342708e-01 0.7557000
## 6313 1.123508e-02 2.548676e-01 0.7338973
## 6317 9.454507e-03 2.240127e-01 0.7665327
## 6319 1.697749e-02 3.383243e-01 0.6446982
## 6320 6.575263e-03 1.678022e-01 0.8256225
## 6322 1.749199e-02 3.447985e-01 0.6377096
## 6323 1.379683e-02 2.948411e-01 0.6913620
## 6334 1.123508e-02 2.548676e-01 0.7338973
## 6336 4.879113e-03 1.304110e-01 0.8647098
## 6339 8.247300e-03 2.014652e-01 0.7902875
## 6341 1.169862e-02 2.624672e-01 0.7258342
## 6342 1.123508e-02 2.548676e-01 0.7338973
## 6343 7.126511e-03 1.792312e-01 0.8136423
## 6345 1.123508e-02 2.548676e-01 0.7338973
## 6347 1.368736e-02 2.932298e-01 0.6930829
## 6349 1.359557e-02 2.918723e-01 0.6945321
## 6350 8.405819e-03 2.045062e-01 0.7870880
## 6351 6.073016e-03 1.570900e-01 0.8368370
## 6353 1.688165e-02 3.371022e-01 0.6460162
## 6354 1.271328e-02 2.785235e-01 0.7087633
## 6359 1.249891e-02 2.751956e-01 0.7123055
## 6362 1.123508e-02 2.548676e-01 0.7338973
## 6366 1.692407e-02 3.376436e-01 0.6454323
## 6367 9.424527e-03 2.234694e-01 0.7671061
## 6368 1.439193e-02 3.034597e-01 0.6821484
## 6375 1.117963e-02 2.539470e-01 0.7348734
## 6377 1.080639e-02 2.476851e-01 0.7415086
## 6384 7.762714e-03 1.920122e-01 0.8002251
## 6386 1.491176e-02 3.107984e-01 0.6742899
## 6387 1.437093e-02 3.031596e-01 0.6824695
## 6388 1.648732e-02 3.320192e-01 0.6514935
## 6395 1.692407e-02 3.376436e-01 0.6454323
## 6396 1.523761e-02 3.153110e-01 0.6694514
## 6406 1.003215e-02 2.343230e-01 0.7556449
## 6407 2.375897e-02 4.133704e-01 0.5628707
## 6411 9.352471e-03 2.221602e-01 0.7684873
## 6414 1.487825e-02 3.103305e-01 0.6747912
## 6418 6.450746e-03 1.651735e-01 0.8283757
## 6419 1.241171e-02 2.738322e-01 0.7137561
## 6420 1.119952e-02 2.542774e-01 0.7345230
## 6427 1.751287e-02 3.450581e-01 0.6374290
## 6428 8.442760e-03 2.052113e-01 0.7863460
## 6430 1.095328e-02 2.501632e-01 0.7388835
## 6433 1.119952e-02 2.542774e-01 0.7345230
## 6434 9.570525e-03 2.261076e-01 0.7643219
## 6435 3.526590e-02 5.031564e-01 0.4615777
## 6438 6.332052e-03 1.626512e-01 0.8310167
## 6439 1.692319e-02 3.376324e-01 0.6454444
## 6443 1.523761e-02 3.153110e-01 0.6694514
## 6445 1.548975e-02 3.187575e-01 0.6657527
## 6446 1.526191e-02 3.156448e-01 0.6690933
## 6447 1.235191e-02 2.728940e-01 0.7147541
## 6463 1.039540e-02 2.406558e-01 0.7489488
## 6465 1.241171e-02 2.738322e-01 0.7137561
## 6468 1.097775e-02 2.505742e-01 0.7384480
## 6476 4.152727e-03 1.132872e-01 0.8825601
## 6477 1.164221e-02 2.615516e-01 0.7268062
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## 6481 1.482253e-02 3.095509e-01 0.6756265
## 6486 1.652800e-02 3.325477e-01 0.6509243
## 6491 1.184678e-02 2.648606e-01 0.7232926
## 6493 1.303039e-02 2.833850e-01 0.7035846
## 6495 7.771161e-03 1.921791e-01 0.8000498
## 6496 6.422311e-03 1.645707e-01 0.8290069
## 6502 5.852534e-03 1.522942e-01 0.8418532
## 6503 8.974874e-03 2.152206e-01 0.7758045
## 6508 1.479538e-02 3.091705e-01 0.6760342
## 6511 1.587474e-02 3.239456e-01 0.6601797
## 6512 1.447614e-02 3.046604e-01 0.6808634
## 6521 1.047732e-02 2.420683e-01 0.7474544
## 6522 1.106698e-02 2.520691e-01 0.7368639
## 6524 9.262134e-03 2.205120e-01 0.7702258
## 6531 1.829623e-02 3.546342e-01 0.6270696
## 6534 1.320563e-02 2.860406e-01 0.7007538
## 6535 9.571542e-03 2.261259e-01 0.7643026
## 6536 3.563281e-03 9.886085e-02 0.8975759
## 6537 7.879396e-03 1.943103e-01 0.7978103
## 6544 1.795391e-02 3.504893e-01 0.6315568
## 6547 1.497344e-02 3.116576e-01 0.6733689
## 6551 1.652800e-02 3.325477e-01 0.6509243
## 6554 1.359602e-02 2.918790e-01 0.6945250
## 6558 1.521358e-02 3.149804e-01 0.6698061
## 6561 1.935887e-02 3.671224e-01 0.6135187
## 6562 1.356698e-02 2.914484e-01 0.6949847
## 6566 1.164314e-02 2.615667e-01 0.7267902
## 6569 1.564847e-02 3.209072e-01 0.6634443
## 6570 1.839985e-02 3.558769e-01 0.6257233
## 6571 1.553304e-02 3.193454e-01 0.6651216
## 6572 1.373155e-02 2.938811e-01 0.6923873
## 6573 1.219592e-02 2.704338e-01 0.7173702
## 6574 1.912554e-02 3.644283e-01 0.6164462
## 6578 8.003545e-03 1.967400e-01 0.7952564
## 6579 1.029056e-02 2.388398e-01 0.7508696
## 6585 4.848076e-03 1.296936e-01 0.8654583
## 6590 1.402388e-02 2.981573e-01 0.6878188
## 6591 8.517317e-03 2.066303e-01 0.7848524
## 6592 8.410391e-03 2.045935e-01 0.7869961
## 6597 2.110658e-02 3.864902e-01 0.5924032
## 6605 1.432559e-02 3.025105e-01 0.6831639
## 6607 7.585717e-03 1.884994e-01 0.8039149
## 6609 6.699389e-03 1.704052e-01 0.8228954
## 6611 7.001218e-03 1.766630e-01 0.8163358
## 6612 1.445329e-02 3.043350e-01 0.6812117
## 6616 8.353702e-03 2.035091e-01 0.7881372
## 6622 4.294700e-03 1.166897e-01 0.8790156
## 6625 1.518958e-02 3.146499e-01 0.6701605
## 6630 1.687080e-02 3.369634e-01 0.6461657
## 6636 9.886338e-03 2.317485e-01 0.7583652
## 6640 1.717902e-02 3.408775e-01 0.6419434
## 6641 5.460891e-03 1.436313e-01 0.8509078
## 6651 1.116407e-02 2.536881e-01 0.7351478
## 6653 1.237247e-02 2.732168e-01 0.7144107
## 6655 9.820095e-03 2.305727e-01 0.7596072
## 6663 7.609328e-03 1.889698e-01 0.8034208
## 6667 1.470622e-02 3.079174e-01 0.6773763
## 6673 6.874232e-03 1.740425e-01 0.8190833
## 6674 1.318920e-02 2.857925e-01 0.7010183
## 6676 8.841699e-03 2.127410e-01 0.7784173
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## 6680 1.083298e-02 2.481350e-01 0.7410320
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## 6689 2.535717e-02 4.282563e-01 0.5463865
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## 6788 1.745243e-02 3.443057e-01 0.6382419
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## 6968 1.107592e-02 2.522185e-01 0.7367056
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## 6985 1.184663e-02 2.648582e-01 0.7232952
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## 6999 1.240604e-02 2.737433e-01 0.7138507
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## 7004 1.107592e-02 2.522185e-01 0.7367056
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## 7006 1.380362e-02 2.949408e-01 0.6912556
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## 7009 7.705041e-03 1.908712e-01 0.8014238
## 7012 1.008648e-02 2.352774e-01 0.7546361
## 7014 8.460448e-03 2.055484e-01 0.7859911
## 7015 1.449873e-02 3.049817e-01 0.6805196
## 7016 5.579254e-03 1.462692e-01 0.8481516
## 7019 1.388798e-02 2.961766e-01 0.6899354
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## 7055 1.040570e-02 2.408337e-01 0.7487606
## 7058 1.107592e-02 2.522185e-01 0.7367056
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## 7066 1.101369e-02 2.511770e-01 0.7378093
## 7069 3.904870e-09 1.207007e-07 0.9999999
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## 7077 1.238321e-02 2.733854e-01 0.7142314
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## 7082 1.319440e-02 2.858710e-01 0.7009346
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## 7088 1.252022e-02 2.755280e-01 0.7119518
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## 7094 1.107592e-02 2.522185e-01 0.7367056
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## 7110 9.139662e-03 2.182655e-01 0.7725949
## 7112 1.431540e-02 3.023645e-01 0.6833201
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## 7115 8.750453e-03 2.110324e-01 0.7802172
## 7116 7.292012e-03 1.825975e-01 0.8101105
## 7120 3.687902e-03 1.019518e-01 0.8943603
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## 7158 1.325613e-02 2.868019e-01 0.6999420
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## 7161 5.325356e-03 1.405895e-01 0.8540851
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## 7179 1.869349e-02 3.593688e-01 0.6219377
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## 7192 1.534621e-02 3.168002e-01 0.6678536
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## 7207 1.514563e-02 3.140438e-01 0.6708106
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## 7210 1.215223e-02 2.697415e-01 0.7181063
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## 7222 7.313135e-03 1.830250e-01 0.8096619
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## 7241 1.634657e-02 3.301835e-01 0.6534699
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## 7285 9.977025e-03 2.333519e-01 0.7566711
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## 7344 1.045627e-02 2.417059e-01 0.7478379
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## 7408 3.909842e-03 1.074019e-01 0.8886883
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## 7428 1.049577e-02 2.423857e-01 0.7471186
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## 7433 1.034518e-02 2.397871e-01 0.7498677
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## 7463 8.962261e-03 2.149865e-01 0.7760513
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## 7467 1.213300e-02 2.694363e-01 0.7184307
## 7472 1.199916e-02 2.673045e-01 0.7206963
## 7475 9.790908e-03 2.300534e-01 0.7601557
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## 7498 1.355893e-02 2.913289e-01 0.6951122
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## 7529 1.668568e-02 3.345870e-01 0.6487273
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## 7531 6.710410e-03 1.706355e-01 0.8226541
## 7532 4.794234e-03 1.284461e-01 0.8667596
## 7533 1.668568e-02 3.345870e-01 0.6487273
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## 7547 1.553056e-02 3.193117e-01 0.6651577
## 7549 5.470626e-03 1.438489e-01 0.8506805
## 7551 1.259422e-02 2.766794e-01 0.7107264
## 7552 1.223609e-02 2.710691e-01 0.7166948
## 7553 4.544144e-03 1.226018e-01 0.8728541
## 7556 1.286648e-02 2.808812e-01 0.7062523
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## 7566 1.122434e-02 2.546895e-01 0.7340862
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## 7570 1.009873e-02 2.354923e-01 0.7544090
## 7573 9.149469e-03 2.184459e-01 0.7724046
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## 7586 1.104086e-02 2.516321e-01 0.7373270
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## 7598 7.684281e-03 1.904596e-01 0.8018561
## 7601 1.282808e-02 2.802919e-01 0.7068800
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## 7620 1.349798e-02 2.904227e-01 0.6960793
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## 7627 1.104086e-02 2.516321e-01 0.7373270
## 7629 1.502262e-02 3.123410e-01 0.6726363
## 7631 1.199916e-02 2.673045e-01 0.7206963
## 7633 1.668568e-02 3.345870e-01 0.6487273
## 7640 1.104086e-02 2.516321e-01 0.7373270
## 7645 1.668568e-02 3.345870e-01 0.6487273
## 7650 1.502262e-02 3.123410e-01 0.6726363
## 7651 1.326903e-02 2.869960e-01 0.6997350
## 7652 1.788261e-02 3.496182e-01 0.6324991
## 7654 8.104305e-03 1.987005e-01 0.7931952
## 7655 8.510775e-03 2.065060e-01 0.7849832
## 7659 1.104086e-02 2.516321e-01 0.7373270
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## 7673 1.563995e-02 3.207922e-01 0.6635678
## 7674 1.104086e-02 2.516321e-01 0.7373270
## 7676 3.878512e-03 1.066367e-01 0.8894848
## 7677 1.495518e-02 3.114035e-01 0.6736413
## 7678 1.074940e-02 2.467188e-01 0.7425318
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## 7704 3.019076e-02 4.681505e-01 0.5016587
## 7709 7.562077e-03 1.880277e-01 0.8044102
## 7712 1.256424e-02 2.762134e-01 0.7112224
## 7720 1.022029e-02 2.376173e-01 0.7521624
## 7721 1.305784e-02 2.838024e-01 0.7031398
## 7729 1.077939e-02 2.472277e-01 0.7419929
## 7730 5.621382e-03 1.472039e-01 0.8471747
## 7736 1.139946e-02 2.575821e-01 0.7310184
## 7739 1.332343e-02 2.878136e-01 0.6988630
## 7740 1.815025e-02 3.528740e-01 0.6289758
## 7741 1.668568e-02 3.345870e-01 0.6487273
## 7742 1.361825e-02 2.922082e-01 0.6941735
## 7743 6.002056e-03 1.555528e-01 0.8384452
## 7750 2.172238e-02 3.929892e-01 0.5852885
## 7753 1.495518e-02 3.114035e-01 0.6736413
## 7755 1.104086e-02 2.516321e-01 0.7373270
## 7757 1.104086e-02 2.516321e-01 0.7373270
## 7759 1.223609e-02 2.710691e-01 0.7166948
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## 7763 1.084861e-02 2.483992e-01 0.7407521
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## 7774 1.742955e-02 3.440204e-01 0.6385500
## 7778 6.574355e-03 1.677831e-01 0.8256425
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## 7788 9.846874e-03 2.310485e-01 0.7591046
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## 7793 3.022954e-03 8.519708e-02 0.9117800
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## 7807 1.102337e-02 2.513393e-01 0.7376374
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## 7815 1.221673e-02 2.707630e-01 0.7170202
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## 7849 1.102337e-02 2.513393e-01 0.7376374
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## 7857 1.102337e-02 2.513393e-01 0.7376374
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## 7876 1.395891e-02 2.972119e-01 0.6888292
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## 7883 1.649546e-02 3.321250e-01 0.6513795
## 7884 1.376063e-02 2.943091e-01 0.6919302
## 7888 1.104049e-02 2.516259e-01 0.7373336
## 7891 1.045903e-02 2.417535e-01 0.7477875
## 7892 9.846874e-03 2.310485e-01 0.7591046
## 7894 1.172551e-02 2.629029e-01 0.7253716
## 7896 1.102337e-02 2.513393e-01 0.7376374
## 7898 1.617740e-02 3.279620e-01 0.6558606
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## 7911 4.786591e-03 1.282687e-01 0.8669447
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## 7926 1.102337e-02 2.513393e-01 0.7376374
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## 7928 1.264015e-02 2.773920e-01 0.7099678
## 7929 1.355505e-02 2.912713e-01 0.6951737
## 7933 1.213169e-02 2.694156e-01 0.7184527
## 7936 1.301892e-02 2.832105e-01 0.7037706
## 7937 1.091428e-02 2.495069e-01 0.7395789
## 7939 1.499891e-02 3.120118e-01 0.6729893
## 7949 1.382227e-02 2.952144e-01 0.6909633
## 7953 1.249157e-02 2.750811e-01 0.7124273
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## 7957 1.161427e-02 2.610970e-01 0.7272888
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## 7965 1.221673e-02 2.707630e-01 0.7170202
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## 7967 1.318020e-02 2.856566e-01 0.7011632
## 7971 1.412327e-02 2.995981e-01 0.6862787
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## 7981 1.610566e-02 3.270148e-01 0.6568795
## 7983 8.349475e-03 2.034281e-01 0.7882224
## 7984 2.148297e-02 3.904818e-01 0.5880352
## 7988 6.926587e-03 1.751251e-01 0.8179484
## 7989 1.663315e-02 3.339093e-01 0.6494576
## 7991 7.268368e-03 1.821184e-01 0.8106133
## 7999 1.196121e-02 2.666975e-01 0.7213413
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## 8012 1.663315e-02 3.339093e-01 0.6494576
## 8013 1.802467e-02 3.513510e-01 0.6306243
## 8015 1.423871e-02 3.012632e-01 0.6844981
## 8017 1.191537e-02 2.659629e-01 0.7221217
## 8018 1.501494e-02 3.122345e-01 0.6727506
## 8019 1.054693e-02 2.432642e-01 0.7461889
## 8023 7.836310e-03 1.934633e-01 0.7987004
## 8026 1.663315e-02 3.339093e-01 0.6494576
## 8030 1.196121e-02 2.666975e-01 0.7213413
## 8034 5.633562e-03 1.474737e-01 0.8468927
## 8035 7.240382e-03 1.815505e-01 0.8112091
## 8043 1.014903e-02 2.363732e-01 0.7534778
## 8044 1.212004e-02 2.692304e-01 0.7186495
## 8049 1.262910e-02 2.772208e-01 0.7101501
## 8054 8.866893e-03 2.132114e-01 0.7779217
## 8065 1.345535e-02 2.897875e-01 0.6967572
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## 8067 1.165538e-02 2.617656e-01 0.7265790
## 8076 1.092400e-02 2.496706e-01 0.7394054
## 8083 1.134248e-02 2.566436e-01 0.7320139
## 8089 1.991128e-02 3.733968e-01 0.6066920
## 8090 1.258065e-02 2.764685e-01 0.7109508
## 8104 1.054502e-02 2.432313e-01 0.7462237
## 8108 4.260461e-03 1.158717e-01 0.8798679
## 8110 1.034851e-02 2.398449e-01 0.7498066
## 8111 1.066473e-02 2.452783e-01 0.7440570
## 8113 1.380044e-02 2.948940e-01 0.6913055
## 8118 6.516991e-03 1.665742e-01 0.8269088
## 8125 9.831256e-03 2.307711e-01 0.7593977
## 8127 5.633562e-03 1.474737e-01 0.8468927
## 8128 2.460913e-02 4.214041e-01 0.5539868
## 8133 1.294153e-02 2.820300e-01 0.7050285
## 8137 9.057325e-03 2.167473e-01 0.7741954
## 8138 1.497525e-02 3.116828e-01 0.6733420
## 8147 5.348255e-03 1.411050e-01 0.8535467
## 8150 5.633562e-03 1.474737e-01 0.8468927
## 8156 9.633255e-03 2.272352e-01 0.7631316
## 8167 1.270013e-02 2.783203e-01 0.7089795
## 8174 1.146010e-02 2.585780e-01 0.7299619
## 8176 1.712271e-02 3.401664e-01 0.6427109
## 8182 5.633562e-03 1.474737e-01 0.8468927
## 8198 1.559067e-02 3.201261e-01 0.6642833
## 8199 1.497525e-02 3.116828e-01 0.6733420
## 8206 1.042479e-02 2.411633e-01 0.7484119
## 8207 7.197910e-03 1.806871e-01 0.8121150
## 8208 1.325473e-02 2.867808e-01 0.6999644
## 8214 1.663315e-02 3.339093e-01 0.6494576
## 8215 7.360882e-03 1.839896e-01 0.8086495
## 8216 1.626942e-02 3.291724e-01 0.6545582
## 8218 9.328673e-03 2.217267e-01 0.7689446
## 8222 1.693711e-02 3.378099e-01 0.6452530
## 8223 1.262016e-02 2.770820e-01 0.7102978
## 8224 8.478013e-03 2.058829e-01 0.7856391
## 8226 1.645583e-02 3.316095e-01 0.6519347
## 8227 7.295880e-03 1.826758e-01 0.8100283
## 8230 7.599154e-03 1.887672e-01 0.8036337
## 8234 1.743546e-02 3.440941e-01 0.6384704
## 8235 4.687717e-03 1.259670e-01 0.8693453
## 8237 1.319681e-02 2.859075e-01 0.7008957
## 8239 2.115993e-02 3.870596e-01 0.5917804
## 8242 1.100590e-02 2.510466e-01 0.7379475
## 8243 1.100590e-02 2.510466e-01 0.7379475
## 8247 7.483410e-03 1.864539e-01 0.8060627
## 8248 1.314894e-02 2.851839e-01 0.7016672
## 8253 1.219740e-02 2.704572e-01 0.7173454
## 8256 7.352033e-03 1.838110e-01 0.8088370
## 8257 1.858718e-02 3.581097e-01 0.6233032
## 8259 1.022366e-02 2.376759e-01 0.7521004
## 8267 8.400482e-03 2.044042e-01 0.7871953
## 8271 2.302136e-02 4.061792e-01 0.5707994
## 8272 1.388377e-02 2.961150e-01 0.6900012
## 8282 7.977657e-03 1.962347e-01 0.7957877
## 8288 6.844700e-03 1.734305e-01 0.8197248
## 8290 5.435085e-03 1.430539e-01 0.8515110
## 8291 1.022366e-02 2.376759e-01 0.7521004
## 8294 4.792954e-03 1.284164e-01 0.8667906
## 8295 1.418266e-02 3.004557e-01 0.6853616
## 8302 1.260020e-02 2.767722e-01 0.7106276
## 8303 2.289168e-03 6.593162e-02 0.9317792
## 8306 3.839322e-03 1.056777e-01 0.8904830
## 8308 1.063068e-02 2.446973e-01 0.7446720
## 8319 3.827151e-03 1.053794e-01 0.8907934
## 8321 1.495162e-02 3.113539e-01 0.6736945
## 8322 1.495162e-02 3.113539e-01 0.6736945
## 8325 1.484348e-02 3.098443e-01 0.6753122
## 8326 2.127666e-02 3.883015e-01 0.5904219
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## 8337 1.013274e-02 2.360882e-01 0.7537791
## 8340 6.147230e-03 1.586913e-01 0.8351615
## 8344 1.020475e-02 2.373463e-01 0.7524489
## 8345 4.609736e-03 1.241426e-01 0.8712477
## 8352 4.635307e-03 1.247417e-01 0.8706230
## 8359 8.277742e-03 2.020511e-01 0.7896711
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## 8370 1.292106e-02 2.817171e-01 0.7053618
## 8381 8.835997e-03 2.126345e-01 0.7785295
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## 8395 1.019535e-02 2.371823e-01 0.7526224
## 8396 7.640059e-03 1.895813e-01 0.8027786
## 8400 1.194228e-02 2.663943e-01 0.7216634
## 8405 1.044594e-02 2.415279e-01 0.7480261
## 8406 1.098847e-02 2.507541e-01 0.7382574
## 8408 1.029624e-02 2.389384e-01 0.7507654
## 8409 3.840162e-03 1.056983e-01 0.8904616
## 8413 1.968502e-02 3.708444e-01 0.6094705
## 8415 1.410097e-02 2.992753e-01 0.6866237
## 8417 6.544736e-03 1.671594e-01 0.8262959
## 8418 9.837883e-03 2.308888e-01 0.7592733
## 8419 2.552108e-03 7.293175e-02 0.9245161
## 8420 1.534976e-02 3.168487e-01 0.6678015
## 8425 1.030133e-02 2.390268e-01 0.7506719
## 8426 1.605020e-02 3.262805e-01 0.6576694
## 8428 5.525486e-03 1.450730e-01 0.8494015
## 8430 1.068921e-02 2.456954e-01 0.7436153
## 8433 1.139411e-02 2.574941e-01 0.7311118
## 8437 4.771342e-03 1.279146e-01 0.8673141
## 8439 1.037549e-02 2.403116e-01 0.7493129
## 8442 2.959259e-02 4.635920e-01 0.5068154
## 8445 4.786280e-03 1.282615e-01 0.8669522
## 8448 6.655892e-03 1.694951e-01 0.8238490
## 8449 4.771342e-03 1.279146e-01 0.8673141
## 8459 7.058454e-03 1.778383e-01 0.8151032
## 8460 1.098847e-02 2.507541e-01 0.7382574
## 8464 7.256809e-03 1.818839e-01 0.8108593
## 8466 1.144195e-02 2.582803e-01 0.7302778
## 8468 1.170424e-02 2.625583e-01 0.7257374
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## 8474 4.093218e-03 1.118528e-01 0.8840540
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## 8477 7.465977e-03 1.861043e-01 0.8064298
## 8486 8.410356e-03 2.045928e-01 0.7869968
## 8488 1.499125e-02 3.119053e-01 0.6731034
## 8490 1.660695e-02 3.335706e-01 0.6498225
## 8496 2.255567e-02 4.015293e-01 0.5759151
## 8497 9.138607e-03 2.182461e-01 0.7726153
## 8498 9.913883e-03 2.322363e-01 0.7578498
## 8501 4.771342e-03 1.279146e-01 0.8673141
## 8502 8.170136e-03 1.999758e-01 0.7918540
## 8504 9.389882e-03 2.228405e-01 0.7677696
## 8505 6.524345e-03 1.667294e-01 0.8267462
## 8508 4.969539e-03 1.324941e-01 0.8625363
## 8509 1.302448e-02 2.832951e-01 0.7036804
## 8510 2.361958e-02 4.120274e-01 0.5643530
## 8511 4.771342e-03 1.279146e-01 0.8673141
## 8513 1.160722e-02 2.609823e-01 0.7274105
## 8514 6.691618e-03 1.702428e-01 0.8230656
## 8517 8.144212e-03 1.994741e-01 0.7923816
## 8527 9.913883e-03 2.322363e-01 0.7578498
## 8528 1.194228e-02 2.663943e-01 0.7216634
## 8534 1.098847e-02 2.507541e-01 0.7382574
## 8535 8.508308e-03 2.064591e-01 0.7850326
## 8540 1.098847e-02 2.507541e-01 0.7382574
## 8542 1.098847e-02 2.507541e-01 0.7382574
## 8543 5.411395e-03 1.425231e-01 0.8520655
## 8545 3.541873e-03 9.832763e-02 0.8981305
## 8546 1.040827e-02 2.408781e-01 0.7487137
## 8547 1.098847e-02 2.507541e-01 0.7382574
## 8548 1.065408e-02 2.450966e-01 0.7442493
## 8551 1.421623e-02 3.009396e-01 0.6848442
## 8560 4.634987e-03 1.247342e-01 0.8706308
## 8561 1.098847e-02 2.507541e-01 0.7382574
## 8566 4.680381e-03 1.257957e-01 0.8695239
## 8567 1.217810e-02 2.701516e-01 0.7176703
## 8569 4.136025e-02 5.378991e-01 0.4207407
## 8570 4.576249e-03 1.233567e-01 0.8720671
## 8571 1.170700e-02 2.626030e-01 0.7256900
## 8575 6.872273e-03 1.740020e-01 0.8191258
## 8580 5.922510e-03 1.538226e-01 0.8402549
## 8584 2.111900e-02 3.866229e-01 0.5922581
## 8587 1.285194e-02 2.806581e-01 0.7064899
## 8600 1.349476e-02 2.903748e-01 0.6961305
## 8603 2.138242e-03 6.186356e-02 0.9359982
## 8607 1.098847e-02 2.507541e-01 0.7382574
## 8623 7.491448e-03 1.866150e-01 0.8058935
## 8626 1.098847e-02 2.507541e-01 0.7382574
## 8627 7.526069e-03 1.873081e-01 0.8051658
## 8629 3.314184e-03 9.261517e-02 0.9040706
## 8630 6.544736e-03 1.671594e-01 0.8262959
## 8635 9.815662e-03 2.304939e-01 0.7596905
## 8637 1.096194e-02 2.503088e-01 0.7387293
## 8646 7.234216e-03 1.814253e-01 0.8113405
## 8649 7.806687e-03 1.928799e-01 0.7993134
## 8651 7.357390e-03 1.839192e-01 0.8087235
## 8652 9.679436e-03 2.280630e-01 0.7622575
## 8656 8.327682e-03 2.030103e-01 0.7886620
## 8664 9.840096e-03 2.309281e-01 0.7592318
## 8667 5.000900e-03 1.332141e-01 0.8617850
## 8669 1.830137e-02 3.546959e-01 0.6270027
## 8672 5.781935e-03 1.507464e-01 0.8434717
## 8680 7.199757e-03 1.807246e-01 0.8120756
## 8681 5.833419e-03 1.518757e-01 0.8422908
## 8682 1.326987e-02 2.870087e-01 0.6997214
## 8683 3.682808e-03 1.018259e-01 0.8944913
## 8691 1.554845e-02 3.195544e-01 0.6648972
## 8700 1.652859e-02 3.325553e-01 0.6509161
## 8701 7.990148e-03 1.964786e-01 0.7955313
## 8707 1.154945e-02 2.600403e-01 0.7284103
## 8711 1.035201e-02 2.399054e-01 0.7497426
## 8715 3.611103e-02 5.084085e-01 0.4554805
## 8716 7.222243e-03 1.811820e-01 0.8115958
## 8721 9.769027e-03 2.296636e-01 0.7605674
## 8722 1.559241e-02 3.201497e-01 0.6642578
## 8724 1.652859e-02 3.325553e-01 0.6509161
## 8725 1.652859e-02 3.325553e-01 0.6509161
## 8729 4.748558e-03 1.273849e-01 0.8678666
## 8730 1.048022e-02 2.421183e-01 0.7474015
## 8731 7.611281e-03 1.890087e-01 0.8033800
## 8733 4.748558e-03 1.273849e-01 0.8678666
## 8735 1.488095e-02 3.103682e-01 0.6747509
## 8743 1.701741e-02 3.388317e-01 0.6441509
## 8744 2.117674e-02 3.872389e-01 0.5915844
## 8747 1.130037e-02 2.559484e-01 0.7327513
## 8758 1.237570e-02 2.732676e-01 0.7143567
## 8759 1.627351e-02 3.292261e-01 0.6545004
## 8762 9.014376e-03 2.159528e-01 0.7750328
## 8764 8.428655e-03 2.049422e-01 0.7866291
## 8769 8.242834e-03 2.013792e-01 0.7903780
## 8772 8.428655e-03 2.049422e-01 0.7866291
## 8773 2.003123e-02 3.747401e-01 0.6052287
## 8774 4.238887e-03 1.153554e-01 0.8804057
## 8775 1.756244e-02 3.456737e-01 0.6367638
## 8783 1.831259e-02 3.548307e-01 0.6268567
## 8784 1.524433e-02 3.154033e-01 0.6693524
## 8786 1.797962e-02 3.508027e-01 0.6312177
## 8790 8.693805e-03 2.099676e-01 0.7813386
## 8796 8.359659e-03 2.036232e-01 0.7880171
## 8798 1.364628e-02 2.926230e-01 0.6937308
## 8799 4.029978e-03 1.103231e-01 0.8856469
## 8804 1.616711e-02 3.278262e-01 0.6560067
## 8805 5.204133e-03 1.378495e-01 0.8569464
## 8806 1.549255e-02 3.187956e-01 0.6657118
## 8807 1.683067e-02 3.364499e-01 0.6467195
## 8811 1.443297e-02 3.040455e-01 0.6815216
## 8817 1.781754e-02 3.488209e-01 0.6333616
## 8818 4.713368e-03 1.265654e-01 0.8687213
## 8819 1.894765e-02 3.623562e-01 0.6186961
## 8820 1.635981e-02 3.303567e-01 0.6532835
## 8826 1.055232e-02 2.433565e-01 0.7460912
## 8830 1.477332e-02 3.088608e-01 0.6763659
## 8832 2.229129e-03 6.431774e-02 0.9334531
## 8835 1.973447e-02 3.714043e-01 0.6088613
## 8836 7.851736e-03 1.937668e-01 0.7983815
## 8845 1.261997e-02 2.770792e-01 0.7103009
## 8847 7.024826e-03 1.771482e-01 0.8158270
## 8850 1.459356e-02 3.063269e-01 0.6790795
## 8851 1.028778e-02 2.387915e-01 0.7509208
## 8854 1.488095e-02 3.103682e-01 0.6747509
## 8860 1.093632e-02 2.498780e-01 0.7391857
## 8861 8.979715e-03 2.153104e-01 0.7757099
## 8862 1.652859e-02 3.325553e-01 0.6509161
## 8866 2.122498e-02 3.877524e-01 0.5910226
## 8867 2.054838e-03 5.959963e-02 0.9383455
## 8871 1.006447e-02 2.348911e-01 0.7550444
## 8872 1.061812e-02 2.444828e-01 0.7448991
## 8881 4.238887e-03 1.153554e-01 0.8804057
## 8882 1.415941e-02 3.001202e-01 0.6857203
## 8884 9.769027e-03 2.296636e-01 0.7605674
## 8891 9.769027e-03 2.296636e-01 0.7605674
## 8892 8.238353e-03 2.012928e-01 0.7904688
## 8893 1.093632e-02 2.498780e-01 0.7391857
## 8895 1.212037e-02 2.692358e-01 0.7186438
## 8896 1.795456e-02 3.504971e-01 0.6315484
## 8900 1.329828e-02 2.874359e-01 0.6992658
## 8903 1.306001e-02 2.838354e-01 0.7031046
## 8904 9.495995e-03 2.247633e-01 0.7657407
## 8905 1.212037e-02 2.692358e-01 0.7186438
## 8906 1.203600e-02 2.678927e-01 0.7200713
## 8907 7.222243e-03 1.811820e-01 0.8115958
## 8911 1.818849e-02 3.533361e-01 0.6284754
## 8919 1.186471e-02 2.651491e-01 0.7229862
## 8920 1.242899e-02 2.741029e-01 0.7134681
## 8922 9.489792e-03 2.246511e-01 0.7658591
## 8927 1.364380e-02 2.925862e-01 0.6937700
## 8935 9.432238e-03 2.236092e-01 0.7669585
## 8942 1.651328e-02 3.323566e-01 0.6511301
## 8945 4.145241e-03 1.131070e-01 0.8827477
## 8948 1.054331e-02 2.432020e-01 0.7462546
## 8949 6.624471e-03 1.688362e-01 0.8245393
## 8951 1.129532e-02 2.558649e-01 0.7328398
## 8952 1.222733e-02 2.709307e-01 0.7168420
## 8953 8.951227e-03 2.147815e-01 0.7762672
## 8955 1.483402e-02 3.097119e-01 0.6754541
## 8959 1.156085e-02 2.602262e-01 0.7282129
## 8961 6.593856e-03 1.681932e-01 0.8252129
## 8965 1.166042e-02 2.618474e-01 0.7264922
## 8967 1.886198e-02 3.613529e-01 0.6197851
## 8970 2.602801e-03 7.426877e-02 0.9231284
## 8971 3.716282e-03 1.026526e-01 0.8936311
## 8973 8.401901e-03 2.044313e-01 0.7871668
## 8978 1.443613e-02 3.040904e-01 0.6814735
## 8982 1.208204e-02 2.686263e-01 0.7192916
## 8984 1.090170e-02 2.492949e-01 0.7398034
## 8985 8.600769e-03 2.082121e-01 0.7831871
## 8986 1.187189e-02 2.652646e-01 0.7228636
## 8990 5.969422e-03 1.548439e-01 0.8391867
## 8992 1.466131e-02 3.072844e-01 0.6780543
## 8998 1.023892e-02 2.379418e-01 0.7518192
## 9001 6.526473e-03 1.667743e-01 0.8266992
## 9006 7.490548e-03 1.865970e-01 0.8059125
## 9011 1.144598e-02 2.583464e-01 0.7302076
## 9012 1.056625e-02 2.435952e-01 0.7458386
## 9013 8.919458e-03 2.141909e-01 0.7768897
## 9015 1.819609e-02 3.534279e-01 0.6283760
## 9017 1.351700e-02 2.907057e-01 0.6957773
## 9018 2.181611e-02 3.939641e-01 0.5842198
## 9021 1.000222e-02 2.337961e-01 0.7562017
## 9025 5.731429e-03 1.496353e-01 0.8446332
## 9033 9.722612e-03 2.288353e-01 0.7614421
## 9037 1.062662e-02 2.446280e-01 0.7447454
## 9041 9.998217e-03 2.337255e-01 0.7562763
## 9046 6.450967e-03 1.651782e-01 0.8283708
## 9049 5.129742e-03 1.361589e-01 0.8587114
## 9054 1.238649e-02 2.734368e-01 0.7141767
## 9057 1.088442e-02 2.490037e-01 0.7401118
## 9063 1.315963e-02 2.853456e-01 0.7014948
## 9076 6.695212e-03 1.703179e-01 0.8229869
## 9077 1.171516e-02 2.627353e-01 