# Library
library(tidyverse)
library(dplyr)
library(janitor) #clean_names()
bi <- read_csv("bioimplants.csv")glimpse(bi)## Rows: 1,470
## Columns: 29
## $ age <dbl> 41, 49, 37, 33, 27, 32, 59, 30, 38, 36, 35,…
## $ business_travel <chr> "Travel_Rarely", "Travel_Frequently", "Trav…
## $ department <chr> "Sales", "Research & Development", "Researc…
## $ distance_from_home <dbl> 1, 8, 2, 3, 2, 2, 3, 24, 23, 27, 16, 15, 26…
## $ education <dbl> 2, 1, 2, 4, 1, 2, 3, 1, 3, 3, 3, 2, 1, 2, 3…
## $ education_field <chr> "Life Sciences", "Life Sciences", "Other", …
## $ environment_satisfaction <dbl> 2, 3, 4, 4, 1, 4, 3, 4, 4, 3, 1, 4, 1, 2, 3…
## $ gender <chr> "Female", "Male", "Male", "Female", "Male",…
## $ job_involvement <dbl> 3, 2, 2, 3, 3, 3, 4, 3, 2, 3, 4, 2, 3, 3, 2…
## $ job_level <dbl> 2, 2, 1, 1, 1, 1, 1, 1, 3, 2, 1, 2, 1, 1, 1…
## $ job_role <chr> "Sales Executive", "Research Scientist", "L…
## $ job_satisfaction <dbl> 4, 2, 3, 3, 2, 4, 1, 3, 3, 3, 2, 3, 3, 4, 3…
## $ marital_status <chr> "Single", "Married", "Single", "Married", "…
## $ monthly_income <dbl> 5993, 5130, 2090, 2909, 3468, 3068, 2670, 2…
## $ num_companies_worked <dbl> 8, 1, 6, 1, 9, 0, 4, 1, 0, 6, 0, 0, 1, 0, 5…
## $ over_time <chr> "Yes", "No", "Yes", "Yes", "No", "No", "Yes…
## $ percent_salary_hike <dbl> 11, 23, 15, 11, 12, 13, 20, 22, 21, 13, 13,…
## $ performance_rating <dbl> 3, 4, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3…
## $ relationship_satisfaction <dbl> 1, 4, 2, 3, 4, 3, 1, 2, 2, 2, 3, 4, 4, 3, 2…
## $ stock_option_level <dbl> 0, 1, 0, 0, 1, 0, 3, 1, 0, 2, 1, 0, 1, 1, 0…
## $ total_working_years <dbl> 8, 10, 7, 8, 6, 8, 12, 1, 10, 17, 6, 10, 5,…
## $ training_times_last_year <dbl> 0, 3, 3, 3, 3, 2, 3, 2, 2, 3, 5, 3, 1, 2, 4…
## $ work_life_balance <dbl> 1, 3, 3, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3…
## $ years_at_company <dbl> 6, 10, 0, 8, 2, 7, 1, 1, 9, 7, 5, 9, 5, 2, …
## $ years_in_current_role <dbl> 4, 7, 0, 7, 2, 7, 0, 0, 7, 7, 4, 5, 2, 2, 2…
## $ years_since_last_promotion <dbl> 0, 1, 0, 3, 2, 3, 0, 0, 1, 7, 0, 0, 4, 1, 0…
## $ years_with_curr_manager <dbl> 5, 7, 0, 0, 2, 6, 0, 0, 8, 7, 3, 8, 3, 2, 3…
## $ attrition <chr> "Yes", "No", "Yes", "No", "No", "No", "No",…
## $ employee_number <dbl> 1, 2, 4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 1…# Cleaning
bi <- bi %>%
clean_names() %>%
na.omit %>%
mutate(attrition = factor(attrition, levels = c("Yes", "No"))) %>%
select(-employee_number)
summary(bi)## age business_travel department distance_from_home
## Min. :18.00 Length:1470 Length:1470 Min. : 1.000
## 1st Qu.:30.00 Class :character Class :character 1st Qu.: 2.000
## Median :36.00 Mode :character Mode :character Median : 7.000
## Mean :36.92 Mean : 9.193
## 3rd Qu.:43.00 3rd Qu.:14.000
## Max. :60.00 Max. :29.000
## education education_field environment_satisfaction gender
## Min. :1.000 Length:1470 Min. :1.000 Length:1470
## 1st Qu.:2.000 Class :character 1st Qu.:2.000 Class :character
## Median :3.000 Mode :character Median :3.000 Mode :character
## Mean :2.913 Mean :2.722
## 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :4.000
## job_involvement job_level job_role job_satisfaction
## Min. :1.00 Min. :1.000 Length:1470 Min. :1.000
## 1st Qu.:2.00 1st Qu.:1.000 Class :character 1st Qu.:2.000
## Median :3.00 Median :2.000 Mode :character Median :3.000
## Mean :2.73 Mean :2.064 Mean :2.729
## 3rd Qu.:3.00 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :4.00 Max. :5.000 Max. :4.000
## marital_status monthly_income num_companies_worked over_time
## Length:1470 Min. : 1009 Min. :0.000 Length:1470
## Class :character 1st Qu.: 2911 1st Qu.:1.000 Class :character
## Mode :character Median : 4919 Median :2.000 Mode :character
## Mean : 6503 Mean :2.693
## 3rd Qu.: 8379 3rd Qu.:4.000
## Max. :19999 Max. :9.000
## percent_salary_hike performance_rating relationship_satisfaction
## Min. :11.00 Min. :3.000 Min. :1.000
## 1st Qu.:12.00 1st Qu.:3.000 1st Qu.:2.000
## Median :14.00 Median :3.000 Median :3.000
## Mean :15.21 Mean :3.154 Mean :2.712
## 3rd Qu.:18.00 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :25.00 Max. :4.000 Max. :4.000
## stock_option_level total_working_years training_times_last_year
## Min. :0.0000 Min. : 0.00 Min. :0.000
## 1st Qu.:0.0000 1st Qu.: 6.00 1st Qu.:2.000
## Median :1.0000 Median :10.00 Median :3.000
## Mean :0.7939 Mean :11.28 Mean :2.799
## 3rd Qu.:1.0000 3rd Qu.:15.00 3rd Qu.:3.000
## Max. :3.0000 Max. :40.00 Max. :6.000
## work_life_balance years_at_company years_in_current_role
## Min. :1.000 Min. : 0.000 Min. : 0.000
## 1st Qu.:2.000 1st Qu.: 3.000 1st Qu.: 2.000
## Median :3.000 Median : 5.000 Median : 3.000
## Mean :2.761 Mean : 7.008 Mean : 4.229
## 3rd Qu.:3.000 3rd Qu.: 9.000 3rd Qu.: 7.000
## Max. :4.000 Max. :40.000 Max. :18.000
## years_since_last_promotion years_with_curr_manager attrition
## Min. : 0.000 Min. : 0.000 Yes: 237
## 1st Qu.: 0.000 1st Qu.: 2.000 No :1233
## Median : 1.000 Median : 3.000
## Mean : 2.188 Mean : 4.123
## 3rd Qu.: 3.000 3rd Qu.: 7.000
## Max. :15.000 Max. :17.000What is the attrition rate for employees at BI? (A rate, remember, is expressed as a proportion.)
Calculate overall attrition rate.