0.7255495
## 9079 8.579032e-03 2.078007e-01 0.7836202
## 9080 5.716740e-03 1.493116e-01 0.8449716
## 9083 1.061885e-02 2.444952e-01 0.7448860
## 9084 9.603715e-03 2.267047e-01 0.7636916
## 9090 8.189667e-03 2.003534e-01 0.7914570
## 9092 1.243469e-02 2.741921e-01 0.7133732
## 9095 1.816747e-02 3.530822e-01 0.6287503
## 9097 1.257264e-02 2.763440e-01 0.7110834
## 9098 2.353207e-02 4.111805e-01 0.5652874
## 9100 2.042083e-02 3.790575e-01 0.6005217
## 9101 5.896714e-03 1.532598e-01 0.8408435
## 9105 1.661311e-02 3.336502e-01 0.6497367
## 9108 2.104422e-02 3.858229e-01 0.5931329
## 9109 7.154989e-03 1.798125e-01 0.8130325
## 9117 1.075961e-02 2.468922e-01 0.7423482
## 9119 1.171022e-02 2.626553e-01 0.7256345
## 9127 2.457061e-03 7.041403e-02 0.9271289
## 9130 1.086718e-02 2.487127e-01 0.7404201
## 9133 1.125501e-02 2.551978e-01 0.7335472
## 9136 8.443915e-03 2.052333e-01 0.7863228
## 9139 1.356024e-02 2.913482e-01 0.6950915
## 9151 1.108468e-02 2.523648e-01 0.7365505
## 9153 1.311432e-02 2.846596e-01 0.7022260
## 9156 1.438611e-02 3.033766e-01 0.6822373
## 9158 1.126839e-02 2.554195e-01 0.7333121
## 9162 1.443834e-02 3.041220e-01 0.6814396
## 9163 1.646259e-02 3.316975e-01 0.6518399
## 9166 1.425000e-02 3.014255e-01 0.6843245
## 9170 1.859875e-02 3.582470e-01 0.6231543
## 9180 1.642467e-02 3.312036e-01 0.6523718
## 9182 4.718348e-03 1.266815e-01 0.8686002
## 9186 4.225652e-03 1.150383e-01 0.8807360
## 9187 1.698061e-02 3.383640e-01 0.6446554
## 9192 1.184389e-02 2.648141e-01 0.7233420
## 9194 9.804336e-03 2.302924e-01 0.7599033
## 9197 1.311432e-02 2.846596e-01 0.7022260
## 9199 1.672488e-02 3.350919e-01 0.6481832
## 9201 1.153110e-02 2.597404e-01 0.7287285
## 9202 1.482644e-02 3.096057e-01 0.6755678
## 9203 8.967077e-03 2.150759e-01 0.7759570
## 9205 1.478724e-02 3.090562e-01 0.6761566
## 9208 1.169379e-02 2.623890e-01 0.7259172
## 9209 4.492894e-03 1.213939e-01 0.8741132
## 9214 1.517360e-02 3.144297e-01 0.6703967
## 9216 8.321927e-03 2.028999e-01 0.7887781
## 9217 1.786675e-02 3.494241e-01 0.6327092
## 9219 1.086718e-02 2.487127e-01 0.7404201
## 9220 4.217995e-03 1.148548e-01 0.8809272
## 9224 9.052875e-03 2.166650e-01 0.7742821
## 9229 8.831014e-03 2.125414e-01 0.7786276
## 9234 2.084697e-02 3.837010e-01 0.5954520
## 9235 1.341625e-02 2.892037e-01 0.6973800
## 9237 5.840596e-03 1.520329e-01 0.8421265
## 9238 2.458017e-03 7.043942e-02 0.9271026
## 9246 2.213771e-02 3.972816e-01 0.5805807
## 9249 7.196374e-03 1.806558e-01 0.8121478
## 9252 3.336145e-03 9.316945e-02 0.9034944
## 9253 1.169885e-02 2.624709e-01 0.7258302
## 9254 1.627000e-02 3.291800e-01 0.6545500
## 9257 1.769874e-02 3.473596e-01 0.6349416
## 9262 1.464775e-02 3.070930e-01 0.6782593
## 9266 7.830406e-03 1.933471e-01 0.7988225
## 9267 7.738732e-03 1.915381e-01 0.8007231
## 9271 1.059361e-02 2.440636e-01 0.7453428
## 9272 1.076427e-02 2.469712e-01 0.7422645
## 9274 5.327562e-03 1.406392e-01 0.8540332
## 9277 1.064260e-02 2.449009e-01 0.7444565
## 9279 2.442012e-02 4.196410e-01 0.5559389
## 9280 1.299041e-02 2.827761e-01 0.7042335
## 9281 6.654326e-03 1.694622e-01 0.8238834
## 9282 9.542073e-03 2.255950e-01 0.7648629
## 9283 9.216143e-03 2.196700e-01 0.7711138
## 9288 1.080040e-02 2.475837e-01 0.7416159
## 9290 8.250019e-03 2.015176e-01 0.7902324
## 9294 5.538663e-03 1.453665e-01 0.8490949
## 9305 4.207019e-03 1.145916e-01 0.8812014
## 9318 1.400359e-02 2.978623e-01 0.6881341
## 9319 1.062219e-02 2.445524e-01 0.7448254
## 9323 5.957709e-03 1.545891e-01 0.8394532
## 9325 1.029748e-02 2.389599e-01 0.7507426
## 9328 1.074721e-02 2.466817e-01 0.7425711
## 9329 8.718035e-03 2.104234e-01 0.7808585
## 9330 7.074795e-03 1.781732e-01 0.8147520
## 9336 8.282542e-03 2.021434e-01 0.7895740
## 9338 1.902818e-02 3.632962e-01 0.6176756
## 9344 6.146251e-03 1.586702e-01 0.8351836
## 9345 1.062165e-02 2.445431e-01 0.7448353
## 9346 1.470355e-02 3.078798e-01 0.6774167
## 9351 8.151085e-03 1.996072e-01 0.7922417
## 9352 1.038034e-02 2.403956e-01 0.7492240
## 9353 8.233316e-03 2.011957e-01 0.7905710
## 9360 3.608575e-03 9.998685e-02 0.8964046
## 9362 1.377136e-02 2.944669e-01 0.6917617
## 9363 9.924011e-03 2.324155e-01 0.7576605
## 9366 1.753264e-02 3.453038e-01 0.6371635
## 9369 6.495584e-03 1.661221e-01 0.8273823
## 9373 1.621876e-02 3.285067e-01 0.6552746
## 9377 6.728018e-03 1.710031e-01 0.8222688
## 9378 1.077063e-02 2.470791e-01 0.7421502
## 9383 1.725067e-02 3.417798e-01 0.6409695
## 9384 1.008066e-02 2.351754e-01 0.7547439
## 9386 2.149263e-02 3.905834e-01 0.5879240
## 9387 8.507792e-03 2.064493e-01 0.7850429
## 9388 1.460155e-02 3.064399e-01 0.6789586
## 9390 2.137935e-02 3.893890e-01 0.5892316
## 9393 9.976211e-03 2.333375e-01 0.7566863
## 9401 8.731199e-03 2.106708e-01 0.7805980
## 9402 1.365927e-02 2.928150e-01 0.6935258
## 9404 1.073018e-02 2.463924e-01 0.7428774
## 9405 1.043169e-02 2.412822e-01 0.7482861
## 9409 1.365927e-02 2.928150e-01 0.6935258
## 9413 1.166183e-02 2.618703e-01 0.7264678
## 9414 9.184371e-03 2.190872e-01 0.7717284
## 9418 1.251715e-02 2.754801e-01 0.7120028
## 9419 1.464027e-02 3.069873e-01 0.6783725
## 9425 7.574457e-03 1.882748e-01 0.8041508
## 9430 2.276139e-02 4.035941e-01 0.5736445
## 9431 1.130603e-02 2.560418e-01 0.7326521
## 9434 1.621876e-02 3.285067e-01 0.6552746
## 9435 1.095655e-02 2.502180e-01 0.7388254
## 9436 9.680606e-03 2.280840e-01 0.7622354
## 9437 1.565222e-02 3.209578e-01 0.6633900
## 9439 1.621876e-02 3.285067e-01 0.6552746
## 9442 1.047599e-02 2.420455e-01 0.7474785
## 9443 1.621876e-02 3.285067e-01 0.6552746
## 9446 1.073018e-02 2.463924e-01 0.7428774
## 9447 9.680606e-03 2.280840e-01 0.7622354
## 9448 1.710275e-02 3.399139e-01 0.6429834
## 9450 1.985757e-02 3.727931e-01 0.6073494
## 9452 7.850728e-03 1.937469e-01 0.7984023
## 9454 1.876752e-02 3.602423e-01 0.6209901
## 9462 6.891898e-03 1.744081e-01 0.8187000
## 9464 1.073018e-02 2.463924e-01 0.7428774
## 9465 1.688712e-03 4.952530e-02 0.9487860
## 9466 1.574714e-02 3.222359e-01 0.6620170
## 9467 9.361079e-03 2.223168e-01 0.7683221
## 9472 1.031136e-02 2.392008e-01 0.7504879
## 9473 1.230726e-02 2.721916e-01 0.7155012
## 9482 1.583894e-02 3.234668e-01 0.6606943
## 9486 1.043065e-02 2.412643e-01 0.7483050
## 9491 8.377918e-03 2.039727e-01 0.7876493
## 9492 1.457850e-02 3.061136e-01 0.6793079
## 9497 2.271334e-02 4.031133e-01 0.5741734
## 9504 1.076669e-02 2.470124e-01 0.7422209
## 9505 8.629966e-03 2.087639e-01 0.7826061
## 9506 1.457850e-02 3.061136e-01 0.6793079
## 9510 1.277472e-02 2.794711e-01 0.7077542
## 9516 2.091747e-02 3.844614e-01 0.5946211
## 9517 1.041738e-02 2.410354e-01 0.7485473
## 9519 6.880935e-03 1.741813e-01 0.8189378
## 9521 8.691258e-03 2.099197e-01 0.7813891
## 9530 1.201594e-02 2.675725e-01 0.7204116
## 9534 6.809520e-03 1.727003e-01 0.8204902
## 9541 1.159241e-02 2.607409e-01 0.7276667
## 9545 1.404874e-02 2.985182e-01 0.6874330
## 9548 1.604842e-02 3.262569e-01 0.6576947
## 9549 1.199103e-02 2.671746e-01 0.7208344
view(predictions2_n)
#MNL best model of train data
# Convert the probability value into a category 
pred_class1_1_n <- ifelse(predictions1_n[,1] > 0.002, 1, 0 )
pred_class1_1_n #. If the probability is greater than 0.01, the prediction is a positive class (1), otherwise negative class (0)
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    0 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    0    1    1    0    0    0    1    0    1    1    1    0    0    0    0 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    0    1    1    1    1    1    1    1    0    1    1    1    1    0 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    0    1    0    1    0    1    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    0    1    0    1    1    1    1    1    1    0    1    0    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    0    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    0    1    1    1    1    1    1    1    1    0    1    1    0    0    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    1    1    1    1    0    1    1    1    1    1    1    0    0    1    1    0 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    1    0    1    1    1    1    1    0    1    1    0    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    0    1    1    0    1    1    1    1    1    1    0    1    1    1    1    0 
##  588  591  593  595  598  605  606  608  614  619  620  621  622  623  627  628 
##    0    1    1    0    0    1    1    0    0    0    1    1    1    1    1    1 
##  630  632  634  654  658  663  664  666  674  683  686  691  693  696  697  701 
##    1    1    0    1    1    1    1    1    1    1    0    1    1    0    0    1 
##  703  713  714  716  717  721  724  727  735  738  743  744  746  747  751  769 
##    1    1    0    1    1    1    1    1    1    1    0    0    1    1    0    1 
##  770  771  772  773  775  778  779  780  781  784  786  788  789  790  793  794 
##    1    1    1    1    1    1    0    1    1    0    1    1    1    0    1    0 
##  796  801  808  809  810  811  814  817  819  823  831  840  841  842  848  851 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  853  854  855  856  858  861  868  870  872  873  874  877  882  883  884  885 
##    1    1    1    1    1    1    1    1    0    0    1    0    0    1    1    1 
##  886  887  889  890  893  897  898  900  901  904  908  911  915  917  919  923 
##    0    1    1    1    1    0    1    1    0    0    1    1    1    1    1    1 
##  934  937  942  943  945  949  952  953  957  958  963  964  965  969  970  975 
##    1    0    1    1    1    1    0    1    1    0    1    1    1    1    1    1 
##  982  983  985  986  987  988  990  991  994  995 1003 1004 1011 1012 1014 1016 
##    0    0    0    0    1    1    0    0    1    0    1    1    1    0    1    0 
## 1017 1021 1023 1024 1026 1027 1034 1035 1038 1042 1043 1044 1045 1047 1048 1051 
##    1    1    1    1    0    1    0    1    0    1    1    1    1    1    1    1 
## 1052 1053 1063 1069 1071 1072 1073 1074 1075 1076 1077 1092 1096 1103 1104 1108 
##    1    1    1    1    1    1    1    0    1    1    1    1    0    0    1    0 
## 1109 1110 1116 1119 1125 1126 1127 1131 1132 1143 1147 1150 1151 1160 1162 1168 
##    1    1    0    1    1    1    0    1    0    1    1    1    1    1    1    0 
## 1169 1170 1171 1173 1177 1178 1180 1181 1182 1196 1198 1199 1205 1206 1216 1218 
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##    1    1    1    1    1    1    1    0    1    1    1    1    0    1    1    1 
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##    0    1    1    0    1    0    0    1    1    1    0    0    1    1    1    1 
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##    1    1    1    1    1    1    1    0    1    0    0    0    0    1    1    1 
## 8243 8247 8248 8253 8256 8257 8259 8267 8271 8272 8282 8288 8290 8291 8294 8295 
##    1    1    1    1    0    1    1    1    1    1    1    1    0    1    0    0 
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##    1    1    0    1    0    1    1    1    1    0    1    0    1    0    0    1 
## 8364 8365 8370 8381 8385 8387 8391 8395 8396 8400 8405 8406 8408 8409 8413 8415 
##    0    1    1    1    0    1    1    1    0    1    1    1    0    0    1    1 
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##    1    1    0    1    0    1    0    1    0    1    1    0    0    0    0    1 
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##    1    1    1    1    1    1    1    0    1    1    0    1    0    1    1    1 
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##    1    0    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    0    1    0    1    1    1    1    1    1    1    1    1 
## 9108 9109 9117 9119 9127 9130 9133 9136 9139 9151 9153 9156 9158 9162 9163 9166 
##    1    0    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    0    0    0    1    1    1    0    1    1    0    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    0    1    1    1    0    1    1    1    1    0    1    1    1    1    0 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    0    1    1    1    0    1    1    1    1    1    1    1    0    0 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
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##    1    0    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    0 
## 9549 
##    1
#225个0,775个1
library(fpp3)
view(pred_class1_1_n)
pred_class1_1_f
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1    0 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    0    1    1    0    0    0    1    0    1    1    1    0    0    0    0 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    0    1    1    1    1    1    1    1    0    1    1    1    1    0 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    0    1    0    1    0    1    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    0    1    0    1    1    1    1    1    1    0    1    0    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    0    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    0    1    1    1    1    1    1    1    1    0    1    1    0    0    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    0    1    1    1    0    1    1    1    1    1    0    0    0    1    1    0 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    1    0    1    1    1    1    1    0    1    1    0    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    0    1    1    0    1    1    1    1    1    1    0    1    1    1    1    0 
##  588  591  593  595  598  605  606  608  614  619  620  621  622  623  627  628 
##    0    1    1    0    0    1    1    0    0    0    1    1    1    1    1    1 
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##    1    1    0    1    1    1    1    1    1    1    0    0    1    1    0    1 
##  770  771  772  773  775  778  779  780  781  784  786  788  789  790  793  794 
##    1    1    1    1    1    1    0    1    1    0    1    1    1    0    1    0 
##  796  801  808  809  810  811  814  817  819  823  831  840  841  842  848  851 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##  886  887  889  890  893  897  898  900  901  904  908  911  915  917  919  923 
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##    1    0    1    1    1    1    0    1    1    0    1    1    1    1    1    1 
##  982  983  985  986  987  988  990  991  994  995 1003 1004 1011 1012 1014 1016 
##    0    1    0    0    1    1    0    0    1    1    1    1    1    0    1    0 
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##    1    1    1    1    1    1    1    0    1    1    1    1    0    0    1    0 
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##    0    1    1    1    1    0    0    1    1    1    1    1    0    1    1    0 
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##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    0    0    1    1    1    1    0    1    0    1    1    0    1    1    0 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
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##    0    1    1    1    1    1    0    1    1    1    0    1    0    1    1    1 
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##    0    1    0    1    1    1    1    0    1    1    1    1    1    1    0    0 
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## 1957 1958 1961 1968 1969 1971 1972 1975 1979 1981 1985 1986 1988 1989 1990 1991 
##    0    1    1    1    1    1    1    1    1    0    1    1    1    0    0    1 
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##    1    0    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 2155 2156 2160 2163 2164 2174 2182 2198 2205 2207 2210 2212 2214 2218 2219 2221 
##    1    0    1    1    1    1    1    1    0    1    1    1    0    1    1    1 
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##    0    0    0    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 2280 2286 2288 2293 2297 2303 2305 2308 2309 2312 2313 2319 2323 2328 2332 2333 
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## 2383 2395 2396 2398 2401 2405 2411 2412 2418 2427 2430 2434 2435 2438 2439 2446 
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## 7112 7114 7115 7116 7120 7130 7133 7139 7141 7144 7152 7155 7157 7158 7160 7161 
##    1    1    0    0    1    1    1    1    1    1    1    1    1    1    1    0 
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##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
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##    1    1    1    0    1    1    1    1    1    1    1    0    1    0    1    1 
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##    1    0    1    1    1    1    1    1    0    1    1    0    1    1    1    0 
## 7844 7846 7847 7849 7855 7857 7862 7869 7871 7876 7882 7883 7884 7888 7891 7892 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 7894 7896 7898 7910 7911 7921 7923 7926 7927 7928 7929 7933 7936 7937 7939 7949 
##    1    1    1    1    0    1    0    1    0    1    1    1    1    1    1    1 
## 7953 7955 7957 7960 7962 7964 7965 7966 7967 7971 7976 7981 7983 7984 7988 7989 
##    1    1    1    1    1    1    1    0    1    1    1    1    0    1    1    1 
## 7991 7999 8008 8012 8013 8015 8017 8018 8019 8023 8026 8030 8034 8035 8043 8044 
##    1    1    0    1    1    1    0    1    1    1    1    1    0    0    1    0 
## 8049 8054 8065 8066 8067 8076 8083 8089 8090 8104 8108 8110 8111 8113 8118 8125 
##    1    1    1    0    1    1    1    1    1    1    0    0    1    1    0    1 
## 8127 8128 8133 8137 8138 8147 8150 8156 8167 8174 8176 8182 8198 8199 8206 8207 
##    0    1    1    0    1    0    0    1    1    1    0    0    1    1    1    1 
## 8208 8214 8215 8216 8218 8222 8223 8224 8226 8227 8230 8234 8235 8237 8239 8242 
##    1    1    1    1    1    1    1    0    1    0    0    0    0    1    1    1 
## 8243 8247 8248 8253 8256 8257 8259 8267 8271 8272 8282 8288 8290 8291 8294 8295 
##    1    1    1    1    0    1    1    1    1    1    1    1    0    1    0    0 
## 8302 8303 8306 8308 8319 8321 8322 8325 8326 8328 8337 8340 8344 8345 8352 8359 
##    1    1    0    1    0    1    1    1    1    0    1    0    1    0    0    1 
## 8364 8365 8370 8381 8385 8387 8391 8395 8396 8400 8405 8406 8408 8409 8413 8415 
##    0    1    1    1    0    1    1    1    0    1    1    1    0    0    1    1 
## 8417 8418 8419 8420 8425 8426 8428 8430 8433 8437 8439 8442 8445 8448 8449 8459 
##    0    1    0    1    1    1    0    1    1    0    1    0    0    0    0    1 
## 8460 8464 8466 8468 8471 8474 8475 8476 8477 8486 8488 8490 8496 8497 8498 8501 
##    1    1    1    1    1    0    1    1    0    1    1    1    1    1    1    0 
## 8502 8504 8505 8508 8509 8510 8511 8513 8514 8517 8527 8528 8534 8535 8540 8542 
##    1    1    0    0    1    1    0    1    0    1    1    1    1    1    1    1 
## 8543 8545 8546 8547 8548 8551 8560 8561 8566 8567 8569 8570 8571 8575 8580 8584 
##    0    0    1    1    1    1    0    1    1    1    0    0    1    1    0    1 
## 8587 8600 8603 8607 8623 8626 8627 8629 8630 8635 8637 8646 8649 8651 8652 8656 
##    1    1    0    1    0    1    0    1    1    1    1    0    0    0    0    1 
## 8664 8667 8669 8672 8680 8681 8682 8683 8691 8700 8701 8707 8711 8715 8716 8721 
##    1    0    1    1    0    0    1    0    1    1    1    1    0    0    1    1 
## 8722 8724 8725 8729 8730 8731 8733 8735 8743 8744 8747 8758 8759 8762 8764 8769 
##    1    1    1    0    1    0    0    1    0    1    1    1    1    1    1    1 
## 8772 8773 8774 8775 8783 8784 8786 8790 8796 8798 8799 8804 8805 8806 8807 8811 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8817 8818 8819 8820 8826 8830 8832 8835 8836 8845 8847 8850 8851 8854 8860 8861 
##    1    0    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8862 8866 8867 8871 8872 8881 8882 8884 8891 8892 8893 8895 8896 8900 8903 8904 
##    1    1    0    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8905 8906 8907 8911 8919 8920 8922 8927 8935 8942 8945 8948 8949 8951 8952 8953 
##    1    1    1    1    1    1    0    0    1    1    0    1    0    1    0    1 
## 8955 8959 8961 8965 8967 8970 8971 8973 8978 8982 8984 8985 8986 8990 8992 8998 
##    1    0    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
## 9001 9006 9011 9012 9013 9015 9017 9018 9021 9025 9033 9037 9041 9046 9049 9054 
##    0    1    1    1    1    1    1    1    0    0    1    1    1    0    0    1 
## 9057 9063 9076 9077 9079 9080 9083 9084 9090 9092 9095 9097 9098 9100 9101 9105 
##    1    1    1    1    0    1    0    1    1    1    1    1    1    1    1    1 
## 9108 9109 9117 9119 9127 9130 9133 9136 9139 9151 9153 9156 9158 9162 9163 9166 
##    1    0    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    0    0    0    1    1    1    0    1    1    0    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    0    1    1    1    0    1    1    1    1    0    1    1    1    1    0 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    0    1    1    1    0    1    1    1    1    1    1    1    0    0 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
## 9404 9405 9409 9413 9414 9418 9419 9425 9430 9431 9434 9435 9436 9437 9439 9442 
##    1    0    1    1    1    1    1    0    1    1    1    1    1    1    1    0 
## 9443 9446 9447 9448 9450 9452 9454 9462 9464 9465 9466 9467 9472 9473 9482 9486 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 9549 
##    1
pred_class1_2_n <- ifelse(predictions1_n[,2] > 0.1126, 1, 0 )
pred_class1_2_n #. If the probability is greater than 0.24, the prediction is a positive class (1), otherwise negative class (0)
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    0    1 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    0 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
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## 6875 6885 6889 6891 6893 6897 6898 6907 6910 6913 6916 6918 6923 6926 6928 6930 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6936 6937 6939 6945 6949 6950 6951 6952 6954 6957 6959 6960 6961 6962 6966 6968 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6971 6974 6978 6980 6984 6985 6987 6992 6993 6995 6998 6999 7001 7004 7005 7006 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7008 7009 7012 7014 7015 7016 7019 7026 7028 7029 7036 7043 7048 7051 7055 7058 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7065 7066 7069 7073 7077 7079 7082 7083 7088 7091 7094 7100 7103 7106 7109 7110 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7112 7114 7115 7116 7120 7130 7133 7139 7141 7144 7152 7155 7157 7158 7160 7161 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 7166 7167 7168 7178 7179 7181 7182 7186 7188 7191 7192 7196 7197 7202 7203 7207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7209 7210 7221 7222 7226 7228 7229 7237 7238 7241 7247 7248 7250 7270 7273 7275 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7279 7280 7281 7282 7283 7285 7287 7294 7299 7302 7305 7314 7315 7317 7320 7330 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 7332 7337 7338 7339 7341 7342 7344 7346 7350 7355 7360 7364 7365 7366 7371 7373 
##    1    1    1    1    1    1    1    1    0    0    1    1    1    1    1    1 
## 7376 7380 7381 7387 7389 7392 7399 7402 7403 7408 7410 7412 7416 7419 7426 7428 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 7431 7432 7433 7436 7438 7440 7441 7447 7456 7457 7458 7462 7463 7466 7467 7472 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7475 7484 7485 7487 7488 7490 7497 7498 7502 7507 7511 7519 7520 7523 7525 7526 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7529 7530 7531 7532 7533 7534 7536 7538 7539 7543 7547 7549 7551 7552 7553 7556 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7560 7566 7569 7570 7573 7580 7586 7597 7598 7601 7606 7612 7615 7616 7620 7626 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7627 7629 7631 7633 7640 7645 7650 7651 7652 7654 7655 7659 7660 7665 7673 7674 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7676 7677 7678 7685 7692 7697 7700 7704 7709 7712 7720 7721 7729 7730 7736 7739 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7740 7741 7742 7743 7750 7753 7755 7757 7759 7761 7763 7764 7774 7778 7785 7788 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7791 7793 7796 7797 7802 7805 7807 7811 7813 7814 7815 7826 7831 7837 7838 7842 
##    1    0    1    0    1    1    1    1    1    1    1    0    1    1    1    0 
## 7844 7846 7847 7849 7855 7857 7862 7869 7871 7876 7882 7883 7884 7888 7891 7892 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7894 7896 7898 7910 7911 7921 7923 7926 7927 7928 7929 7933 7936 7937 7939 7949 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 7953 7955 7957 7960 7962 7964 7965 7966 7967 7971 7976 7981 7983 7984 7988 7989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7991 7999 8008 8012 8013 8015 8017 8018 8019 8023 8026 8030 8034 8035 8043 8044 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8049 8054 8065 8066 8067 8076 8083 8089 8090 8104 8108 8110 8111 8113 8118 8125 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8127 8128 8133 8137 8138 8147 8150 8156 8167 8174 8176 8182 8198 8199 8206 8207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8208 8214 8215 8216 8218 8222 8223 8224 8226 8227 8230 8234 8235 8237 8239 8242 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
## 8243 8247 8248 8253 8256 8257 8259 8267 8271 8272 8282 8288 8290 8291 8294 8295 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8302 8303 8306 8308 8319 8321 8322 8325 8326 8328 8337 8340 8344 8345 8352 8359 
##    1    0    0    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 8364 8365 8370 8381 8385 8387 8391 8395 8396 8400 8405 8406 8408 8409 8413 8415 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 8417 8418 8419 8420 8425 8426 8428 8430 8433 8437 8439 8442 8445 8448 8449 8459 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8460 8464 8466 8468 8471 8474 8475 8476 8477 8486 8488 8490 8496 8497 8498 8501 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8502 8504 8505 8508 8509 8510 8511 8513 8514 8517 8527 8528 8534 8535 8540 8542 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8543 8545 8546 8547 8548 8551 8560 8561 8566 8567 8569 8570 8571 8575 8580 8584 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8587 8600 8603 8607 8623 8626 8627 8629 8630 8635 8637 8646 8649 8651 8652 8656 
##    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8664 8667 8669 8672 8680 8681 8682 8683 8691 8700 8701 8707 8711 8715 8716 8721 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8722 8724 8725 8729 8730 8731 8733 8735 8743 8744 8747 8758 8759 8762 8764 8769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8772 8773 8774 8775 8783 8784 8786 8790 8796 8798 8799 8804 8805 8806 8807 8811 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8817 8818 8819 8820 8826 8830 8832 8835 8836 8845 8847 8850 8851 8854 8860 8861 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8862 8866 8867 8871 8872 8881 8882 8884 8891 8892 8893 8895 8896 8900 8903 8904 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8905 8906 8907 8911 8919 8920 8922 8927 8935 8942 8945 8948 8949 8951 8952 8953 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8955 8959 8961 8965 8967 8970 8971 8973 8978 8982 8984 8985 8986 8990 8992 8998 
##    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
## 9001 9006 9011 9012 9013 9015 9017 9018 9021 9025 9033 9037 9041 9046 9049 9054 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9057 9063 9076 9077 9079 9080 9083 9084 9090 9092 9095 9097 9098 9100 9101 9105 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9108 9109 9117 9119 9127 9130 9133 9136 9139 9151 9153 9156 9158 9162 9163 9166 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    0    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    0    1    1    1    1    1    0    1    1    0    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    0 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9404 9405 9409 9413 9414 9418 9419 9425 9430 9431 9434 9435 9436 9437 9439 9442 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9443 9446 9447 9448 9450 9452 9454 9462 9464 9465 9466 9467 9472 9473 9482 9486 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9549 
##    1
#25个0,975个1
view(pred_class1_2_n)  

#19个0,981个1
pred_class1_3_n <- ifelse(predictions1_n[,3] > 0.6, 1, 0 )
pred_class1_3_n #. If the probability is greater than 0.75, the prediction is a positive class (1), otherwise negative class (0)
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    1    1    1    1    0    1    1    0    1    1    1    1    1    1 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
##  588  591  593  595  598  605  606  608  614  619  620  621  622  623  627  628 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  630  632  634  654  658  663  664  666  674  683  686  691  693  696  697  701 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  703  713  714  716  717  721  724  727  735  738  743  744  746  747  751  769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  770  771  772  773  775  778  779  780  781  784  786  788  789  790  793  794 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
##  796  801  808  809  810  811  814  817  819  823  831  840  841  842  848  851 
##    1    1    1    1    1    1    0    1    1    1    1    0    1    1    1    0 
##  853  854  855  856  858  861  868  870  872  873  874  877  882  883  884  885 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  886  887  889  890  893  897  898  900  901  904  908  911  915  917  919  923 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  934  937  942  943  945  949  952  953  957  958  963  964  965  969  970  975 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
##  982  983  985  986  987  988  990  991  994  995 1003 1004 1011 1012 1014 1016 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1017 1021 1023 1024 1026 1027 1034 1035 1038 1042 1043 1044 1045 1047 1048 1051 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1052 1053 1063 1069 1071 1072 1073 1074 1075 1076 1077 1092 1096 1103 1104 1108 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1109 1110 1116 1119 1125 1126 1127 1131 1132 1143 1147 1150 1151 1160 1162 1168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1169 1170 1171 1173 1177 1178 1180 1181 1182 1196 1198 1199 1205 1206 1216 1218 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1220 1226 1229 1236 1237 1238 1242 1243 1245 1251 1253 1255 1256 1258 1259 1261 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1264 1265 1267 1270 1271 1275 1286 1298 1299 1305 1307 1312 1318 1322 1325 1327 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 1335 1340 1343 1347 1348 1349 1353 1356 1370 1372 1376 1380 1381 1383 1386 1389 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1395 1399 1405 1412 1413 1419 1425 1426 1427 1430 1439 1451 1453 1454 1465 1471 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 1472 1475 1477 1478 1479 1480 1483 1491 1498 1501 1505 1506 1507 1509 1510 1511 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1519 1525 1526 1534 1535 1537 1538 1540 1542 1543 1545 1559 1560 1561 1562 1566 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1568 1573 1582 1593 1603 1604 1610 1614 1622 1623 1625 1627 1633 1635 1637 1645 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1647 1648 1652 1653 1659 1664 1665 1670 1672 1673 1688 1691 1695 1700 1702 1703 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1709 1725 1735 1738 1743 1748 1750 1755 1757 1758 1760 1761 1765 1769 1771 1772 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 1777 1781 1787 1789 1790 1798 1803 1804 1807 1808 1809 1811 1820 1821 1828 1829 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1834 1837 1838 1845 1848 1849 1855 1862 1865 1869 1870 1871 1875 1876 1878 1881 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1883 1884 1885 1887 1890 1891 1893 1894 1895 1896 1898 1900 1901 1912 1914 1915 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1917 1918 1919 1923 1924 1926 1929 1931 1933 1936 1937 1939 1940 1942 1948 1956 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1957 1958 1961 1968 1969 1971 1972 1975 1979 1981 1985 1986 1988 1989 1990 1991 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1994 1995 2000 2001 2002 2007 2014 2016 2024 2026 2027 2028 2029 2030 2032 2039 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 2045 2047 2049 2050 2051 2055 2062 2064 2065 2068 2070 2079 2089 2091 2096 2098 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2106 2107 2111 2113 2116 2125 2127 2130 2133 2134 2136 2137 2142 2143 2148 2153 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 2155 2156 2160 2163 2164 2174 2182 2198 2205 2207 2210 2212 2214 2218 2219 2221 
##    1    1    1    1    1    1    0    0    1    1    1    1    1    0    1    1 
## 2223 2231 2233 2239 2246 2248 2250 2252 2255 2258 2259 2261 2264 2266 2269 2275 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2280 2286 2288 2293 2297 2303 2305 2308 2309 2312 2313 2319 2323 2328 2332 2333 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 2334 2337 2339 2343 2344 2346 2352 2355 2359 2368 2371 2374 2375 2376 2381 2382 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    0    1    1 
## 2383 2395 2396 2398 2401 2405 2411 2412 2418 2427 2430 2434 2435 2438 2439 2446 
##    1    0    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 2454 2456 2458 2459 2462 2466 2472 2475 2476 2478 2481 2484 2491 2495 2496 2498 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 2499 2500 2501 2504 2505 2507 2510 2511 2516 2518 2519 2522 2524 2526 2530 2537 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2546 2553 2564 2566 2567 2568 2573 2576 2587 2588 2589 2590 2591 2594 2595 2597 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2599 2602 2604 2606 2608 2609 2613 2617 2619 2631 2634 2635 2636 2637 2641 2642 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2644 2649 2653 2654 2660 2662 2663 2664 2669 2670 2672 2675 2676 2680 2682 2683 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2684 2685 2688 2698 2699 2704 2709 2710 2713 2717 2719 2730 2735 2740 2748 2749 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2751 2754 2762 2768 2769 2777 2784 2786 2788 2792 2799 2801 2806 2813 2814 2815 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2819 2824 2825 2828 2831 2835 2848 2852 2853 2857 2861 2864 2868 2869 2880 2888 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2889 2890 2892 2894 2900 2909 2916 2920 2927 2930 2932 2939 2942 2947 2948 2952 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2956 2963 2965 2970 2972 2975 2976 2980 2984 2991 2997 3002 3008 3010 3013 3015 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3021 3023 3024 3026 3032 3038 3041 3046 3047 3055 3062 3063 3072 3074 3084 3091 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 3098 3099 3104 3109 3110 3117 3118 3120 3129 3133 3140 3141 3143 3145 3148 3151 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    0    1 
## 3152 3155 3156 3163 3165 3167 3169 3174 3175 3178 3181 3182 3186 3188 3189 3191 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3196 3200 3201 3205 3207 3208 3209 3210 3212 3214 3218 3222 3234 3235 3238 3246 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3249 3250 3252 3253 3255 3257 3262 3264 3266 3267 3268 3270 3271 3275 3281 3282 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3283 3287 3288 3289 3295 3298 3300 3314 3316 3319 3320 3327 3329 3331 3340 3341 
##    0    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 3344 3345 3346 3347 3354 3357 3359 3361 3363 3366 3370 3372 3376 3384 3386 3389 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 9549 
##    1
view(pred_class1_3_n)  #0.5时全是1