Create a summary table of conditional attrition rates by department and job role. (The table should have 3 columns: department, job role, and the calculated conditional attrition rate.) Sort this table by attrition rate in descending order.
Note: The simplest possible classification model would be to use the attrition majority class—“Yes” or “No”—as the prediction. This is called “majority class” prediction. The in-sample accuracy of the majority class model is simply the proportion of the majority class. This is an important performance benchmark.
# Overall Attrition Rate
bi %>%
dplyr::summarize(attrition= mean(attrition=="Yes")) ## # A tibble: 1 × 1
## attrition
## <dbl>
## 1 0.161# By Department & Job Role
bi %>%
group_by(department, job_role) %>%
dplyr::summarize(attrition = mean(attrition=="Yes")) %>%
arrange(desc(attrition))## `summarise()` has grouped output by 'department'. You can override using the
## `.groups` argument.## # A tibble: 11 × 3
## # Groups: department [3]
## department job_role attrition
## <chr> <chr> <dbl>
## 1 Sales Sales Representative 0.398
## 2 Research & Development Laboratory Technician 0.239
## 3 Human Resources Human Resources 0.231
## 4 Sales Sales Executive 0.175
## 5 Research & Development Research Scientist 0.161
## 6 Research & Development Manufacturing Director 0.0690
## 7 Research & Development Healthcare Representative 0.0687
## 8 Research & Development Manager 0.0556
## 9 Sales Manager 0.0541
## 10 Research & Development Research Director 0.025
## 11 Human Resources Manager 0The attrition rate for employees at BI is 0.161 * 100% = 16.1%.
Fit a logistic regression model of attrition using all the predictors. (Note: employee_number is NOT a predictor!)
Report accuracy for this model with a decision threshold of .5. (Accuracy is defined as the proportion of correct predictions.)
Comment on whether the model offers an improvement over predicting with the majority class.
# Logistic Regression Model
logistic_mod <- glm(ifelse(attrition=="Yes", 1, 0) ~., # Change attrition to 0/1 on the fly
data = bi,
family = binomial)
options(scipen = 999)