pred_class1_n <- cbind(pred_class1_1_n, pred_class1_2_n,pred_class1_3_n)
pred_class1_n
##      pred_class1_1_n pred_class1_2_n pred_class1_3_n
## 2                  1               1               1
## 4                  1               1               1
## 8                  1               1               1
## 13                 1               1               1
## 16                 0               1               1
## 18                 1               1               1
## 29                 1               1               1
## 30                 1               1               1
## 32                 1               1               1
## 36                 1               1               1
## 39                 1               1               1
## 41                 1               1               1
## 43                 1               1               1
## 48                 1               1               1
## 49                 1               1               1
## 55                 0               1               1
## 58                 1               1               1
## 59                 0               1               1
## 60                 1               1               1
## 62                 1               1               1
## 63                 0               1               1
## 71                 0               1               1
## 73                 0               0               1
## 80                 1               1               1
## 84                 0               1               1
## 86                 1               1               1
## 87                 1               1               1
## 98                 1               1               1
## 102                0               1               1
## 104                0               1               1
## 107                0               0               1
## 109                0               1               1
## 110                1               1               1
## 113                1               1               1
## 123                0               1               1
## 125                1               1               1
## 136                1               1               1
## 137                1               1               1
## 138                1               1               0
## 143                1               1               1
## 145                1               1               1
## 147                1               1               0
## 149                0               0               1
## 151                1               1               1
## 153                1               1               1
## 160                1               1               1
## 162                1               1               1
## 165                0               0               1
## 167                1               1               1
## 168                1               1               1
## 171                1               1               1
## 175                1               1               1
## 177                1               1               1
## 184                0               1               1
## 187                1               1               1
## 188                0               1               1
## 198                1               1               1
## 199                0               1               1
## 205                1               0               1
## 206                1               1               1
## 214                1               1               1
## 217                1               1               1
## 220                1               1               1
## 221                1               1               1
## 225                1               1               1
## 227                1               1               1
## 230                0               1               1
## 231                1               1               1
## 242                0               0               1
## 249                1               1               1
## 251                1               1               1
## 253                1               1               1
## 261                1               1               1
## 262                1               1               1
## 281                1               1               1
## 283                0               1               1
## 284                1               1               1
## 286                0               1               1
## 292                1               1               1
## 294                1               1               1
## 295                1               1               1
## 296                0               1               1
## 300                1               1               0
## 302                1               1               1
## 303                1               1               1
## 306                1               1               1
## 308                1               1               1
## 309                1               1               1
## 314                1               1               1
## 316                0               1               1
## 318                1               1               1
## 321                1               1               1
## 322                1               1               1
## 329                1               1               1
## 332                1               1               1
## 333                1               1               1
## 340                1               1               1
## 350                0               1               1
## 351                1               1               1
## 354                1               1               1
## 366                1               1               1
## 368                1               1               1
## 371                1               1               1
## 374                1               1               1
## 378                1               1               1
## 382                1               1               1
## 387                0               1               1
## 391                1               1               1
## 393                1               1               1
## 394                0               1               1
## 396                0               1               1
## 399                1               1               1
## 402                1               1               1
## 408                1               1               1
## 412                1               1               1
## 413                1               1               1
## 414                0               1               1
## 416                1               1               1
## 417                1               1               1
## 421                1               1               1
## 423                1               1               1
## 426                1               1               1
## 429                1               1               1
## 430                0               1               1
## 437                0               1               1
## 441                1               1               1
## 444                1               1               1
## 450                0               1               1
## 456                1               1               1
## 460                1               1               1
## 462                1               1               1
## 463                1               1               1
## 465                1               1               0
## 469                0               1               1
## 473                1               1               1
## 481                1               1               1
## 484                1               1               1
## 487                1               1               1
## 493                1               1               1
## 500                0               1               1
## 507                1               1               1
## 525                1               1               1
## 527                0               1               1
## 532                1               1               1
## 535                0               1               1
## 537                1               1               1
## 538                1               1               1
## 541                0               1               1
## 544                1               1               1
## 549                1               0               1
## 552                1               1               0
## 553                1               1               1
## 555                1               1               1
## 558                1               1               1
## 559                0               1               1
## 562                1               1               1
## 566                1               1               1
## 571                1               1               1
## 573                1               1               1
## 582                0               1               1
## 588                0               1               1
## 591                1               1               1
## 593                1               1               1
## 595                0               1               1
## 598                0               1               1
## 605                1               1               1
## 606                1               1               1
## 608                0               1               1
## 614                0               1               1
## 619                0               1               1
## 620                1               1               1
## 621                1               1               1
## 622                1               1               0
## 623                1               1               1
## 627                1               1               1
## 628                1               1               1
## 630                1               1               1
## 632                1               1               1
## 634                0               1               1
## 654                1               1               1
## 658                1               1               1
## 663                1               1               1
## 664                1               1               1
## 666                1               1               1
## 674                1               1               1
## 683                1               1               0
## 686                0               1               1
## 691                1               1               1
## 693                1               1               1
## 696                0               1               1
## 697                0               0               1
## 701                1               1               1
## 703                1               1               1
## 713                1               1               1
## 714                0               1               1
## 716                1               0               1
## 717                1               1               1
## 721                1               1               1
## 724                1               1               1
## 727                1               1               1
## 735                1               1               1
## 738                1               1               1
## 743                0               0               1
## 744                0               1               1
## 746                1               1               1
## 747                1               1               1
## 751                0               1               1
## 769                1               1               1
## 770                1               1               1
## 771                1               1               1
## 772                1               1               1
## 773                1               1               1
## 775                1               1               1
## 778                1               1               1
## 779                0               1               1
## 780                1               1               1
## 781                1               1               1
## 784                0               1               1
## 786                1               1               1
## 788                1               1               1
## 789                1               1               1
## 790                0               1               0
## 793                1               1               1
## 794                0               1               1
## 796                1               1               1
## 801                1               1               1
## 808                0               0               1
## 809                1               1               1
## 810                1               1               1
## 811                1               1               1
## 814                1               1               0
## 817                1               1               1
## 819                1               1               1
## 823                1               1               1
## 831                1               1               1
## 840                1               1               0
## 841                1               1               1
## 842                1               1               1
## 848                1               1               1
## 851                1               1               0
## 853                1               1               1
## 854                1               1               1
## 855                1               1               1
## 856                1               0               1
## 858                1               1               1
## 861                1               1               1
## 868                1               1               1
## 870                1               1               1
## 872                0               1               1
## 873                0               1               1
## 874                1               1               1
## 877                0               1               1
## 882                0               1               1
## 883                1               1               1
## 884                1               1               1
## 885                1               1               1
## 886                0               1               1
## 887                1               1               1
## 889                1               1               1
## 890                1               1               1
## 893                1               1               1
## 897                0               1               1
## 898                1               1               1
## 900                1               1               1
## 901                0               1               1
## 904                0               0               1
## 908                1               1               1
## 911                1               1               1
## 915                1               1               1
## 917                1               1               1
## 919                1               1               1
## 923                1               1               1
## 934                1               1               1
## 937                0               1               1
## 942                1               1               1
## 943                1               1               1
## 945                1               1               1
## 949                1               1               1
## 952                0               1               1
## 953                1               1               1
## 957                1               1               1
## 958                0               0               1
## 963                1               1               1
## 964                1               1               0
## 965                1               1               1
## 969                1               1               1
## 970                1               1               1
## 975                1               1               1
## 982                0               1               1
## 983                0               1               1
## 985                0               1               1
## 986                0               1               1
## 987                1               1               1
## 988                1               1               1
## 990                0               1               1
## 991                0               0               1
## 994                1               1               1
## 995                0               1               1
## 1003               1               1               1
## 1004               1               1               1
## 1011               1               1               1
## 1012               0               1               1
## 1014               1               1               1
## 1016               0               1               1
## 1017               1               1               1
## 1021               1               1               1
## 1023               1               1               1
## 1024               1               1               1
## 1026               0               1               1
## 1027               1               1               1
## 1034               0               1               1
## 1035               1               1               1
## 1038               0               1               1
## 1042               1               1               1
## 1043               1               1               1
## 1044               1               1               1
## 1045               1               1               1
## 1047               1               1               1
## 1048               1               1               1
## 1051               1               1               1
## 1052               1               1               1
## 1053               1               1               1
## 1063               1               1               1
## 1069               1               1               1
## 1071               1               1               1
## 1072               1               1               1
## 1073               1               1               1
## 1074               0               1               1
## 1075               1               1               1
## 1076               1               1               1
## 1077               1               1               1
## 1092               1               1               1
## 1096               0               1               1
## 1103               0               1               1
## 1104               1               1               1
## 1108               0               1               1
## 1109               1               1               1
## 1110               1               1               1
## 1116               0               1               1
## 1119               1               1               1
## 1125               1               1               1
## 1126               1               1               1
## 1127               0               1               1
## 1131               1               1               1
## 1132               0               1               1
## 1143               1               1               1
## 1147               1               1               1
## 1150               1               1               1
## 1151               1               1               1
## 1160               1               1               1
## 1162               1               1               1
## 1168               0               0               1
## 1169               0               1               1
## 1170               1               1               1
## 1171               1               1               1
## 1173               1               1               1
## 1177               1               1               1
## 1178               0               1               1
## 1180               0               1               1
## 1181               1               1               1
## 1182               1               0               1
## 1196               1               1               1
## 1198               1               1               1
## 1199               1               1               1
## 1205               0               0               1
## 1206               1               1               1
## 1216               1               1               1
## 1218               0               1               1
## 1220               1               1               1
## 1226               1               1               1
## 1229               1               1               1
## 1236               1               0               1
## 1237               1               1               1
## 1238               1               1               1
## 1242               0               0               1
## 1243               1               1               1
## 1245               0               1               1
## 1251               1               1               1
## 1253               1               1               1
## 1255               1               1               1
## 1256               0               1               1
## 1258               1               1               1
## 1259               1               1               1
## 1261               1               1               1
## 1264               1               1               1
## 1265               1               0               1
## 1267               0               0               1
## 1270               1               1               1
## 1271               1               1               1
## 1275               1               1               1
## 1286               1               1               1
## 1298               1               1               1
## 1299               1               1               1
## 1305               1               1               1
## 1307               1               1               1
## 1312               1               1               1
## 1318               1               1               1
## 1322               1               1               0
## 1325               1               1               1
## 1327               1               1               1
## 1335               1               1               1
## 1340               0               1               1
## 1343               0               1               1
## 1347               1               1               1
## 1348               1               1               1
## 1349               1               1               1
## 1353               1               1               1
## 1356               0               0               1
## 1370               1               1               1
## 1372               0               1               1
## 1376               1               1               1
## 1380               1               1               1
## 1381               0               1               1
## 1383               1               1               1
## 1386               1               1               1
## 1389               0               1               1
## 1395               1               1               1
## 1399               1               1               1
## 1405               1               1               1
## 1412               1               0               1
## 1413               1               1               1
## 1419               0               1               1
## 1425               1               1               1
## 1426               1               1               1
## 1427               1               1               1
## 1430               1               1               1
## 1439               1               1               1
## 1451               1               1               1
## 1453               1               1               1
## 1454               1               1               0
## 1465               1               1               1
## 1471               0               1               1
## 1472               1               1               1
## 1475               0               0               1
## 1477               1               1               1
## 1478               1               1               1
## 1479               1               1               1
## 1480               1               1               1
## 1483               1               1               1
## 1491               1               1               1
## 1498               0               1               1
## 1501               1               1               1
## 1505               1               1               1
## 1506               1               1               1
## 1507               1               1               1
## 1509               0               1               1
## 1510               1               1               1
## 1511               1               1               1
## 1519               0               1               1
## 1525               1               1               1
## 1526               1               1               1
## 1534               1               1               1
## 1535               1               1               1
## 1537               1               1               1
## 1538               1               1               1
## 1540               1               1               1
## 1542               1               1               0
## 1543               1               1               1
## 1545               0               1               1
## 1559               1               1               1
## 1560               0               1               1
## 1561               1               1               1
## 1562               1               1               1
## 1566               1               1               1
## 1568               0               0               1
## 1573               1               1               1
## 1582               0               1               1
## 1593               1               1               1
## 1603               1               1               1
## 1604               1               1               1
## 1610               1               1               1
## 1614               0               1               1
## 1622               1               1               1
## 1623               1               1               1
## 1625               1               1               1
## 1627               1               1               1
## 1633               1               1               1
## 1635               1               1               1
## 1637               0               1               1
## 1645               0               1               1
## 1647               0               1               1
## 1648               1               1               1
## 1652               0               1               1
## 1653               1               1               1
## 1659               1               1               1
## 1664               1               1               1
## 1665               0               1               1
## 1670               1               1               1
## 1672               0               1               0
## 1673               1               1               1
## 1688               1               1               1
## 1691               1               1               1
## 1695               1               1               1
## 1700               1               1               1
## 1702               1               1               1
## 1703               1               1               1
## 1709               1               1               1
## 1725               1               1               1
## 1735               1               1               1
## 1738               1               1               0
## 1743               1               1               1
## 1748               0               1               1
## 1750               1               1               1
## 1755               1               1               1
## 1757               1               1               1
## 1758               0               1               1
## 1760               1               1               1
## 1761               1               1               1
## 1765               1               1               1
## 1769               1               1               1
## 1771               1               1               1
## 1772               0               1               1
## 1777               0               1               1
## 1781               1               1               1
## 1787               1               1               1
## 1789               1               1               1
## 1790               1               1               1
## 1798               1               1               1
## 1803               0               1               1
## 1804               1               1               1
## 1807               1               1               1
## 1808               1               1               1
## 1809               1               1               1
## 1811               0               1               1
## 1820               1               1               1
## 1821               1               1               1
## 1828               1               1               1
## 1829               1               1               1
## 1834               1               1               1
## 1837               1               1               1
## 1838               1               1               1
## 1845               0               1               1
## 1848               1               1               1
## 1849               1               1               1
## 1855               1               1               1
## 1862               1               1               1
## 1865               1               1               0
## 1869               0               1               1
## 1870               0               1               1
## 1871               0               1               1
## 1875               1               1               1
## 1876               1               1               1
## 1878               0               1               1
## 1881               1               1               1
## 1883               1               0               1
## 1884               1               1               1
## 1885               1               1               1
## 1887               1               1               1
## 1890               0               1               1
## 1891               1               1               1
## 1893               1               1               1
## 1894               1               1               1
## 1895               0               1               1
## 1896               1               1               1
## 1898               1               1               1
## 1900               1               1               1
## 1901               0               1               1
## 1912               1               1               1
## 1914               1               1               1
## 1915               1               1               1
## 1917               1               1               1
## 1918               1               1               1
## 1919               1               1               1
## 1923               0               1               1
## 1924               0               1               1
## 1926               0               1               1
## 1929               1               1               1
## 1931               1               1               1
## 1933               0               1               1
## 1936               1               1               1
## 1937               1               1               1
## 1939               1               1               1
## 1940               1               1               1
## 1942               1               1               1
## 1948               1               1               1
## 1956               1               1               1
## 1957               1               1               1
## 1958               1               1               1
## 1961               1               1               1
## 1968               1               1               1
## 1969               1               1               1
## 1971               1               0               1
## 1972               1               1               1
## 1975               1               1               1
## 1979               1               1               1
## 1981               0               1               1
## 1985               1               1               1
## 1986               1               1               1
## 1988               1               1               1
## 1989               0               1               1
## 1990               0               1               1
## 1991               1               1               1
## 1994               1               1               1
## 1995               0               0               1
## 2000               1               1               1
## 2001               0               1               1
## 2002               1               1               1
## 2007               1               1               1
## 2014               1               1               1
## 2016               1               1               1
## 2024               1               1               0
## 2026               1               1               1
## 2027               1               1               1
## 2028               1               1               1
## 2029               1               1               1
## 2030               1               1               1
## 2032               1               1               1
## 2039               1               1               1
## 2045               1               1               1
## 2047               1               1               1
## 2049               1               1               1
## 2050               1               1               1
## 2051               1               1               1
## 2055               1               1               1
## 2062               0               1               1
## 2064               0               1               1
## 2065               0               1               1
## 2068               0               1               1
## 2070               1               1               1
## 2079               1               1               1
## 2089               1               1               1
## 2091               0               0               1
## 2096               1               1               1
## 2098               1               1               1
## 2106               1               1               1
## 2107               1               1               1
## 2111               1               1               1
## 2113               1               1               1
## 2116               1               1               1
## 2125               1               1               1
## 2127               1               1               1
## 2130               1               1               1
## 2133               1               1               1
## 2134               1               1               1
## 2136               1               1               1
## 2137               1               1               0
## 2142               1               1               1
## 2143               1               1               1
## 2148               0               0               1
## 2153               1               1               1
## 2155               1               1               1
## 2156               0               0               1
## 2160               1               1               1
## 2163               1               1               1
## 2164               1               1               1
## 2174               1               1               1
## 2182               1               1               0
## 2198               1               1               0
## 2205               0               1               1
## 2207               1               1               1
## 2210               1               1               1
## 2212               1               1               1
## 2214               0               1               1
## 2218               1               1               0
## 2219               1               1               1
## 2221               1               1               1
## 2223               0               1               1
## 2231               0               1               1
## 2233               1               1               1
## 2239               1               1               1
## 2246               1               1               1
## 2248               0               1               1
## 2250               1               1               1
## 2252               1               1               1
## 2255               1               1               1
## 2258               1               1               1
## 2259               1               1               1
## 2261               1               1               1
## 2264               1               1               1
## 2266               1               1               1
## 2269               1               1               1
## 2275               1               1               1
## 2280               1               1               1
## 2286               0               1               1
## 2288               0               1               1
## 2293               0               1               1
## 2297               0               1               1
## 2303               1               1               1
## 2305               1               1               1
## 2308               0               1               0
## 2309               0               1               1
## 2312               0               1               1
## 2313               1               1               1
## 2319               0               1               1
## 2323               0               1               1
## 2328               0               1               1
## 2332               1               1               1
## 2333               1               1               1
## 2334               1               0               1
## 2337               1               1               1
## 2339               0               1               1
## 2343               0               1               1
## 2344               1               1               1
## 2346               1               1               1
## 2352               1               1               1
## 2355               1               1               1
## 2359               1               1               0
## 2368               0               1               1
## 2371               1               1               1
## 2374               0               1               1
## 2375               0               1               1
## 2376               1               1               0
## 2381               0               1               1
## 2382               1               1               1
## 2383               0               0               1
## 2395               1               1               0
## 2396               1               1               1
## 2398               0               1               1
## 2401               0               1               1
## 2405               1               1               1
## 2411               1               1               1
## 2412               0               1               1
## 2418               0               1               0
## 2427               0               1               1
## 2430               0               1               1
## 2434               1               1               1
## 2435               0               1               1
## 2438               0               1               1
## 2439               1               1               1
## 2446               0               1               1
## 2454               0               0               1
## 2456               1               1               1
## 2458               0               1               1
## 2459               1               1               1
## 2462               1               1               1
## 2466               1               1               1
## 2472               1               1               1
## 2475               1               1               1
## 2476               0               1               1
## 2478               1               1               0
## 2481               1               1               1
## 2484               1               1               1
## 2491               1               1               1
## 2495               1               1               1
## 2496               1               1               1
## 2498               1               1               1
## 2499               0               1               1
## 2500               1               1               0
## 2501               0               1               1
## 2504               1               1               1
## 2505               1               1               1
## 2507               1               1               1
## 2510               1               1               1
## 2511               0               1               1
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## 9517               1               1               1
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## 9521               1               1               1
## 9530               1               1               1
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## 9548               0               1               1
## 9549               1               1               1
view(pred_class1_n)