summary(logistic_mod)##
## Call:
## glm(formula = ifelse(attrition == "Yes", 1, 0) ~ ., family = binomial,
## data = bi)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6316 -0.4902 -0.2510 -0.0909 3.4150
##
## Coefficients:
## Estimate Std. Error z value
## (Intercept) -10.595163985 383.607521446 -0.028
## age -0.031325746 0.013517203 -2.317
## business_travelTravel_Frequently 1.924530910 0.410150606 4.692
## business_travelTravel_Rarely 1.040657620 0.378117017 2.752
## departmentResearch & Development 12.785729260 383.604840875 0.033
## departmentSales 12.609731506 383.605081734 0.033
## distance_from_home 0.045841049 0.010733370 4.271
## education 0.003183545 0.087453001 0.036
## education_fieldLife Sciences -0.791011425 0.802979460 -0.985
## education_fieldMarketing -0.366640754 0.852249819 -0.430
## education_fieldMedical -0.893865820 0.802537940 -1.114
## education_fieldOther -0.871595611 0.861374836 -1.012
## education_fieldTechnical Degree 0.118235221 0.820727466 0.144
## environment_satisfaction -0.433428942 0.082682709 -5.242
## genderMale 0.387912250 0.183925890 2.109
## job_involvement -0.531195400 0.122174410 -4.348
## job_level -0.075918365 0.314728569 -0.241
## job_roleHuman Resources 14.021954445 383.605141684 0.037
## job_roleLaboratory Technician 1.491851833 0.483310026 3.087
## job_roleManager 0.390921742 0.886737765 0.441
## job_roleManufacturing Director 0.258357628 0.530052955 0.487
## job_roleResearch Director -1.051263651 1.001808709 -1.049
## job_roleResearch Scientist 0.553465173 0.494259238 1.120
## job_roleSales Executive 1.202226483 1.125590277 1.068
## job_roleSales Representative 2.144367279 1.180374099 1.817
## job_satisfaction -0.418436234 0.081181836 -5.154
## marital_statusMarried 0.321256876 0.265686125 1.209
## marital_statusSingle 1.159553172 0.343850974 3.372
## monthly_income 0.000008216 0.000081165 0.101
## num_companies_worked 0.193460215 0.038677352 5.002
## over_timeYes 1.970112072 0.192943818 10.211
## percent_salary_hike -0.021921266 0.039074163 -0.561
## performance_rating 0.106838125 0.396596302 0.269
## relationship_satisfaction -0.257087401 0.082397826 -3.120
## stock_option_level -0.208707036 0.156756429 -1.331
## total_working_years -0.061305541 0.029397140 -2.085
## training_times_last_year -0.191816832 0.073038159 -2.626
## work_life_balance -0.363296200 0.123437047 -2.943
## years_at_company 0.094425163 0.038918533 2.426
## years_in_current_role -0.151758830 0.045212964 -3.357
## years_since_last_promotion 0.178028761 0.042052096 4.234
## years_with_curr_manager -0.134569886 0.047072284 -2.859
## Pr(>|z|)
## (Intercept) 0.977965
## age 0.020478 *
## business_travelTravel_Frequently 0.000002702 ***
## business_travelTravel_Rarely 0.005919 **
## departmentResearch & Development 0.973411
## departmentSales 0.973777
## distance_from_home 0.000019469 ***
## education 0.970961
## education_fieldLife Sciences 0.324577
## education_fieldMarketing 0.667048
## education_fieldMedical 0.265365
## education_fieldOther 0.311602
## education_fieldTechnical Degree 0.885452
## environment_satisfaction 0.000000159 ***
## genderMale 0.034939 *
## job_involvement 0.000013748 ***
## job_level 0.809386
## job_roleHuman Resources 0.970841
## job_roleLaboratory Technician 0.002024 **
## job_roleManager 0.659319
## job_roleManufacturing Director 0.625962
## job_roleResearch Director 0.294010
## job_roleResearch Scientist 0.262804
## job_roleSales Executive 0.285482
## job_roleSales Representative 0.069265 .
## job_satisfaction 0.000000255 ***
## marital_statusMarried 0.226602
## marital_statusSingle 0.000746 ***
## monthly_income 0.919373
## num_companies_worked 0.000000568 ***
## over_timeYes < 0.0000000000000002 ***
## percent_salary_hike 0.574786
## performance_rating 0.787631
## relationship_satisfaction 0.001808 **
## stock_option_level 0.183054
## total_working_years 0.037031 *
## training_times_last_year 0.008633 **
## work_life_balance 0.003249 **
## years_at_company 0.015257 *
## years_in_current_role 0.000789 ***
## years_since_last_promotion 0.000023005 ***
## years_with_curr_manager 0.004253 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1298.58 on 1469 degrees of freedom
## Residual deviance: 860.85 on 1428 degrees of freedom
## AIC: 944.85
##
## Number of Fisher Scoring iterations: 14# Accuracy
predict(logistic_mod, type = "response") # fitted values## 1 2 3 4
## 0.71708957002403 0.01524084428143 0.67736633212300 0.14476906966888
## 5 6 7 8
## 0.34904441016077 0.06889457725727 0.17627684803867 0.10178274126257
## 9 10 11 12
## 0.05010436424418 0.03666481088564 0.04046770086193 0.17417104728163
## 13 14 15 16
## 0.17186723508239 0.05104478754284 0.87183032935166 0.03029192124492
## 17 18 19 20
## 0.05885657642085 0.10279836243666 0.00566554306193 0.18368775996796
## 21 22 23 24
## 0.00234973241178 0.58193475616544 0.00439131140518 0.04236303935068
## 25 26 27 28
## 0.15453536211175 0.00064990240558 0.93153307832655 0.04005926258936
## 29 30 31 32
## 0.00272784220745 0.05007066669905 0.07545174559293 0.00910797010793
## 33 34 35 36
## 0.13036140474860 0.01548717539666 0.41099768771624 0.00118805264168
## 37 38 39 40
## 0.68434795071582 0.06036015938048 0.51690472039344 0.04193650969095
## 41 42 43 44
## 0.02518362977749 0.02130105958614 0.85955569688758 0.05100652362651
## 45 46 47 48
## 0.03518840971371 0.01940689341406 0.15109002351040 0.24578290624669
## 49 50 51 52
## 0.35546723336936 0.01505868433510 0.73550692295084 0.82232929570037
## 53 54 55 56
## 0.38877752868057 0.11472889520370 0.73581726102800 0.04664208262022
## 57 58 59 60
## 0.07994705392881 0.59623500265479 0.00541165706657 0.00647014623725
## 61 62 63 64
## 0.07798573397571 0.27594250136532 0.23841723515750 0.15438732551080
## 65 66 67 68
## 0.01012467816002 0.00690832551039 0.17946607395501 0.01363606068797
## 69 70 71 72
## 0.19004733302648 0.37572780831780 0.20074112272981 0.00732522553820
## 73 74 75 76
## 0.08084066935030 0.01010248509042 0.04479072612374 0.00450346053061
## 77 78 79 80
## 0.06128186240044 0.02195728936669 0.01893821251327 0.25438419074209
## 81 82 83 84
## 0.25655890882103 0.06982762786816 0.00644115257337 0.00909764098575
## 85 86 87 88
## 0.04263931808799 0.01026831032653 0.37699011942852 0.00801194752943
## 89 90 91 92
## 0.00862928358199 0.01847900202812 0.09951391246773 0.41747004383932
## 93 94 95 96
## 0.07284031003233 0.19324919662244 0.14471510702827 0.02149443027499
## 97 98 99 100
## 0.08035577547248 0.00798328215333 0.01609306844855 0.02712114187114
## 101 102 103 104
## 0.47245796229005 0.07948376945794 0.70042998233010 0.00848094454474
## 105 106 107 108
## 0.00156218796140 0.00000000647886 0.04350451142452 0.57251698951159
## 109 110 111 112
## 0.02217718838497 0.13168492625584 0.21366699918998 0.75145160143350
## 113 114 115 116
## 0.00000007034424 0.13132765374095 0.03797597967130 0.04089613815365
## 117 118 119 120
## 0.01477167921962 0.01676732560995 0.10277132641684 0.02227507884574
## 121 122 123 124
## 0.09433034827340 0.01221876031571 0.47690468558608 0.00732012621835
## 125 126 127 128
## 0.68106666268347 0.06535072594534 0.02077009077904 0.88905791053164
## 129 130 131 132
## 0.11590007180234 0.00998118737875 0.09203685793932 0.07539233900102
## 133 134 135 136
## 0.70653988231803 0.04387646152684 0.02921373162495 0.03764584836616
## 137 138 139 140
## 0.08142430501391 0.00779588354276 0.28437914873550 0.23108513294381
## 141 142 143 144
## 0.46027167963724 0.11744307201226 0.22796330998124 0.08897354068147
## 145 146 147 148
## 0.00475239402791 0.05027460069463 0.09752405691218 0.08730091224803
## 149 150 151 152
## 0.09435557822513 0.21750539084847 0.04149641993945 0.01576047063313
## 153 154 155 156
## 0.33754364979717 0.03370014754154 0.06922746777123 0.00319552208781
## 157 158 159 160
## 0.02475253019305 0.32155984068623 0.03375124731029 0.18519029136305
## 161 162 163 164
## 0.02165953795878 0.02902560590252 0.05801535327519 0.04194591318104
## 165 166 167 168
## 0.07052246128739 0.01409154467563 0.02281384271900 0.02517730246730
## 169 170 171 172
## 0.04641817463578 0.07464979220018 0.50465647679864 0.85128289302033
## 173 174 175 176
## 0.42188181299096 0.00817061069779 0.12587106164766 0.05188148811173
## 177 178 179 180
## 0.02995907524318 0.39941632906254 0.05916729459681 0.07543608463214
## 181 182 183 184
## 0.25540398211146 0.04880406804679 0.74773966137738 0.03914005600913
## 185 186 187 188
## 0.00274929097771 0.00281051882187 0.00647084070060 0.00046693247359
## 189 190 191 192
## 0.00984086584293 0.00178758060737 0.00488198064645 0.02179169010936
## 193 194 195 196
## 0.64586402472104 0.00043389717383 0.05229784608150 0.25945021300901
## 197 198 199 200
## 0.26754678536773 0.00167349105407 0.02799213318491 0.03728481816496
## 201 202 203 204
## 0.49741064643643 0.00702099252262 0.08800724612431 0.30755692001898
## 205 206 207 208
## 0.62379957151123 0.02032814933428 0.20623374591028 0.31614141728524
## 209 210 211 212
## 0.00903086330906 0.00523848685464 0.06611976350984 0.00932944733757
## 213 214 215 216
## 0.04191630128323 0.00417397779572 0.45174906574047 0.04113659005434
## 217 218 219 220
## 0.77697801512752 0.09930896824944 0.04033054745439 0.00513973027453
## 221 222 223 224
## 0.04520931587124 0.05461198120617 0.00943641014500 0.00395495210194
## 225 226 227 228
## 0.00464485403507 0.00989463565321 0.15559472876312 0.01417111894711
## 229 230 231 232
## 0.03564604641918 0.48347788263218 0.19973925960811 0.00302458672818
## 233 234 235 236
## 0.10367616792708 0.00036831922246 0.40488534550378 0.00747827330965
## 237 238 239 240
## 0.13039152026434 0.26384574701395 0.08001020326374 0.57142855316590
## 241 242 243 244
## 0.03253304925155 0.05193177931836 0.05519383447083 0.04629298483020
## 245 246 247 248
## 0.00361263412333 0.04714882783445 0.01921020392042 0.02910269057917
## 249 250 251 252
## 0.04415489456778 0.03438579684889 0.05024437788885 0.12976507618847
## 253 254 255 256
## 0.05783050542579 0.24579647128610 0.01772397574968 0.01121810755543
## 257 258 259 260
## 0.12497164187521 0.00056939074625 0.03244119824515 0.56062899755920
## 261 262 263 264
## 0.27972074247358 0.00748675983614 0.27643306440790 0.20976254632391
## 265 266 267 268
## 0.36432173862216 0.13105787832523 0.08373631604251 0.00330535635275
## 269 270 271 272
## 0.03560099830725 0.00523264665685 0.04540887250227 0.25141673681480
## 273 274 275 276
## 0.00660275993420 0.01086951924941 0.07318146371699 0.00384560755080
## 277 278 279 280
## 0.06062518913130 0.35587884195655 0.02355472962948 0.00188457304676
## 281 282 283 284
## 0.00215187746024 0.01989885296500 0.07288381605036 0.11296754514234
## 285 286 287 288
## 0.61365737966038 0.00522775383855 0.53184124221140 0.02505423273599
## 289 290 291 292
## 0.57801129758803 0.01106756715390 0.15123586961156 0.35434089709945
## 293 294 295 296
## 0.14481486588865 0.68430650571237 0.23422430768580 0.17834764898469
## 297 298 299 300
## 0.23749168249169 0.03386824456417 0.09283588051737 0.01221695143991
## 301 302 303 304
## 0.01065438817830 0.44329811537146 0.03549355672493 0.10875179428353
## 305 306 307 308
## 0.00045248281834 0.02610346404246 0.02028325913525 0.01360541974841
## 309 310 311 312
## 0.00879844064587 0.10588483221549 0.53313117528266 0.31547043006737
## 313 314 315 316
## 0.13102550623409 0.07115016128669 0.20219751312157 0.02796577229341
## 317 318 319 320
## 0.13398608189049 0.11314044272619 0.48565573855614 0.46428553972352
## 321 322 323 324
## 0.25208857412554 0.00272218799759 0.03488694948184 0.58718696633482
## 325 326 327 328
## 0.00200364466493 0.03998065057040 0.20675118574536 0.16591344189114
## 329 330 331 332
## 0.24928742790983 0.00143049289529 0.04611214519080 0.09516360053618
## 333 334 335 336
## 0.01779046219132 0.10924194587232 0.02304322650960 0.22961664963427
## 337 338 339 340
## 0.52621231250900 0.23099857020604 0.00874192367615 0.03218780301904
## 341 342 343 344
## 0.00831628895412 0.00466361375045 0.04934603994440 0.13726450533950
## 345 346 347 348
## 0.00796808421509 0.03726614336177 0.29329778020907 0.46595293529121
## 349 350 351 352
## 0.01723229858671 0.01075882016571 0.17989554941461 0.02139278007900
## 353 354 355 356
## 0.06072820101065 0.12103788581970 0.43106450974622 0.02709265540230
## 357 358 359 360
## 0.02698456975398 0.97962318753280 0.00665405885679 0.04831133917835
## 361 362 363 364
## 0.00208929899426 0.02825736286534 0.21798484709589 0.69145668337412
## 365 366 367 368
## 0.06181286221940 0.00239702863843 0.28861052878459 0.02432658259708
## 369 370 371 372
## 0.44786894343654 0.35265395505447 0.32178707546148 0.11752619551660
## 373 374 375 376
## 0.13865008712839 0.03276852385133 0.03568986728363 0.05515607328266
## 377 378 379 380
## 0.00397212522389 0.01307848923554 0.66564459788263 0.01361572042056
## 381 382 383 384
## 0.07700290017059 0.35827627976741 0.26701014747777 0.08698241128932
## 385 386 387 388
## 0.12838492822624 0.86751336945511 0.05576803256913 0.01462585813575
## 389 390 391 392
## 0.05248454862851 0.23908507934679 0.00512648747866 0.06160327463802
## 393 394 395 396
## 0.00529738708389 0.05612816713871 0.00915425562574 0.26559157318411
## 397 398 399 400
## 0.03233052992949 0.42823302806268 0.14360507672887 0.13582857657237
## 401 402 403 404
## 0.06764413852078 0.02409482596031 0.15936852410744 0.01534911824327
## 405 406 407 408
## 0.08882826586673 0.20364175900048 0.00644367021163 0.01676458093275
## 409 410 411 412
## 0.00100630868258 0.04788527095099 0.02833851900631 0.09524058433313
## 413 414 415 416
## 0.00101018258087 0.00666272791569 0.87122905444691 0.20857434978604
## 417 418 419 420
## 0.23945708098372 0.00028774936179 0.06209665919754 0.02049708647267
## 421 422 423 424
## 0.00595893852364 0.34754837051757 0.47395676565494 0.02007677575268
## 425 426 427 428
## 0.02087761628561 0.23272744873622 0.01774240957986 0.12285962866338
## 429 430 431 432
## 0.00317325323182 0.00856442227173 