#repeat
#OL best model of train data
# Convert the probability value into a category
pred_class2_1_n <- ifelse(predictions2_n[,1] > 0.0044, 1, 0 )
pred_class2_1_n #. If the probability is greater than 0.01, the prediction is a positive class (1), otherwise negative class (0)
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    0    1 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
##  588  591  593  595  598  605  606  608  614  619  620  621  622  623  627  628 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  630  632  634  654  658  663  664  666  674  683  686  691  693  696  697  701 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  703  713  714  716  717  721  724  727  735  738  743  744  746  747  751  769 
##    1    1    0    0    1    1    1    1    1    1    0    1    1    1    1    1 
##  770  771  772  773  775  778  779  780  781  784  786  788  789  790  793  794 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  796  801  808  809  810  811  814  817  819  823  831  840  841  842  848  851 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
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## 7112 7114 7115 7116 7120 7130 7133 7139 7141 7144 7152 7155 7157 7158 7160 7161 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 7166 7167 7168 7178 7179 7181 7182 7186 7188 7191 7192 7196 7197 7202 7203 7207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7209 7210 7221 7222 7226 7228 7229 7237 7238 7241 7247 7248 7250 7270 7273 7275 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 7332 7337 7338 7339 7341 7342 7344 7346 7350 7355 7360 7364 7365 7366 7371 7373 
##    1    1    1    1    1    1    1    1    0    0    1    1    1    1    1    1 
## 7376 7380 7381 7387 7389 7392 7399 7402 7403 7408 7410 7412 7416 7419 7426 7428 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 7431 7432 7433 7436 7438 7440 7441 7447 7456 7457 7458 7462 7463 7466 7467 7472 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7475 7484 7485 7487 7488 7490 7497 7498 7502 7507 7511 7519 7520 7523 7525 7526 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7529 7530 7531 7532 7533 7534 7536 7538 7539 7543 7547 7549 7551 7552 7553 7556 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7676 7677 7678 7685 7692 7697 7700 7704 7709 7712 7720 7721 7729 7730 7736 7739 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7740 7741 7742 7743 7750 7753 7755 7757 7759 7761 7763 7764 7774 7778 7785 7788 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 7791 7793 7796 7797 7802 7805 7807 7811 7813 7814 7815 7826 7831 7837 7838 7842 
##    1    0    1    1    1    1    1    1    1    1    1    0    1    1    1    0 
## 7844 7846 7847 7849 7855 7857 7862 7869 7871 7876 7882 7883 7884 7888 7891 7892 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7894 7896 7898 7910 7911 7921 7923 7926 7927 7928 7929 7933 7936 7937 7939 7949 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 7953 7955 7957 7960 7962 7964 7965 7966 7967 7971 7976 7981 7983 7984 7988 7989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7991 7999 8008 8012 8013 8015 8017 8018 8019 8023 8026 8030 8034 8035 8043 8044 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8049 8054 8065 8066 8067 8076 8083 8089 8090 8104 8108 8110 8111 8113 8118 8125 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8127 8128 8133 8137 8138 8147 8150 8156 8167 8174 8176 8182 8198 8199 8206 8207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8208 8214 8215 8216 8218 8222 8223 8224 8226 8227 8230 8234 8235 8237 8239 8242 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8243 8247 8248 8253 8256 8257 8259 8267 8271 8272 8282 8288 8290 8291 8294 8295 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8302 8303 8306 8308 8319 8321 8322 8325 8326 8328 8337 8340 8344 8345 8352 8359 
##    1    0    0    1    0    1    1    1    1    0    1    1    1    1    1    1 
## 8364 8365 8370 8381 8385 8387 8391 8395 8396 8400 8405 8406 8408 8409 8413 8415 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    0    1    1 
## 8417 8418 8419 8420 8425 8426 8428 8430 8433 8437 8439 8442 8445 8448 8449 8459 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8460 8464 8466 8468 8471 8474 8475 8476 8477 8486 8488 8490 8496 8497 8498 8501 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8502 8504 8505 8508 8509 8510 8511 8513 8514 8517 8527 8528 8534 8535 8540 8542 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8543 8545 8546 8547 8548 8551 8560 8561 8566 8567 8569 8570 8571 8575 8580 8584 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8587 8600 8603 8607 8623 8626 8627 8629 8630 8635 8637 8646 8649 8651 8652 8656 
##    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8664 8667 8669 8672 8680 8681 8682 8683 8691 8700 8701 8707 8711 8715 8716 8721 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8722 8724 8725 8729 8730 8731 8733 8735 8743 8744 8747 8758 8759 8762 8764 8769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8772 8773 8774 8775 8783 8784 8786 8790 8796 8798 8799 8804 8805 8806 8807 8811 
##    1    1    0    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8817 8818 8819 8820 8826 8830 8832 8835 8836 8845 8847 8850 8851 8854 8860 8861 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8862 8866 8867 8871 8872 8881 8882 8884 8891 8892 8893 8895 8896 8900 8903 8904 
##    1    1    0    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8905 8906 8907 8911 8919 8920 8922 8927 8935 8942 8945 8948 8949 8951 8952 8953 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8955 8959 8961 8965 8967 8970 8971 8973 8978 8982 8984 8985 8986 8990 8992 8998 
##    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
## 9001 9006 9011 9012 9013 9015 9017 9018 9021 9025 9033 9037 9041 9046 9049 9054 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9057 9063 9076 9077 9079 9080 9083 9084 9090 9092 9095 9097 9098 9100 9101 9105 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9108 9109 9117 9119 9127 9130 9133 9136 9139 9151 9153 9156 9158 9162 9163 9166 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    0    1    1    1    1    1    0    1    1    0    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9404 9405 9409 9413 9414 9418 9419 9425 9430 9431 9434 9435 9436 9437 9439 9442 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9443 9446 9447 9448 9450 9452 9454 9462 9464 9465 9466 9467 9472 9473 9482 9486 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9549 
##    1
view(pred_class2_1_n)
#39个0,961个1
pred_class2_1_n
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    0    1 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
##  588  591  593  595  598  605  606  608  614  619  620  621  622  623  627  628 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  630  632  634  654  658  663  664  666  674  683  686  691  693  696  697  701 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
##  703  713  714  716  717  721  724  727  735  738  743  744  746  747  751  769 
##    1    1    0    0    1    1    1    1    1    1    0    1    1    1    1    1 
##  770  771  772  773  775  778  779  780  781  784  786  788  789  790  793  794 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  796  801  808  809  810  811  814  817  819  823  831  840  841  842  848  851 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  853  854  855  856  858  861  868  870  872  873  874  877  882  883  884  885 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  886  887  889  890  893  897  898  900  901  904  908  911  915  917  919  923 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  934  937  942  943  945  949  952  953  957  958  963  964  965  969  970  975 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  982  983  985  986  987  988  990  991  994  995 1003 1004 1011 1012 1014 1016 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 1017 1021 1023 1024 1026 1027 1034 1035 1038 1042 1043 1044 1045 1047 1048 1051 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1052 1053 1063 1069 1071 1072 1073 1074 1075 1076 1077 1092 1096 1103 1104 1108 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1109 1110 1116 1119 1125 1126 1127 1131 1132 1143 1147 1150 1151 1160 1162 1168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 1169 1170 1171 1173 1177 1178 1180 1181 1182 1196 1198 1199 1205 1206 1216 1218 
##    1    1    1    1    1    1    1    1    0    1    1    1    0    1    1    1 
## 1220 1226 1229 1236 1237 1238 1242 1243 1245 1251 1253 1255 1256 1258 1259 1261 
##    1    1    1    0    1    1    0    1    1    1    1    1    1    1    1    1 
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##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1335 1340 1343 1347 1348 1349 1353 1356 1370 1372 1376 1380 1381 1383 1386 1389 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 1395 1399 1405 1412 1413 1419 1425 1426 1427 1430 1439 1451 1453 1454 1465 1471 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 1472 1475 1477 1478 1479 1480 1483 1491 1498 1501 1505 1506 1507 1509 1510 1511 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1519 1525 1526 1534 1535 1537 1538 1540 1542 1543 1545 1559 1560 1561 1562 1566 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1568 1573 1582 1593 1603 1604 1610 1614 1622 1623 1625 1627 1633 1635 1637 1645 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 1647 1648 1652 1653 1659 1664 1665 1670 1672 1673 1688 1691 1695 1700 1702 1703 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1709 1725 1735 1738 1743 1748 1750 1755 1757 1758 1760 1761 1765 1769 1771 1772 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1777 1781 1787 1789 1790 1798 1803 1804 1807 1808 1809 1811 1820 1821 1828 1829 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1834 1837 1838 1845 1848 1849 1855 1862 1865 1869 1870 1871 1875 1876 1878 1881 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 1883 1884 1885 1887 1890 1891 1893 1894 1895 1896 1898 1900 1901 1912 1914 1915 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1917 1918 1919 1923 1924 1926 1929 1931 1933 1936 1937 1939 1940 1942 1948 1956 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1957 1958 1961 1968 1969 1971 1972 1975 1979 1981 1985 1986 1988 1989 1990 1991 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    0    1 
## 1994 1995 2000 2001 2002 2007 2014 2016 2024 2026 2027 2028 2029 2030 2032 2039 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2045 2047 2049 2050 2051 2055 2062 2064 2065 2068 2070 2079 2089 2091 2096 2098 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 2106 2107 2111 2113 2116 2125 2127 2130 2133 2134 2136 2137 2142 2143 2148 2153 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 2155 2156 2160 2163 2164 2174 2182 2198 2205 2207 2210 2212 2214 2218 2219 2221 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2223 2231 2233 2239 2246 2248 2250 2252 2255 2258 2259 2261 2264 2266 2269 2275 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2280 2286 2288 2293 2297 2303 2305 2308 2309 2312 2313 2319 2323 2328 2332 2333 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2334 2337 2339 2343 2344 2346 2352 2355 2359 2368 2371 2374 2375 2376 2381 2382 
##    0    1    1    1    1    1    1    1    1    0    1    0    1    1    1    1 
## 2383 2395 2396 2398 2401 2405 2411 2412 2418 2427 2430 2434 2435 2438 2439 2446 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2454 2456 2458 2459 2462 2466 2472 2475 2476 2478 2481 2484 2491 2495 2496 2498 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2499 2500 2501 2504 2505 2507 2510 2511 2516 2518 2519 2522 2524 2526 2530 2537 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2546 2553 2564 2566 2567 2568 2573 2576 2587 2588 2589 2590 2591 2594 2595 2597 
##    0    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2599 2602 2604 2606 2608 2609 2613 2617 2619 2631 2634 2635 2636 2637 2641 2642 
##    1    0    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 2644 2649 2653 2654 2660 2662 2663 2664 2669 2670 2672 2675 2676 2680 2682 2683 
##    1    0    1    1    1    0    1    1    1    1    1    0    1    0    1    1 
## 2684 2685 2688 2698 2699 2704 2709 2710 2713 2717 2719 2730 2735 2740 2748 2749 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
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##    1    1    0    1    1    0    1    1    1    1    1    1    1    0    0    1 
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##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2889 2890 2892 2894 2900 2909 2916 2920 2927 2930 2932 2939 2942 2947 2948 2952 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2956 2963 2965 2970 2972 2975 2976 2980 2984 2991 2997 3002 3008 3010 3013 3015 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3021 3023 3024 3026 3032 3038 3041 3046 3047 3055 3062 3063 3072 3074 3084 3091 
##    1    1    1    1    1    1    0    1    0    1    1    1    1    1    1    1 
## 3098 3099 3104 3109 3110 3117 3118 3120 3129 3133 3140 3141 3143 3145 3148 3151 
##    1    1    1    1    1    1    1    1    1    1    0    0    1    1    1    1 
## 3152 3155 3156 3163 3165 3167 3169 3174 3175 3178 3181 3182 3186 3188 3189 3191 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    0    1 
## 3196 3200 3201 3205 3207 3208 3209 3210 3212 3214 3218 3222 3234 3235 3238 3246 
##    1    1    1    0    1    0    1    1    1    1    0    1    1    1    1    1 
## 3249 3250 3252 3253 3255 3257 3262 3264 3266 3267 3268 3270 3271 3275 3281 3282 
##    1    1    1    0    1    1    0    1    1    1    1    1    1    1    1    1 
## 3283 3287 3288 3289 3295 3298 3300 3314 3316 3319 3320 3327 3329 3331 3340 3341 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 3344 3345 3346 3347 3354 3357 3359 3361 3363 3366 3370 3372 3376 3384 3386 3389 
##    1    1    1    1    1    1    1    1    0    1    1    0    0    1    0    1 
## 3390 3394 3398 3402 3405 3408 3413 3419 3421 3425 3426 3428 3431 3432 3445 3448 
##    1    1    1    1    0    1    1    1    0    1    1    1    1    0    1    1 
## 3451 3456 3457 3458 3463 3469 3471 3475 3476 3481 3482 3486 3489 3492 3494 3498 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3499 3503 3504 3505 3506 3508 3511 3513 3515 3516 3518 3521 3525 3526 3530 3533 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3535 3539 3540 3543 3544 3547 3549 3550 3553 3556 3561 3567 3573 3577 3581 3586 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3587 3589 3590 3591 3601 3606 3608 3610 3620 3621 3623 3631 3633 3634 3640 3641 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 6562 6566 6569 6570 6571 6572 6573 6574 6578 6579 6585 6590 6591 6592 6597 6605 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7065 7066 7069 7073 7077 7079 7082 7083 7088 7091 7094 7100 7103 7106 7109 7110 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7112 7114 7115 7116 7120 7130 7133 7139 7141 7144 7152 7155 7157 7158 7160 7161 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 7166 7167 7168 7178 7179 7181 7182 7186 7188 7191 7192 7196 7197 7202 7203 7207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7209 7210 7221 7222 7226 7228 7229 7237 7238 7241 7247 7248 7250 7270 7273 7275 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 7332 7337 7338 7339 7341 7342 7344 7346 7350 7355 7360 7364 7365 7366 7371 7373 
##    1    1    1    1    1    1    1    1    0    0    1    1    1    1    1    1 
## 7376 7380 7381 7387 7389 7392 7399 7402 7403 7408 7410 7412 7416 7419 7426 7428 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 7431 7432 7433 7436 7438 7440 7441 7447 7456 7457 7458 7462 7463 7466 7467 7472 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7475 7484 7485 7487 7488 7490 7497 7498 7502 7507 7511 7519 7520 7523 7525 7526 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7529 7530 7531 7532 7533 7534 7536 7538 7539 7543 7547 7549 7551 7552 7553 7556 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7560 7566 7569 7570 7573 7580 7586 7597 7598 7601 7606 7612 7615 7616 7620 7626 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7627 7629 7631 7633 7640 7645 7650 7651 7652 7654 7655 7659 7660 7665 7673 7674 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7676 7677 7678 7685 7692 7697 7700 7704 7709 7712 7720 7721 7729 7730 7736 7739 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7740 7741 7742 7743 7750 7753 7755 7757 7759 7761 7763 7764 7774 7778 7785 7788 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 7791 7793 7796 7797 7802 7805 7807 7811 7813 7814 7815 7826 7831 7837 7838 7842 
##    1    0    1    1    1    1    1    1    1    1    1    0    1    1    1    0 
## 7844 7846 7847 7849 7855 7857 7862 7869 7871 7876 7882 7883 7884 7888 7891 7892 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7894 7896 7898 7910 7911 7921 7923 7926 7927 7928 7929 7933 7936 7937 7939 7949 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 7953 7955 7957 7960 7962 7964 7965 7966 7967 7971 7976 7981 7983 7984 7988 7989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7991 7999 8008 8012 8013 8015 8017 8018 8019 8023 8026 8030 8034 8035 8043 8044 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8049 8054 8065 8066 8067 8076 8083 8089 8090 8104 8108 8110 8111 8113 8118 8125 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8127 8128 8133 8137 8138 8147 8150 8156 8167 8174 8176 8182 8198 8199 8206 8207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8208 8214 8215 8216 8218 8222 8223 8224 8226 8227 8230 8234 8235 8237 8239 8242 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8243 8247 8248 8253 8256 8257 8259 8267 8271 8272 8282 8288 8290 8291 8294 8295 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8302 8303 8306 8308 8319 8321 8322 8325 8326 8328 8337 8340 8344 8345 8352 8359 
##    1    0    0    1    0    1    1    1    1    0    1    1    1    1    1    1 
## 8364 8365 8370 8381 8385 8387 8391 8395 8396 8400 8405 8406 8408 8409 8413 8415 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    0    1    1 
## 8417 8418 8419 8420 8425 8426 8428 8430 8433 8437 8439 8442 8445 8448 8449 8459 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8460 8464 8466 8468 8471 8474 8475 8476 8477 8486 8488 8490 8496 8497 8498 8501 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8502 8504 8505 8508 8509 8510 8511 8513 8514 8517 8527 8528 8534 8535 8540 8542 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8543 8545 8546 8547 8548 8551 8560 8561 8566 8567 8569 8570 8571 8575 8580 8584 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8587 8600 8603 8607 8623 8626 8627 8629 8630 8635 8637 8646 8649 8651 8652 8656 
##    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8664 8667 8669 8672 8680 8681 8682 8683 8691 8700 8701 8707 8711 8715 8716 8721 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8722 8724 8725 8729 8730 8731 8733 8735 8743 8744 8747 8758 8759 8762 8764 8769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8772 8773 8774 8775 8783 8784 8786 8790 8796 8798 8799 8804 8805 8806 8807 8811 
##    1    1    0    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8817 8818 8819 8820 8826 8830 8832 8835 8836 8845 8847 8850 8851 8854 8860 8861 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8862 8866 8867 8871 8872 8881 8882 8884 8891 8892 8893 8895 8896 8900 8903 8904 
##    1    1    0    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8905 8906 8907 8911 8919 8920 8922 8927 8935 8942 8945 8948 8949 8951 8952 8953 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8955 8959 8961 8965 8967 8970 8971 8973 8978 8982 8984 8985 8986 8990 8992 8998 
##    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
## 9001 9006 9011 9012 9013 9015 9017 9018 9021 9025 9033 9037 9041 9046 9049 9054 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9057 9063 9076 9077 9079 9080 9083 9084 9090 9092 9095 9097 9098 9100 9101 9105 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9108 9109 9117 9119 9127 9130 9133 9136 9139 9151 9153 9156 9158 9162 9163 9166 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    0    1    1    1    1    1    0    1    1    0    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9404 9405 9409 9413 9414 9418 9419 9425 9430 9431 9434 9435 9436 9437 9439 9442 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9443 9446 9447 9448 9450 9452 9454 9462 9464 9465 9466 9467 9472 9473 9482 9486 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9549 
##    1
pred_class2_2_n <- ifelse(predictions2_n[,2] > 0.1126, 1, 0 )
pred_class2_2_n #. If the probability is greater than 0.24, the prediction is a positive class (1), otherwise negative class (0)
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    0    1 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6511 6512 6521 6522 6524 6531 6534 6535 6536 6537 6544 6547 6551 6554 6558 6561 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 6562 6566 6569 6570 6571 6572 6573 6574 6578 6579 6585 6590 6591 6592 6597 6605 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6607 6609 6611 6612 6616 6622 6625 6630 6636 6640 6641 6651 6653 6655 6663 6667 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6673 6674 6676 6677 6678 6679 6680 6687 6689 6696 6697 6698 6700 6703 6709 6711 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6718 6721 6725 6727 6729 6731 6732 6740 6745 6746 6748 6751 6752 6755 6761 6764 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6766 6777 6779 6780 6783 6786 6788 6797 6801 6803 6807 6812 6813 6814 6822 6823 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 6824 6825 6827 6832 6834 6838 6839 6842 6843 6845 6852 6854 6862 6863 6864 6872 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6875 6885 6889 6891 6893 6897 6898 6907 6910 6913 6916 6918 6923 6926 6928 6930 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6936 6937 6939 6945 6949 6950 6951 6952 6954 6957 6959 6960 6961 6962 6966 6968 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 6971 6974 6978 6980 6984 6985 6987 6992 6993 6995 6998 6999 7001 7004 7005 7006 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7008 7009 7012 7014 7015 7016 7019 7026 7028 7029 7036 7043 7048 7051 7055 7058 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7065 7066 7069 7073 7077 7079 7082 7083 7088 7091 7094 7100 7103 7106 7109 7110 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7112 7114 7115 7116 7120 7130 7133 7139 7141 7144 7152 7155 7157 7158 7160 7161 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 7166 7167 7168 7178 7179 7181 7182 7186 7188 7191 7192 7196 7197 7202 7203 7207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7209 7210 7221 7222 7226 7228 7229 7237 7238 7241 7247 7248 7250 7270 7273 7275 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7279 7280 7281 7282 7283 7285 7287 7294 7299 7302 7305 7314 7315 7317 7320 7330 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 7332 7337 7338 7339 7341 7342 7344 7346 7350 7355 7360 7364 7365 7366 7371 7373 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 7376 7380 7381 7387 7389 7392 7399 7402 7403 7408 7410 7412 7416 7419 7426 7428 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 7431 7432 7433 7436 7438 7440 7441 7447 7456 7457 7458 7462 7463 7466 7467 7472 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7475 7484 7485 7487 7488 7490 7497 7498 7502 7507 7511 7519 7520 7523 7525 7526 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7529 7530 7531 7532 7533 7534 7536 7538 7539 7543 7547 7549 7551 7552 7553 7556 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7560 7566 7569 7570 7573 7580 7586 7597 7598 7601 7606 7612 7615 7616 7620 7626 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7627 7629 7631 7633 7640 7645 7650 7651 7652 7654 7655 7659 7660 7665 7673 7674 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7676 7677 7678 7685 7692 7697 7700 7704 7709 7712 7720 7721 7729 7730 7736 7739 
##    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7740 7741 7742 7743 7750 7753 7755 7757 7759 7761 7763 7764 7774 7778 7785 7788 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7791 7793 7796 7797 7802 7805 7807 7811 7813 7814 7815 7826 7831 7837 7838 7842 
##    1    0    1    1    1    1    1    1    1    1    1    0    1    1    1    0 
## 7844 7846 7847 7849 7855 7857 7862 7869 7871 7876 7882 7883 7884 7888 7891 7892 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7894 7896 7898 7910 7911 7921 7923 7926 7927 7928 7929 7933 7936 7937 7939 7949 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 7953 7955 7957 7960 7962 7964 7965 7966 7967 7971 7976 7981 7983 7984 7988 7989 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 7991 7999 8008 8012 8013 8015 8017 8018 8019 8023 8026 8030 8034 8035 8043 8044 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8049 8054 8065 8066 8067 8076 8083 8089 8090 8104 8108 8110 8111 8113 8118 8125 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8127 8128 8133 8137 8138 8147 8150 8156 8167 8174 8176 8182 8198 8199 8206 8207 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8208 8214 8215 8216 8218 8222 8223 8224 8226 8227 8230 8234 8235 8237 8239 8242 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8243 8247 8248 8253 8256 8257 8259 8267 8271 8272 8282 8288 8290 8291 8294 8295 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8302 8303 8306 8308 8319 8321 8322 8325 8326 8328 8337 8340 8344 8345 8352 8359 
##    1    0    0    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 8364 8365 8370 8381 8385 8387 8391 8395 8396 8400 8405 8406 8408 8409 8413 8415 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    0    1    1 
## 8417 8418 8419 8420 8425 8426 8428 8430 8433 8437 8439 8442 8445 8448 8449 8459 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8460 8464 8466 8468 8471 8474 8475 8476 8477 8486 8488 8490 8496 8497 8498 8501 
##    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1 
## 8502 8504 8505 8508 8509 8510 8511 8513 8514 8517 8527 8528 8534 8535 8540 8542 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8543 8545 8546 8547 8548 8551 8560 8561 8566 8567 8569 8570 8571 8575 8580 8584 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8587 8600 8603 8607 8623 8626 8627 8629 8630 8635 8637 8646 8649 8651 8652 8656 
##    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8664 8667 8669 8672 8680 8681 8682 8683 8691 8700 8701 8707 8711 8715 8716 8721 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 8722 8724 8725 8729 8730 8731 8733 8735 8743 8744 8747 8758 8759 8762 8764 8769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8772 8773 8774 8775 8783 8784 8786 8790 8796 8798 8799 8804 8805 8806 8807 8811 
##    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1 
## 8817 8818 8819 8820 8826 8830 8832 8835 8836 8845 8847 8850 8851 8854 8860 8861 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
## 8862 8866 8867 8871 8872 8881 8882 8884 8891 8892 8893 8895 8896 8900 8903 8904 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8905 8906 8907 8911 8919 8920 8922 8927 8935 8942 8945 8948 8949 8951 8952 8953 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 8955 8959 8961 8965 8967 8970 8971 8973 8978 8982 8984 8985 8986 8990 8992 8998 
##    1    1    1    1    1    0    0    1    1    1    1    1    1    1    1    1 
## 9001 9006 9011 9012 9013 9015 9017 9018 9021 9025 9033 9037 9041 9046 9049 9054 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9057 9063 9076 9077 9079 9080 9083 9084 9090 9092 9095 9097 9098 9100 9101 9105 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9108 9109 9117 9119 9127 9130 9133 9136 9139 9151 9153 9156 9158 9162 9163 9166 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    1    1    1    1    1    1    0    1    1    0    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    0 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9404 9405 9409 9413 9414 9418 9419 9425 9430 9431 9434 9435 9436 9437 9439 9442 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9443 9446 9447 9448 9450 9452 9454 9462 9464 9465 9466 9467 9472 9473 9482 9486 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9549 
##    1
#34个0,966个1
view(pred_class2_2_n)