0.35259996329348 0.07150131112075
## 433 434 435 436
## 0.01218181809051 0.08581738288391 0.00094034981196 0.25246369104924
## 437 438 439 440
## 0.30959897256488 0.32821830834710 0.08988714871956 0.23597943713912
## 441 442 443 444
## 0.89966917838098 0.11592117407914 0.06578808368041 0.76089476181369
## 445 446 447 448
## 0.01945373619735 0.01120179447035 0.01039724960324 0.11067950675571
## 449 450 451 452
## 0.03416787438718 0.05218076887811 0.19765531812909 0.05588711968010
## 453 454 455 456
## 0.00366956906017 0.56742539910552 0.02438831589520 0.00180231837511
## 457 458 459 460
## 0.03830052556003 0.95542050460030 0.05939306440143 0.04618037628369
## 461 462 463 464
## 0.21162547526131 0.03599517648134 0.01904476120631 0.97794304350142
## 465 466 467 468
## 0.01814581401136 0.02413150457575 0.03507924576524 0.01157430636136
## 469 470 471 472
## 0.07139504341129 0.01908592764085 0.15497085694742 0.00351947484056
## 473 474 475 476
## 0.07827587480643 0.00347466435905 0.11094261015055 0.09316002470229
## 477 478 479 480
## 0.16604506514249 0.00000081596721 0.12939420486335 0.51817858360477
## 481 482 483 484
## 0.63494748994958 0.07956893050138 0.21389005576832 0.35810809048506
## 485 486 487 488
## 0.00420110994717 0.01716011615983 0.23994752817603 0.08924347686338
## 489 490 491 492
## 0.00375536604875 0.02082724096444 0.06614712127342 0.18887368667969
## 493 494 495 496
## 0.03797605802654 0.16241355100490 0.23732297447743 0.13524099155460
## 497 498 499 500
## 0.68029882486451 0.01295719853579 0.04466667862330 0.03764204565955
## 501 502 503 504
## 0.09361605738601 0.03035484674048 0.03900924454336 0.00942025207098
## 505 506 507 508
## 0.20394701087822 0.16438970554883 0.00804950698611 0.06074500201754
## 509 510 511 512
## 0.16636896447318 0.01090277655744 0.06159460247640 0.15790915582678
## 513 514 515 516
## 0.14710148236689 0.24330148274535 0.89495625606974 0.02334759944851
## 517 518 519 520
## 0.06352820687660 0.01355673223868 0.02409644576792 0.01302166729318
## 521 522 523 524
## 0.02814899233781 0.02542388065014 0.04410746180677 0.05634015994214
## 525 526 527 528
## 0.02132892130788 0.61064143924494 0.08295743762716 0.01983897924471
## 529 530 531 532
## 0.44971692312973 0.00194553911681 0.00458667898844 0.00162443908862
## 533 534 535 536
## 0.02447679740484 0.14269925667739 0.00036569253665 0.00000075135945
## 537 538 539 540
## 0.58964051656618 0.01259003597385 0.00000002727337 0.18383258569960
## 541 542 543 544
## 0.62742369876973 0.00691280063827 0.06919773903153 0.20406845921978
## 545 546 547 548
## 0.40805379953949 0.14567263919759 0.19878199209164 0.31505343087266
## 549 550 551 552
## 0.04165989974283 0.05527406283991 0.09791034438545 0.17624978527545
## 553 554 555 556
## 0.00529594853009 0.10969597309776 0.16458392118955 0.09084075102306
## 557 558 559 560
## 0.00839090359807 0.00208491934282 0.11709247317661 0.39080135546926
## 561 562 563 564
## 0.03068089982996 0.01202387660545 0.10746667680021 0.06081423289709
## 565 566 567 568
## 0.61228801776791 0.05941437279739 0.59481568454414 0.00871569660340
## 569 570 571 572
## 0.02800384847473 0.08259023602285 0.00270946879741 0.49119711522886
## 573 574 575 576
## 0.06245038221657 0.70118473917625 0.01448189441379 0.12369080536399
## 577 578 579 580
## 0.08715262877843 0.14515199283715 0.41879777359211 0.06411344789684
## 581 582 583 584
## 0.15525010549152 0.06090776952867 0.00298092212350 0.13197071382400
## 585 586 587 588
## 0.10222377398336 0.42705960473940 0.03724455177257 0.04061273762013
## 589 590 591 592
## 0.00038773806223 0.67914411435190 0.00062882942771 0.51780621499607
## 593 594 595 596
## 0.02178302001596 0.00441318994516 0.00604348220376 0.05491980515952
## 597 598 599 600
## 0.02284635872555 0.04742083868605 0.12509948784323 0.20071626884831
## 601 602 603 604
## 0.00440392478110 0.56935098945996 0.24599713287462 0.05465645354219
## 605 606 607 608
## 0.04312850631086 0.14158047626597 0.11190583063262 0.00868782117648
## 609 610 611 612
## 0.05575543741917 0.01521139347925 0.01294934562790 0.01031409353126
## 613 614 615 616
## 0.55659649678273 0.07425610665781 0.18529851736310 0.00201650153634
## 617 618 619 620
## 0.01088514576393 0.08317758762913 0.36866482775073 0.00909448149302
## 621 622 623 624
## 0.22876267570372 0.03198781554280 0.03453915374774 0.18871506165546
## 625 626 627 628
## 0.06940109454943 0.14760300341811 0.01441765299676 0.00623272821765
## 629 630 631 632
## 0.04814888401736 0.01771476493960 0.08315480488315 0.20153671903591
## 633 634 635 636
## 0.49865591305163 0.15279796695833 0.21845830631775 0.01015343338900
## 637 638 639 640
## 0.55317193525816 0.00608575961086 0.25210845328598 0.04402350424510
## 641 642 643 644
## 0.07054543290767 0.10022915283659 0.19271885396048 0.06769127733684
## 645 646 647 648
## 0.08699864434884 0.39926032446694 0.02421254946842 0.09878085173527
## 649 650 651 652
## 0.18611313013607 0.00110714246994 0.01396234546401 0.09076734294599
## 653 654 655 656
## 0.34913048911103 0.05476754477287 0.01467236899101 0.14971261837522
## 657 658 659 660
## 0.91111471808482 0.03828885575929 0.55102767829543 0.12466030690224
## 661 662 663 664
## 0.51296828280762 0.03001822428042 0.20670107635416 0.09619357151302
## 665 666 667 668
## 0.04029476930835 0.47917139860297 0.07468421448523 0.41872274376261
## 669 670 671 672
## 0.03022180180364 0.68938193058048 0.07322116743404 0.14032673563541
## 673 674 675 676
## 0.09882035945367 0.69595837140064 0.02868775836446 0.24651460654901
## 677 678 679 680
## 0.01886444576558 0.05208746494252 0.03005925087390 0.01006800627683
## 681 682 683 684
## 0.02748081487716 0.00157629581245 0.07109539366789 0.83649794666225
## 685 686 687 688
## 0.27837461031270 0.20244764438509 0.05310395612644 0.01878798869155
## 689 690 691 692
## 0.90468795632918 0.83217547872472 0.05636482191081 0.42655684035082
## 693 694 695 696
## 0.01724479886611 0.08357837541122 0.03764802991723 0.70187164784420
## 697 698 699 700
## 0.00519357955553 0.27028627087880 0.05645200018672 0.00158797943060
## 701 702 703 704
## 0.06432573017651 0.01662263272024 0.07401610999164 0.25461025646447
## 705 706 707 708
## 0.00410993806948 0.00951675862538 0.22082091593849 0.01951104796537
## 709 710 711 712
## 0.00539482020132 0.55456943280500 0.02043904420492 0.63591627194832
## 713 714 715 716
## 0.06494955596455 0.00351143419808 0.00053304818098 0.10243107284362
## 717 718 719 720
## 0.00053761573823 0.63755696908854 0.05181469314912 0.10257782264160
## 721 722 723 724
## 0.62081870760057 0.01172497998609 0.08583732231234 0.00226218116060
## 725 726 727 728
## 0.01103557699681 0.53298354889476 0.03970727381249 0.03402654428561
## 729 730 731 732
## 0.00964001037955 0.21876292713002 0.00748899673240 0.75516290000786
## 733 734 735 736
## 0.37452186127743 0.00298706756729 0.64283410038143 0.04797886635009
## 737 738 739 740
## 0.01537414219604 0.02064568467530 0.00959331139613 0.01819152693648
## 741 742 743 744
## 0.06663844259576 0.00953917529907 0.07450560232534 0.04076496024318
## 745 746 747 748
## 0.31559607685273 0.07211256475783 0.00029524193194 0.54885194224590
## 749 750 751 752
## 0.55274450407219 0.00686435521329 0.02732726605177 0.00041091857386
## 753 754 755 756
## 0.14663718836959 0.39416677993649 0.09601892577280 0.00140584695187
## 757 758 759 760
## 0.24186078925846 0.00937397261942 0.10023497831866 0.25254758200038
## 761 762 763 764
## 0.03372284169567 0.33180658108596 0.86268699938563 0.30309787724802
## 765 766 767 768
## 0.11675097739690 0.06640532509022 0.01499721046087 0.03033315310120
## 769 770 771 772
## 0.27228236778211 0.03471280575798 0.00073697171778 0.09927562967784
## 773 774 775 776
## 0.01097102053192 0.02612580125563 0.02081791860597 0.02531857261426
## 777 778 779 780
## 0.75126312232172 0.58950128494240 0.06280186719884 0.22315742828869
## 781 782 783 784
## 0.21438493376954 0.32234453746435 0.08237433323663 0.00745365057409
## 785 786 787 788
## 0.00504466585981 0.08809828071652 0.05573039657103 0.00530758202579
## 789 790 791 792
## 0.00721557227296 0.25665761197554 0.00698454652477 0.55501379030017
## 793 794 795 796
## 0.25131235088167 0.11436674497171 0.09213033114058 0.03697330282896
## 797 798 799 800
## 0.19204808504641 0.35282099068855 0.95096985558548 0.02903333252089
## 801 802 803 804
## 0.49055975903724 0.26618918064087 0.02807313844541 0.00492698700522
## 805 806 807 808
## 0.00268643699284 0.00264388993383 0.05113936612753 0.11101453360392
## 809 810 811 812
## 0.02175148246097 0.00143184783112 0.00467688876731 0.19387790013943
## 813 814 815 816
## 0.13861871385324 0.05977329863273 0.01152611347061 0.37262168161562
## 817 818 819 820
## 0.19362976183535 0.01113932022939 0.15814949057534 0.19668413392843
## 821 822 823 824
## 0.02733510973154 0.05022423133454 0.04749674053686 0.02056940685591
## 825 826 827 828
## 0.52007881737346 0.15393105783312 0.03473188299264 0.29865964564654
## 829 830 831 832
## 0.12623009687482 0.78664186169444 0.44578097145965 0.16514637932345
## 833 834 835 836
## 0.02666664935017 0.05265973975632 0.05495231576469 0.31948102102377
## 837 838 839 840
## 0.09261140101264 0.02419210952925 0.85078039136830 0.19404289577676
## 841 842 843 844
## 0.09903186418755 0.49460678995875 0.25137472573127 0.01485288281174
## 845 846 847 848
## 0.11069288048068 0.32327386723028 0.01352689108377 0.02912112065765
## 849 850 851 852
## 0.07848633984369 0.73576123391358 0.02452289284132 0.00828149044358
## 853 854 855 856
## 0.00732335013923 0.15753989567200 0.20597600227422 0.00259124603679
## 857 858 859 860
## 0.67987034263345 0.16383760044318 0.00030448554243 0.39149821082004
## 861 862 863 864
## 0.30475445504754 0.14763741301764 0.03538683107148 0.05725599239860
## 865 866 867 868
## 0.26954580490920 0.14724264051306 0.11760077251796 0.00321347140955
## 869 870 871 872
## 0.14567694184913 0.00304658065400 0.10065875751283 0.25403778903271
## 873 874 875 876
## 0.17911457014657 0.02014114830019 0.03825052367382 0.02235214149631
## 877 878 879 880
## 0.31307648538593 0.00530676039957 0.00987325703164 0.01304636593766
## 881 882 883 884
## 0.26605570649627 0.10276126675073 0.24476419942864 0.00521707360413
## 885 886 887 888
## 0.32005546118334 0.06445039879553 0.06837387256111 0.13860851463464
## 889 890 891 892
## 0.07817094818916 0.41632680298103 0.00546697169206 0.00431943245800
## 893 894 895 896
## 0.51559822292521 0.00949489666176 0.00006899768153 0.19245277127718
## 897 898 899 900
## 0.04458167983522 0.02057932817447 0.00073979369873 0.01000408694690
## 901 902 903 904
## 0.04529722369283 0.21078018272119 0.02542165895167 0.09972015505778
## 905 906 907 908
## 0.00196342062638 0.00069561174002 0.03095008768559 0.01525392412062
## 909 910 911 912
## 0.00870906880523 0.40483053520117 0.01355431150028 0.95652065478514
## 913 914 915 916
## 0.35839604543555 0.34362729576488 0.12961330122448 0.81619549629470
## 917 918 919 920
## 0.00247136793911 0.36794044697505 0.23100117034924 0.00611738278219
## 921 922 923 924
## 0.04376448953924 0.61483678720071 0.00972110901254 0.02232459422926
## 925 926 927 928
## 0.09973905587146 0.10516203621495 0.03613289390973 0.10371834749865
## 929 930 931 932
## 0.00324553344052 0.52734398096999 0.35800558487023 0.07701188831578
## 933 934 935 936
## 0.55648062572769 0.32040985165741 0.04200554471817 0.00112969736713
## 937 938 939 940
## 0.07852397727135 0.53949626335442 0.02371783652071 0.04868898232069
## 941 942 943 944
## 0.20202577052334 0.20331817029302 0.01440830653245 0.05507161675986
## 945 946 947 948
## 0.00937896006687 0.03619158893781 0.77189886580004 0.78348032955229
## 949 950 951 952
## 0.13357280708175 0.02706197464251 0.03415001280501 0.37025041934294
## 953 954 955 956
## 0.79362677075788 0.12165894554758 0.00700118449754 0.00341599175157
## 957 958 959 960
## 0.00000005053312 0.05931409156568 0.00180931033980 0.01393170258186
## 961 962 963 964
## 0.02583355490899 0.43856812353527 0.00000007418110 0.00840947834469
## 965 966 967 968
## 0.06114986302985 0.02730419706590 0.07222712608949 0.05812075105472
## 969 970 971 972
## 0.10417521461935 0.00170405134205 0.11009567998177 0.04549039438750
## 973 974 975 976
## 0.01077580175991 0.01714049844322 0.32309209228407 0.55837018218824
## 977 978 979 980
## 0.16903777335172 0.04982681006665 0.00659237955952 0.31576054966489
## 981 982 983 984
## 0.49278338250715 0.58975615430082 0.00552649118272 0.00339410090009
## 985 986 987 988
## 0.26518178273259 0.14587399086096 0.26853782865221 0.11239193563772
## 989 990 991 992
## 0.19104600234243 0.19582477676788 0.17367058148394 0.33340317521650
## 993 994 995 996
## 0.00446446831984 0.17909811313921 0.04073981037096 0.45052101396171
## 997 998 999 1000
## 0.24568542133871 0.35973746953505 0.09281132923092 0.00000001759429
## 1001 1002 1003 1004
## 0.16922935886421 0.17323864541467 0.09340660413503 0.34845675934001
## 1005 1006 1007 1008
## 0.03720865169381 0.25693004959138 0.80167427028096 0.34086922002511
## 1009 1010 1011 1012
## 0.00460571044288 0.00085268071671 0.00003092478292 0.44297732375303
## 1013 1014 1015 1016
## 0.71624166580671 0.07026881666885 0.02642431976939 0.03855850845034
## 1017 1018 1019 1020
## 0.20494035827315 0.19468778613665 0.16542698315143 0.23380805574397
## 1021 1022 1023 1024
## 0.07192630160475 0.80306959356722 0.10523492715638 0.01845262115806
## 1025 1026 1027 1028
## 0.00045620346614 0.04483858916675 0.02919749991951 0.12650147509987
## 1029 1030 1031 1032
## 0.11592787933408 0.00205310421863 0.03843869317509 0.02526442181717
## 1033 1034 1035 1036
## 0.57921093330736 0.04045061240898 0.08008374622001 0.08126594877883
## 1037 1038 1039 1040
## 0.81127807021635 0.16692306791005 0.04944394900049 0.24012594696610
## 1041 1042 1043 1044
## 0.00025609748124 0.03756638672830 0.02885486487466 0.00143734792685
## 1045 1046 1047 1048
## 0.04741174018341 0.00584095649996 0.08378272964826 0.07374402529070
## 1049 1050 1051 