pred_class2_3_n <- ifelse(predictions2_n[,3] > 0.6, 1, 0 )
pred_class2_3_n #. If the probability is greater than 0.75, the prediction is a positive class (1), otherwise negative class (0)
##    2    4    8   13   16   18   29   30   32   36   39   41   43   48   49   55 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   58   59   60   62   63   71   73   80   84   86   87   98  102  104  107  109 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  110  113  123  125  136  137  138  143  145  147  149  151  153  160  162  165 
##    1    1    1    1    1    1    0    1    1    0    1    1    1    1    1    1 
##  167  168  171  175  177  184  187  188  198  199  205  206  214  217  220  221 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  225  227  230  231  242  249  251  253  261  262  281  283  284  286  292  294 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  295  296  300  302  303  306  308  309  314  316  318  321  322  329  332  333 
##    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  340  350  351  354  366  368  371  374  378  382  387  391  393  394  396  399 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  402  408  412  413  414  416  417  421  423  426  429  430  437  441  444  450 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  456  460  462  463  465  469  473  481  484  487  493  500  507  525  527  532 
##    1    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1 
##  535  537  538  541  544  549  552  553  555  558  559  562  566  571  573  582 
##    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1    1 
##  588  591  593  595  598  605  606  608  614  619  620  621  622  623  627  628 
##    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1 
##  630  632  634  654  658  663  664  666  674  683  686  691  693  696  697  701 
##    1    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1 
##  703  713  714  716  717  721  724  727  735  738  743  744  746  747  751  769 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  770  771  772  773  775  778  779  780  781  784  786  788  789  790  793  794 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
##  796  801  808  809  810  811  814  817  819  823  831  840  841  842  848  851 
##    1    1    1    1    1    1    0    1    1    1    1    0    1    1    1    0 
##  853  854  855  856  858  861  868  870  872  873  874  877  882  883  884  885 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  886  887  889  890  893  897  898  900  901  904  908  911  915  917  919  923 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  934  937  942  943  945  949  952  953  957  958  963  964  965  969  970  975 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  982  983  985  986  987  988  990  991  994  995 1003 1004 1011 1012 1014 1016 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1017 1021 1023 1024 1026 1027 1034 1035 1038 1042 1043 1044 1045 1047 1048 1051 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1052 1053 1063 1069 1071 1072 1073 1074 1075 1076 1077 1092 1096 1103 1104 1108 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1109 1110 1116 1119 1125 1126 1127 1131 1132 1143 1147 1150 1151 1160 1162 1168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1169 1170 1171 1173 1177 1178 1180 1181 1182 1196 1198 1199 1205 1206 1216 1218 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1220 1226 1229 1236 1237 1238 1242 1243 1245 1251 1253 1255 1256 1258 1259 1261 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1264 1265 1267 1270 1271 1275 1286 1298 1299 1305 1307 1312 1318 1322 1325 1327 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 1335 1340 1343 1347 1348 1349 1353 1356 1370 1372 1376 1380 1381 1383 1386 1389 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1395 1399 1405 1412 1413 1419 1425 1426 1427 1430 1439 1451 1453 1454 1465 1471 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    0    1    1 
## 1472 1475 1477 1478 1479 1480 1483 1491 1498 1501 1505 1506 1507 1509 1510 1511 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1519 1525 1526 1534 1535 1537 1538 1540 1542 1543 1545 1559 1560 1561 1562 1566 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1568 1573 1582 1593 1603 1604 1610 1614 1622 1623 1625 1627 1633 1635 1637 1645 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1647 1648 1652 1653 1659 1664 1665 1670 1672 1673 1688 1691 1695 1700 1702 1703 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1709 1725 1735 1738 1743 1748 1750 1755 1757 1758 1760 1761 1765 1769 1771 1772 
##    1    1    1    0    1    1    1    1    1    1    1    1    1    1    1    1 
## 1777 1781 1787 1789 1790 1798 1803 1804 1807 1808 1809 1811 1820 1821 1828 1829 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1834 1837 1838 1845 1848 1849 1855 1862 1865 1869 1870 1871 1875 1876 1878 1881 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 1883 1884 1885 1887 1890 1891 1893 1894 1895 1896 1898 1900 1901 1912 1914 1915 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1917 1918 1919 1923 1924 1926 1929 1931 1933 1936 1937 1939 1940 1942 1948 1956 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1957 1958 1961 1968 1969 1971 1972 1975 1979 1981 1985 1986 1988 1989 1990 1991 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1994 1995 2000 2001 2002 2007 2014 2016 2024 2026 2027 2028 2029 2030 2032 2039 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 2045 2047 2049 2050 2051 2055 2062 2064 2065 2068 2070 2079 2089 2091 2096 2098 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2106 2107 2111 2113 2116 2125 2127 2130 2133 2134 2136 2137 2142 2143 2148 2153 
##    1    1    1    1    1    1    1    1    1    1    1    0    1    1    1    1 
## 2155 2156 2160 2163 2164 2174 2182 2198 2205 2207 2210 2212 2214 2218 2219 2221 
##    1    1    1    1    1    1    0    0    1    1    1    1    1    0    1    1 
## 2223 2231 2233 2239 2246 2248 2250 2252 2255 2258 2259 2261 2264 2266 2269 2275 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2280 2286 2288 2293 2297 2303 2305 2308 2309 2312 2313 2319 2323 2328 2332 2333 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 2334 2337 2339 2343 2344 2346 2352 2355 2359 2368 2371 2374 2375 2376 2381 2382 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    0    1    1 
## 2383 2395 2396 2398 2401 2405 2411 2412 2418 2427 2430 2434 2435 2438 2439 2446 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2454 2456 2458 2459 2462 2466 2472 2475 2476 2478 2481 2484 2491 2495 2496 2498 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2499 2500 2501 2504 2505 2507 2510 2511 2516 2518 2519 2522 2524 2526 2530 2537 
##    1    0    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2546 2553 2564 2566 2567 2568 2573 2576 2587 2588 2589 2590 2591 2594 2595 2597 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2599 2602 2604 2606 2608 2609 2613 2617 2619 2631 2634 2635 2636 2637 2641 2642 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2644 2649 2653 2654 2660 2662 2663 2664 2669 2670 2672 2675 2676 2680 2682 2683 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2684 2685 2688 2698 2699 2704 2709 2710 2713 2717 2719 2730 2735 2740 2748 2749 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2751 2754 2762 2768 2769 2777 2784 2786 2788 2792 2799 2801 2806 2813 2814 2815 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2819 2824 2825 2828 2831 2835 2848 2852 2853 2857 2861 2864 2868 2869 2880 2888 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2889 2890 2892 2894 2900 2909 2916 2920 2927 2930 2932 2939 2942 2947 2948 2952 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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## 9170 9180 9182 9186 9187 9192 9194 9197 9199 9201 9202 9203 9205 9208 9209 9214 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9216 9217 9219 9220 9224 9229 9234 9235 9237 9238 9246 9249 9252 9253 9254 9257 
##    1    1    1    1    1    1    0    1    1    1    0    1    1    1    1    1 
## 9262 9266 9267 9271 9272 9274 9277 9279 9280 9281 9282 9283 9288 9290 9294 9305 
##    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 9318 9319 9323 9325 9328 9329 9330 9336 9338 9344 9345 9346 9351 9352 9353 9360 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9362 9363 9366 9369 9373 9377 9378 9383 9384 9386 9387 9388 9390 9393 9401 9402 
##    1    1    1    1    1    1    1    1    1    0    1    1    0    1    1    1 
## 9404 9405 9409 9413 9414 9418 9419 9425 9430 9431 9434 9435 9436 9437 9439 9442 
##    1    1    1    1    1    1    1    1    0    1    1    1    1    1    1    1 
## 9443 9446 9447 9448 9450 9452 9454 9462 9464 9465 9466 9467 9472 9473 9482 9486 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 9491 9492 9497 9504 9505 9506 9510 9516 9517 9519 9521 9530 9534 9541 9545 9548 
##    1    1    0    1    1    1    1    0    1    1    1    1    1    1    1    1 
## 9549 
##    1
#39个0,961个1
view(pred_class2_3_n)