1052
## 0.05141885435047 0.16809961456460 0.10592830683294 0.22136932038007
## 1053 1054 1055 1056
## 0.03378117158611 0.00297651765234 0.00069186977645 0.03737045020092
## 1057 1058 1059 1060
## 0.41175907542092 0.91640940648856 0.71375295400330 0.10318057057263
## 1061 1062 1063 1064
## 0.96483189648650 0.05339824373897 0.52853390984536 0.02212011368410
## 1065 1066 1067 1068
## 0.01579310053406 0.02979636266690 0.19638909451227 0.09318883302872
## 1069 1070 1071 1072
## 0.84646676627622 0.11939879687755 0.16874611077545 0.08813752974749
## 1073 1074 1075 1076
## 0.03070503080909 0.10456610773231 0.08342772381625 0.01685081135795
## 1077 1078 1079 1080
## 0.00180887775892 0.61751654992890 0.01477258712723 0.05704713342238
## 1081 1082 1083 1084
## 0.00715849687698 0.04177993146705 0.45369605712691 0.29138591618656
## 1085 1086 1087 1088
## 0.25348192327869 0.28242535062866 0.60702454482200 0.38211958338460
## 1089 1090 1091 1092
## 0.15931596803326 0.02530697056529 0.01623762854489 0.09857551730383
## 1093 1094 1095 1096
## 0.02337110342429 0.17242441361140 0.12040792801179 0.31693197691019
## 1097 1098 1099 1100
## 0.00000043334555 0.41006461210889 0.01100351947717 0.02383843911130
## 1101 1102 1103 1104
## 0.26520072457068 0.04595014730767 0.48938570198170 0.02826352958975
## 1105 1106 1107 1108
## 0.08093009795829 0.13349088927943 0.06258813415193 0.25204237126156
## 1109 1110 1111 1112
## 0.26728077247998 0.29965851882765 0.49403455298856 0.00415923467691
## 1113 1114 1115 1116
## 0.02812577955878 0.03526434261823 0.16881266151242 0.15641670275800
## 1117 1118 1119 1120
## 0.01017097694904 0.08903427986723 0.03824738604232 0.02507242881983
## 1121 1122 1123 1124
## 0.08948802070339 0.10068146833616 0.39157430582566 0.16757348217766
## 1125 1126 1127 1128
## 0.01354329662365 0.01617127836913 0.04626352894764 0.03106885565789
## 1129 1130 1131 1132
## 0.60942016754335 0.02171879702833 0.03983438111978 0.20338323724110
## 1133 1134 1135 1136
## 0.02995818405433 0.19047609902335 0.04217060946207 0.01658519349622
## 1137 1138 1139 1140
## 0.47855726874488 0.40648182340753 0.29257205331693 0.00415073116822
## 1141 1142 1143 1144
## 0.00161158922985 0.12210384673030 0.65322935286575 0.24508584754578
## 1145 1146 1147 1148
## 0.25820075638026 0.29941145889855 0.02861690097442 0.05464086601366
## 1149 1150 1151 1152
## 0.01735166587890 0.05612606881944 0.00540617430524 0.14742506566425
## 1153 1154 1155 1156
## 0.05010881291556 0.79329688348421 0.00000001852609 0.00448656707745
## 1157 1158 1159 1160
## 0.01941427430700 0.00022031623492 0.02965330915531 0.10608735270889
## 1161 1162 1163 1164
## 0.00098839875159 0.00820681453793 0.24863490262045 0.14213621508693
## 1165 1166 1167 1168
## 0.21467958818328 0.51992891596095 0.00850982452204 0.67594095420440
## 1169 1170 1171 1172
## 0.73413354013562 0.10045134867394 0.12583173532390 0.90220501462955
## 1173 1174 1175 1176
## 0.41159213766492 0.00990795974538 0.00090976794605 0.02385868083801
## 1177 1178 1179 1180
## 0.00430376586882 0.00048369532875 0.22486197004398 0.00541607099819
## 1181 1182 1183 1184
## 0.16438116078174 0.00307835910663 0.00118469417859 0.00682797052679
## 1185 1186 1187 1188
## 0.00094664407790 0.00291669228782 0.38420479119946 0.00158712171246
## 1189 1190 1191 1192
## 0.48149119008938 0.00257547574846 0.00336170795459 0.07161147643256
## 1193 1194 1195 1196
## 0.27838795871281 0.24254969023713 0.00183392463988 0.01650312526221
## 1197 1198 1199 1200
## 0.21228099784396 0.44770118573770 0.02500387062295 0.12632511266457
## 1201 1202 1203 1204
## 0.07807231461101 0.71327192200271 0.02724694587595 0.00775092031428
## 1205 1206 1207 1208
## 0.14271491988211 0.25092263322251 0.00880115140175 0.31110637001153
## 1209 1210 1211 1212
## 0.00759363694098 0.00233564419493 0.00306139229510 0.06799025387529
## 1213 1214 1215 1216
## 0.04718045323958 0.31918263393957 0.00957701760735 0.41043965569296
## 1217 1218 1219 1220
## 0.04888781797614 0.00962872032192 0.06753703479449 0.08648881325534
## 1221 1222 1223 1224
## 0.09994363357952 0.00876640954969 0.42692509571455 0.81393003270529
## 1225 1226 1227 1228
## 0.05866688874821 0.11592658048405 0.37298152931510 0.03052268239783
## 1229 1230 1231 1232
## 0.12319465926751 0.12923049435021 0.25562198745904 0.00905959149838
## 1233 1234 1235 1236
## 0.00393789452876 0.04677816020581 0.07288103557896 0.04881274980139
## 1237 1238 1239 1240
## 0.61595163066471 0.67203299310372 0.24954218137470 0.08884731440516
## 1241 1242 1243 1244
## 0.01308433736224 0.15629521766500 0.19757212787400 0.03836741585879
## 1245 1246 1247 1248
## 0.08029993491413 0.16106218117423 0.46063576158099 0.11616283662177
## 1249 1250 1251 1252
## 0.02451804782766 0.70267029113890 0.12311685071918 0.09185001986776
## 1253 1254 1255 1256
## 0.02941549828432 0.03291682399941 0.02737822203834 0.82090865629428
## 1257 1258 1259 1260
## 0.17475821981982 0.17933505157019 0.09303600649603 0.00949643788189
## 1261 1262 1263 1264
## 0.02766248747551 0.25627714031308 0.82882632415708 0.08587938471515
## 1265 1266 1267 1268
## 0.00357804866364 0.00506094930082 0.04930444760966 0.00397822643285
## 1269 1270 1271 1272
## 0.00947004234218 0.01149155887644 0.16391254590248 0.72233132033054
## 1273 1274 1275 1276
## 0.01929842937555 0.40015442893810 0.16739907617569 0.02244194724140
## 1277 1278 1279 1280
## 0.18149464855668 0.00564445335456 0.16426893084253 0.16298918254037
## 1281 1282 1283 1284
## 0.05000093865303 0.41430328233084 0.05177909490636 0.00317195888536
## 1285 1286 1287 1288
## 0.02082305841131 0.39780632348805 0.03772283169785 0.03921057007286
## 1289 1290 1291 1292
## 0.00027480623009 0.01301849171719 0.16304143592605 0.04445045669767
## 1293 1294 1295 1296
## 0.02382798003827 0.08508223381796 0.08902997499239 0.07083602136314
## 1297 1298 1299 1300
## 0.14256099049330 0.26625381438866 0.00293435933541 0.00119716602692
## 1301 1302 1303 1304
## 0.01372724356293 0.00236903366856 0.15520072285485 0.20636882646167
## 1305 1306 1307 1308
## 0.02291863702188 0.00439425176798 0.20895999980342 0.02112035164397
## 1309 1310 1311 1312
## 0.38012428935047 0.08451977778543 0.05533167924635 0.08161197177806
## 1313 1314 1315 1316
## 0.12017845118658 0.88010387648159 0.00239975333701 0.05242746920455
## 1317 1318 1319 1320
## 0.03350773866161 0.36502688270704 0.02693520498674 0.35573843080328
## 1321 1322 1323 1324
## 0.04030974686703 0.20899404388948 0.00132582117448 0.01044620683848
## 1325 1326 1327 1328
## 0.06750267823884 0.07867000618032 0.89301127721961 0.00254646113927
## 1329 1330 1331 1332
## 0.06317626154375 0.08158125393837 0.01087977208613 0.00707680031255
## 1333 1334 1335 1336
## 0.82594181856241 0.00589632801003 0.17626469210768 0.02491101239122
## 1337 1338 1339 1340
## 0.03838244010258 0.09755956225994 0.33695942588804 0.58552810055378
## 1341 1342 1343 1344
## 0.23651933943398 0.08499409710708 0.06319590333983 0.25301255177637
## 1345 1346 1347 1348
## 0.10329569664164 