pred_class2_n <- cbind(pred_class2_1_n, pred_class2_2_n,pred_class2_3_n)
pred_class2_n
##      pred_class2_1_n pred_class2_2_n pred_class2_3_n
## 2                  1               1               1
## 4                  1               1               1
## 8                  1               1               1
## 13                 1               1               1
## 16                 1               1               1
## 18                 1               1               1
## 29                 1               1               1
## 30                 1               1               1
## 32                 1               1               1
## 36                 1               1               1
## 39                 1               1               1
## 41                 1               1               1
## 43                 1               1               1
## 48                 1               1               1
## 49                 1               1               1
## 55                 1               1               1
## 58                 1               1               1
## 59                 1               1               1
## 60                 1               1               1
## 62                 1               1               1
## 63                 1               1               1
## 71                 1               1               1
## 73                 0               0               1
## 80                 1               1               1
## 84                 1               1               1
## 86                 1               1               1
## 87                 1               1               1
## 98                 1               1               1
## 102                1               1               1
## 104                1               1               1
## 107                0               0               1
## 109                1               1               1
## 110                1               1               1
## 113                1               1               1
## 123                1               1               1
## 125                1               1               1
## 136                1               1               1
## 137                1               1               1
## 138                1               1               0
## 143                1               1               1
## 145                1               1               1
## 147                1               1               0
## 149                1               1               1
## 151                1               1               1
## 153                1               1               1
## 160                1               1               1
## 162                1               1               1
## 165                0               0               1
## 167                1               1               1
## 168                1               1               1
## 171                1               1               1
## 175                1               1               1
## 177                1               1               1
## 184                1               1               1
## 187                1               1               1
## 188                1               1               1
## 198                1               1               1
## 199                1               1               1
## 205                0               1               1
## 206                1               1               1
## 214                1               1               1
## 217                1               1               1
## 220                1               1               1
## 221                1               1               1
## 225                1               1               1
## 227                1               1               1
## 230                1               1               1
## 231                1               1               1
## 242                0               0               1
## 249                1               1               1
## 251                1               1               1
## 253                1               1               1
## 261                1               1               1
## 262                1               1               1
## 281                1               1               1
## 283                1               1               1
## 284                1               1               1
## 286                1               1               1
## 292                1               1               1
## 294                1               1               1
## 295                1               1               1
## 296                1               1               1
## 300                1               1               0
## 302                1               1               1
## 303                1               1               1
## 306                1               1               1
## 308                1               1               1
## 309                1               1               1
## 314                1               1               1
## 316                1               1               1
## 318                1               1               1
## 321                1               1               1
## 322                1               1               1
## 329                1               1               1
## 332                1               1               1
## 333                1               1               1
## 340                1               1               1
## 350                1               1               1
## 351                1               1               1
## 354                1               1               1
## 366                1               1               1
## 368                1               1               1
## 371                1               1               1
## 374                1               1               1
## 378                1               1               1
## 382                1               1               1
## 387                1               1               1
## 391                1               1               1
## 393                1               1               1
## 394                1               1               1
## 396                1               1               1
## 399                1               1               1
## 402                1               1               1
## 408                1               1               1
## 412                1               1               1
## 413                1               1               1
## 414                1               1               1
## 416                1               1               1
## 417                1               1               1
## 421                1               1               1
## 423                1               1               1
## 426                1               1               1
## 429                1               1               1
## 430                1               1               1
## 437                1               1               1
## 441                1               1               1
## 444                1               1               1
## 450                1               1               1
## 456                1               1               1
## 460                1               1               1
## 462                1               1               1
## 463                1               1               1
## 465                1               1               0
## 469                1               1               1
## 473                1               1               1
## 481                1               1               1
## 484                1               1               1
## 487                1               1               1
## 493                1               1               1
## 500                1               1               1
## 507                1               1               1
## 525                1               1               1
## 527                1               1               1
## 532                1               1               1
## 535                1               1               1
## 537                1               1               1
## 538                1               1               1
## 541                1               1               1
## 544                1               1               1
## 549                0               0               1
## 552                1               1               0
## 553                1               1               1
## 555                1               1               1
## 558                1               1               1
## 559                1               1               1
## 562                1               1               1
## 566                1               1               1
## 571                1               1               1
## 573                1               1               1
## 582                1               1               1
## 588                1               1               1
## 591                1               1               1
## 593                1               1               1
## 595                1               1               1
## 598                1               1               1
## 605                1               1               1
## 606                1               1               1
## 608                1               1               1
## 614                1               1               1
## 619                1               1               1
## 620                1               1               1
## 621                1               1               1
## 622                1               1               0
## 623                1               1               1
## 627                1               1               1
## 628                1               1               1
## 630                1               1               1
## 632                1               1               1
## 634                1               1               1
## 654                1               1               1
## 658                1               1               1
## 663                1               1               1
## 664                1               1               1
## 666                1               1               1
## 674                1               1               1
## 683                1               1               0
## 686                1               1               1
## 691                1               1               1
## 693                1               1               1
## 696                1               1               1
## 697                0               0               1
## 701                1               1               1
## 703                1               1               1
## 713                1               1               1
## 714                0               1               1
## 716                0               0               1
## 717                1               1               1
## 721                1               1               1
## 724                1               1               1
## 727                1               1               1
## 735                1               1               1
## 738                1               1               1
## 743                0               0               1
## 744                1               1               1
## 746                1               1               1
## 747                1               1               1
## 751                1               1               1
## 769                1               1               1
## 770                1               1               1
## 771                1               1               1
## 772                1               1               1
## 773                1               1               1
## 775                1               1               1
## 778                1               1               1
## 779                1               1               1
## 780                1               1               1
## 781                1               1               1
## 784                1               1               1
## 786                1               1               1
## 788                1               1               1
## 789                1               1               1
## 790                1               1               0
## 793                1               1               1
## 794                1               1               1
## 796                1               1               1
## 801                1               1               1
## 808                0               0               1
## 809                1               1               1
## 810                1               1               1
## 811                1               1               1
## 814                1               1               0
## 817                1               1               1
## 819                1               1               1
## 823                1               1               1
## 831                1               1               1
## 840                1               1               0
## 841                1               1               1
## 842                1               1               1
## 848                1               1               1
## 851                1               1               0
## 853                1               1               1
## 854                1               1               1
## 855                1               1               1
## 856                1               1               1
## 858                1               1               1
## 861                1               1               1
## 868                1               1               1
## 870                1               1               1
## 872                1               1               1
## 873                1               1               1
## 874                1               1               1
## 877                1               1               1
## 882                1               1               1
## 883                1               1               1
## 884                1               1               1
## 885                1               1               1
## 886                1               1               1
## 887                1               1               1
## 889                1               1               1
## 890                1               1               1
## 893                1               1               1
## 897                1               1               1
## 898                1               1               1
## 900                1               1               1
## 901                1               1               1
## 904                0               1               1
## 908                1               1               1
## 911                1               1               1
## 915                1               1               1
## 917                1               1               1
## 919                1               1               1
## 923                1               1               1
## 934                1               1               1
## 937                1               1               1
## 942                1               1               1
## 943                1               1               1
## 945                1               1               1
## 949                1               1               1
## 952                1               1               1
## 953                1               1               1
## 957                1               1               1
## 958                0               0               1
## 963                1               1               1
## 964                1               1               1
## 965                1               1               1
## 969                1               1               1
## 970                1               1               1
## 975                1               1               1
## 982                1               1               1
## 983                1               1               1
## 985                1               1               1
## 986                1               1               1
## 987                1               1               1
## 988                1               1               1
## 990                1               1               1
## 991                0               0               1
## 994                1               1               1
## 995                1               1               1
## 1003               1               1               1
## 1004               1               1               1
## 1011               1               1               1
## 1012               1               1               1
## 1014               1               1               1
## 1016               1               1               1
## 1017               1               1               1
## 1021               1               1               1
## 1023               1               1               1
## 1024               1               1               1
## 1026               1               1               1
## 1027               1               1               1
## 1034               1               1               1
## 1035               1               1               1
## 1038               1               1               1
## 1042               1               1               1
## 1043               1               1               1
## 1044               1               1               1
## 1045               1               1               1
## 1047               1               1               1
## 1048               1               1               1
## 1051               1               1               1
## 1052               1               1               1
## 1053               1               1               1
## 1063               1               1               1
## 1069               1               1               1
## 1071               1               1               1
## 1072               1               1               1
## 1073               1               1               1
## 1074               1               1               1
## 1075               1               1               1
## 1076               1               1               1
## 1077               1               1               1
## 1092               1               1               1
## 1096               1               1               1
## 1103               1               1               1
## 1104               1               1               1
## 1108               1               1               1
## 1109               1               1               1
## 1110               1               1               1
## 1116               1               1               1
## 1119               1               1               1
## 1125               1               1               1
## 1126               1               1               1
## 1127               1               1               1
## 1131               1               1               1
## 1132               1               1               1
## 1143               1               1               1
## 1147               1               1               1
## 1150               1               1               1
## 1151               1               1               1
## 1160               1               1               1
## 1162               1               1               1
## 1168               0               0               1
## 1169               1               1               1
## 1170               1               1               1
## 1171               1               1               1
## 1173               1               1               1
## 1177               1               1               1
## 1178               1               1               1
## 1180               1               1               1
## 1181               1               1               1
## 1182               0               0               1
## 1196               1               1               1
## 1198               1               1               1
## 1199               1               1               1
## 1205               0               0               1
## 1206               1               1               1
## 1216               1               1               1
## 1218               1               1               1
## 1220               1               1               1
## 1226               1               1               1
## 1229               1               1               1
## 1236               0               0               1
## 1237               1               1               1
## 1238               1               1               1
## 1242               0               0               1
## 1243               1               1               1
## 1245               1               1               1
## 1251               1               1               1
## 1253               1               1               1
## 1255               1               1               1
## 1256               1               1               1
## 1258               1               1               1
## 1259               1               1               1
## 1261               1               1               1
## 1264               1               1               1
## 1265               1               1               1
## 1267               0               0               1
## 1270               1               1               1
## 1271               1               1               1
## 1275               1               1               1
## 1286               1               1               1
## 1298               1               1               1
## 1299               1               1               1
## 1305               1               1               1
## 1307               1               1               1
## 1312               1               1               1
## 1318               1               1               1
## 1322               1               1               0
## 1325               1               1               1
## 1327               1               1               1
## 1335               1               1               1
## 1340               1               1               1
## 1343               1               1               1
## 1347               1               1               1
## 1348               1               1               1
## 1349               1               1               1
## 1353               1               1               1
## 1356               0               0               1
## 1370               1               1               1
## 1372               1               1               1
## 1376               1               1               1
## 1380               1               1               1
## 1381               1               1               1
## 1383               1               1               1
## 1386               1               1               1
## 1389               1               1               1
## 1395               1               1               1
## 1399               1               1               1
## 1405               1               1               1
## 1412               0               0               1
## 1413               1               1               1
## 1419               1               1               1
## 1425               1               1               1
## 1426               1               1               1
## 1427               1               1               1
## 1430               1               1               1
## 1439               1               1               1
## 1451               1               1               1
## 1453               1               1               1
## 1454               1               1               0
## 1465               1               1               1
## 1471               1               1               1
## 1472               1               1               1
## 1475               0               0               1
## 1477               1               1               1
## 1478               1               1               1
## 1479               1               1               1
## 1480               1               1               1
## 1483               1               1               1
## 1491               1               1               1
## 1498               1               1               1
## 1501               1               1               1
## 1505               1               1               1
## 1506               1               1               1
## 1507               1               1               1
## 1509               1               1               1
## 1510               1               1               1
## 1511               1               1               1
## 1519               1               1               1
## 1525               1               1               1
## 1526               1               1               1
## 1534               1               1               1
## 1535               1               1               1
## 1537               1               1               1
## 1538               1               1               1
## 1540               1               1               1
## 1542               1               1               0
## 1543               1               1               1
## 1545               1               1               1
## 1559               1               1               1
## 1560               1               1               1
## 1561               1               1               1
## 1562               1               1               1
## 1566               1               1               1
## 1568               0               0               1
## 1573               1               1               1
## 1582               1               1               1
## 1593               1               1               1
## 1603               1               1               1
## 1604               1               1               1
## 1610               1               1               1
## 1614               1               1               1
## 1622               1               1               1
## 1623               1               1               1
## 1625               1               1               1
## 1627               1               1               1
## 1633               1               1               1
## 1635               1               1               1
## 1637               0               1               1
## 1645               1               1               1
## 1647               1               1               1
## 1648               1               1               1
## 1652               1               1               1
## 1653               1               1               1
## 1659               1               1               1
## 1664               1               1               1
## 1665               1               1               1
## 1670               1               1               1
## 1672               1               1               0
## 1673               1               1               1
## 1688               1               1               1
## 1691               1               1               1
## 1695               1               1               1
## 1700               1               1               1
## 1702               1               1               1
## 1703               1               1               1
## 1709               1               1               1
## 1725               1               1               1
## 1735               1               1               1
## 1738               1               1               0
## 1743               1               1               1
## 1748               1               1               1
## 1750               1               1               1
## 1755               1               1               1
## 1757               1               1               1
## 1758               1               1               1
## 1760               1               1               1
## 1761               1               1               1
## 1765               1               1               1
## 1769               1               1               1
## 1771               1               1               1
## 1772               1               1               1
## 1777               1               1               1
## 1781               1               1               1
## 1787               1               1               1
## 1789               1               1               1
## 1790               1               1               1
## 1798               1               1               1
## 1803               1               1               1
## 1804               1               1               1
## 1807               1               1               1
## 1808               1               1               1
## 1809               1               1               1
## 1811               1               1               1
## 1820               1               1               1
## 1821               1               1               1
## 1828               1               1               1
## 1829               1               1               1
## 1834               1               1               1
## 1837               1               1               1
## 1838               1               1               1
## 1845               0               1               1
## 1848               1               1               1
## 1849               1               1               1
## 1855               1               1               1
## 1862               1               1               1
## 1865               1               1               0
## 1869               1               1               1
## 1870               1               1               1
## 1871               1               1               1
## 1875               1               1               1
## 1876               1               1               1
## 1878               1               1               1
## 1881               1               1               1
## 1883               1               1               1
## 1884               1               1               1
## 1885               1               1               1
## 1887               1               1               1
## 1890               1               1               1
## 1891               1               1               1
## 1893               1               1               1
## 1894               1               1               1
## 1895               1               1               1
## 1896               1               1               1
## 1898               1               1               1
## 1900               1               1               1
## 1901               1               1               1
## 1912               1               1               1
## 1914               1               1               1
## 1915               1               1               1
## 1917               1               1               1
## 1918               1               1               1
## 1919               1               1               1
## 1923               1               1               1
## 1924               1               1               1
## 1926               1               1               1
## 1929               1               1               1
## 1931               1               1               1
## 1933               1               1               1
## 1936               1               1               1
## 1937               1               1               1
## 1939               1               1               1
## 1940               1               1               1
## 1942               1               1               1
## 1948               1               1               1
## 1956               1               1               1
## 1957               1               1               1
## 1958               1               1               1
## 1961               1               1               1
## 1968               1               1               1
## 1969               1               1               1
## 1971               0               0               1
## 1972               1               1               1
## 1975               1               1               1
## 1979               1               1               1
## 1981               1               1               1
## 1985               1               1               1
## 1986               1               1               1
## 1988               1               1               1
## 1989               1               1               1
## 1990               0               0               1
## 1991               1               1               1
## 1994               1               1               1
## 1995               0               0               1
## 2000               1               1               1
## 2001               1               1               1
## 2002               1               1               1
## 2007               1               1               1
## 2014               1               1               1
## 2016               1               1               1
## 2024               1               1               0
## 2026               1               1               1
## 2027               1               1               1
## 2028               1               1               1
## 2029               1               1               1
## 2030               1               1               1
## 2032               1               1               1
## 2039               1               1               1
## 2045               1               1               1
## 2047               1               1               1
## 2049               1               1               1
## 2050               1               1               1
## 2051               1               1               1
## 2055               1               1               1
## 2062               1               1               1
## 2064               1               1               1
## 2065               1               1               1
## 2068               1               1               1
## 2070               1               1               1
## 2079               1               1               1
## 2089               1               1               1
## 2091               0               0               1
## 2096               1               1               1
## 2098               1               1               1
## 2106               1               1               1
## 2107               1               1               1
## 2111               1               1               1
## 2113               1               1               1
## 2116               1               1               1
## 2125               1               1               1
## 2127               1               1               1
## 2130               1               1               1
## 2133               1               1               1
## 2134               1               1               1
## 2136               1               1               1
## 2137               1               1               0
## 2142               1               1               1
## 2143               1               1               1
## 2148               0               0               1
## 2153               1               1               1
## 2155               1               1               1
## 2156               0               0               1
## 2160               1               1               1
## 2163               1               1               1
## 2164               1               1               1
## 2174               1               1               1
## 2182               1               1               0
## 2198               1               1               0
## 2205               1               1               1
## 2207               1               1               1
## 2210               1               1               1
## 2212               1               1               1
## 2214               1               1               1
## 2218               1               1               0
## 2219               1               1               1
## 2221               1               1               1
## 2223               1               1               1
## 2231               1               1               1
## 2233               1               1               1
## 2239               1               1               1
## 2246               1               1               1
## 2248               1               1               1
## 2250               1               1               1
## 2252               1               1               1
## 2255               1               1               1
## 2258               1               1               1
## 2259               1               1               1
## 2261               1               1               1
## 2264               1               1               1
## 2266               1               1               1
## 2269               1               1               1
## 2275               1               1               1
## 2280               1               1               1
## 2286               1               1               1
## 2288               1               1               1
## 2293               1               1               1
## 2297               1               1               1
## 2303               1               1               1
## 2305               1               1               1
## 2308               1               1               0
## 2309               1               1               1
## 2312               1               1               1
## 2313               1               1               1
## 2319               1               1               1
## 2323               1               1               1
## 2328               1               1               1
## 2332               1               1               1
## 2333               1               1               1
## 2334               0               1               1
## 2337               1               1               1
## 2339               1               1               1
## 2343               1               1               1
## 2344               1               1               1
## 2346               1               1               1
## 2352               1               1               1
## 2355               1               1               1
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## 9549               1               1               1
#15个0,985个1
view(pred_class2_n)


#💙10_1_1 Calculate Accuracy of prediction
accuracy1_n <- mean(pred_class1_n == test_data_n$legacy_collision_severity)
accuracy1_n 
## [1] 0.009773124
print(paste("Accuracy:", accuracy1_n))
## [1] "Accuracy: 0.00977312390924956"
accuracy2_n <- mean(pred_class2_n == test_data_n$legacy_collision_severity)
accuracy2_n 
## [1] 0.009889471
print(paste("Accuracy:", accuracy2_f))
## [1] "Accuracy: 0.00965677719604421"
#💙10_1_2 AUC: compare predicted results with actual categories

#table(Predicted = pred_class1, Actual = test_data$legacy_collision_severity)
library(pROC)
#plot a ROC curve with True Positive Rate (TPR) as the y axis and False Positive Rate (FPR) as x axis.

#MNL best model on train data
roc_curve1_1_n <- roc(test_data_n$legacy_collision_severity==1, predictions1_n[, 1])     #原本没有  ==1
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve1_1_n)

roc_curve1_2_n <- roc(test_data_n$legacy_collision_severity==2, predictions1_n[, 2])  
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve1_2_n)

roc_curve1_3_n <- roc(test_data_n$legacy_collision_severity==3, predictions1_n[, 3])
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve1_3_n)

#P.S. The closer the curve is to the upper left corner, the better the model performance is.
auc(roc_curve1_1_n) ## Area under the curve: 0.9286
## Area under the curve: 0.6246
auc(roc_curve1_2_n)
## Area under the curve: 0.61
auc(roc_curve1_3_n)
## Area under the curve: 0.614
#P.S. The AUC value is between 0 and 1. The closer the value is to 1, the better the model performance. 0.5 means the model performance is equivalent to random guessing.
roc_curve2_1_n <- roc(test_data_n$legacy_collision_severity==1, predictions2_n[, 1])  #==1
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve2_1_n)

roc_curve2_2_n <- roc(test_data_n$legacy_collision_severity==2, predictions2_n[, 2])
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve2_2_n)

roc_curve2_3_n <- roc(test_data_n$legacy_collision_severity==3, predictions2_n[, 3])
## Setting levels: control = FALSE, case = TRUE
## Setting direction: controls < cases
plot(roc_curve2_3_n)

#P.S. The closer the curve is to the upper left corner, the better the model performance is.
auc(roc_curve2_1_n) ## Area under the curve: 0.9286
## Area under the curve: 0.637
auc(roc_curve2_2_n)
## Area under the curve: 0.6108
auc(roc_curve2_3_n)
## Area under the curve: 0.6152
####


# 💚12 ICC
# 加载必要的包
library(MASS)  # for polr function
library(psych) # for ICC calculation, optional
## Warning: package 'psych' was built under R version 4.3.3
## 
## Attaching package: 'psych'
## The following object is masked from 'package:Hmisc':
## 
##     describe
## The following object is masked from 'package:car':
## 
##     logit
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
# 假设已拟合的 Ordered Logit 模型
# step_test2_ <- polr(legacy_collision_severity ~ ., data = train_data, Hess = TRUE)

# Step 1: 计算模型拟合值
fitted_values <- fitted(step_test2_)  # 模型的拟合概率
library(fpp3)
view(fitted_values)
Var_u <- var(qlogis(fitted_values[,1]))  # 将拟合值转化到Logit标度后计算方差

# Step 3: 误差项方差
Var_e <- pi^2 / 3  # Logit模型的误差项方差

# Step 4: 计算ICC
ICC <- Var_u / (Var_u + Var_e)
ICC
## [1] 0.1248242
cat("Intraclass Correlation Coefficient (ICC):", ICC, "\n")
## Intraclass Correlation Coefficient (ICC): 0.1248242
Var_u <- var(qlogis(fitted_values[,2]))  # 将拟合值转化到Logit标度后计算方差

# Step 3: 误差项方差
Var_e <- pi^2 / 3  # Logit模型的误差项方差

# Step 4: 计算ICC
ICC <- Var_u / (Var_u + Var_e)
ICC
## [1] 0.1124318
Var_u <- var(qlogis(fitted_values[,3]))  # 将拟合值转化到Logit标度后计算方差

# Step 3: 误差项方差
Var_e <- pi^2 / 3  # Logit模型的误差项方差

# Step 4: 计算ICC
ICC <- Var_u / (Var_u + Var_e)
ICC
## [1] 0.1248242