0.10435018553407 0.00680026012390 0.32471013342951
## 1349 1350 1351 1352
## 0.04466343696348 0.36459860178146 0.01593076524711 0.00254960356651
## 1353 1354 1355 1356
## 0.00713459302341 0.68970423448143 0.18118269479174 0.21040546227597
## 1357 1358 1359 1360
## 0.02641796195559 0.01176039208025 0.05928090773107 0.13329533971550
## 1361 1362 1363 1364
## 0.28434002744387 0.04600311447321 0.04410335177712 0.13574030284418
## 1365 1366 1367 1368
## 0.12982964066194 0.82064742453495 0.14865065061304 0.12614314471475
## 1369 1370 1371 1372
## 0.23197586057704 0.63219045678145 0.00767105770094 0.06826129289980
## 1373 1374 1375 1376
## 0.07473041297273 0.03669954750431 0.01763131734845 0.63785873955657
## 1377 1378 1379 1380
## 0.00658118815479 0.00153278619314 0.11768672580296 0.88217371660234
## 1381 1382 1383 1384
## 0.11162215793554 0.03046830843938 0.03778048024127 0.03552630230760
## 1385 1386 1387 1388
## 0.20648305931906 0.01433809038322 0.11200931864716 0.04875545401224
## 1389 1390 1391 1392
## 0.00232203483432 0.10734048665654 0.48780104288874 0.72131783289168
## 1393 1394 1395 1396
## 0.01790330644679 0.01841499711672 0.14190069798601 0.42990672141218
## 1397 1398 1399 1400
## 0.92228966430493 0.01152703824885 0.00286257157859 0.00526582085816
## 1401 1402 1403 1404
## 0.36295638664710 0.00000023439519 0.11600796351738 0.49466087639019
## 1405 1406 1407 1408
## 0.01359400748497 0.00057427792256 0.21446367272493 0.14212093315210
## 1409 1410 1411 1412
## 0.03032977892447 0.20169852211840 0.01568741687344 0.16782242335196
## 1413 1414 1415 1416
## 0.01036564032386 0.28029502201124 0.04162851343546 0.03154199107545
## 1417 1418 1419 1420
## 0.00492907349280 0.13756037016483 0.17778681247556 0.29461608752951
## 1421 1422 1423 1424
## 0.00877805593398 0.00034428764026 0.43694160512314 0.02001802779648
## 1425 1426 1427 1428
## 0.01297249521068 0.10303795077997 0.60928297175178 0.14865623058541
## 1429 1430 1431 1432
## 0.24107327653316 0.11860728036292 0.00130816860718 0.00494789930437
## 1433 1434 1435 1436
## 0.00527871649835 0.19512777520003 0.02990993699510 0.33900777753131
## 1437 1438 1439 1440
## 0.66918259842894 0.00506646693563 0.70296422724944 0.01451072374227
## 1441 1442 1443 1444
## 0.01282133031555 0.00033648679618 0.33086809714551 0.04843091184447
## 1445 1446 1447 1448
## 0.11810134331906 0.01759841867368 0.01749569652755 0.01895398570251
## 1449 1450 1451 1452
## 0.00942434047138 0.10038091411766 0.41195214128343 0.01099071461130
## 1453 1454 1455 1456
## 0.04564317832232 0.22362530536926 0.11331852957138 0.05226111063313
## 1457 1458 1459 1460
## 0.13866686288080 0.00290945169311 0.01001081129788 0.56182909675277
## 1461 1462 1463 1464
## 0.25985676499319 0.53827184469392 0.23493845703923 0.02194953390331
## 1465 1466 1467 1468
## 0.11926447256862 0.04414182800155 0.00880633892494 0.20688429247178
## 1469 1470
## 0.01303536625607 0.05260605780505ifelse(predict(logistic_mod, type = "response") > .5, "Yes", "No") # assign label## 1 2 3 4 5 6 7 8 9 10 11 12 13
## "Yes" "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 14 15 16 17 18 19 20 21 22 23 24 25 26
## "No" "Yes" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No"
## 27 28 29 30 31 32 33 34 35 36 37 38 39
## "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "Yes"
## 40 41 42 43 44 45 46 47 48 49 50 51 52
## "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "Yes" "Yes"
## 53 54 55 56 57 58 59 60 61 62 63 64 65
## "No" "No" "Yes" "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No"
## 66 67 68 69 70 71 72 73 74 75 76 77 78
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 79 80 81 82 83 84 85 86 87 88 89 90 91
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 92 93 94 95 96 97 98 99 100 101 102 103 104
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 105 106 107 108 109 110 111 112 113 114 115 116 117
## "No" "No" "No" "Yes" "No" "No" "No" "Yes" "No" "No" "No" "No" "No"
## 118 119 120 121 122 123 124 125 126 127 128 129 130
## "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "Yes" "No" "No"
## 131 132 133 134 135 136 137 138 139 140 141 142 143
## "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 144 145 146 147 148 149 150 151 152 153 154 155 156
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 157 158 159 160 161 162 163 164 165 166 167 168 169
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 170 171 172 173 174 175 176 177 178 179 180 181 182
## "No" "Yes" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 183 184 185 186 187 188 189 190 191 192 193 194 195
## "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No"
## 196 197 198 199 200 201 202 203 204 205 206 207 208
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No"
## 209 210 211 212 213 214 215 216 217 218 219 220 221
## "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No"
## 222 223 224 225 226 227 228 229 230 231 232 233 234
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 235 236 237 238 239 240 241 242 243 244 245 246 247
## "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No"
## 248 249 250 251 252 253 254 255 256 257 258 259 260
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes"
## 261 262 263 264 265 266 267 268 269 270 271 272 273
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 274 275 276 277 278 279 280 281 282 283 284 285 286
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 287 288 289 290 291 292 293 294 295 296 297 298 299
## "Yes" "No" "Yes" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No"
## 300 301 302 303 304 305 306 307 308 309 310 311 312
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 313 314 315 316 317 318 319 320 321 322 323 324 325
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 326 327 328 329 330 331 332 333 334 335 336 337 338
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 339 340 341 342 343 344 345 346 347 348 349 350 351
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 352 353 354 355 356 357 358 359 360 361 362 363 364
## "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "Yes"
## 365 366 367 368 369 370 371 372 373 374 375 376 377
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 378 379 380 381 382 383 384 385 386 387 388 389 390
## "No" "Yes" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No"
## 391 392 393 394 395 396 397 398 399 400 401 402 403
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 404 405 406 407 408 409 410 411 412 413 414 415 416
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 417 418 419 420 421 422 423 424 425 426 427 428 429
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 430 431 432 433 434 435 436 437 438 439 440 441 442
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 443 444 445 446 447 448 449 450 451 452 453 454 455
## "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 456 457 458 459 460 461 462 463 464 465 466 467 468
## "No" "No" "Yes" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No"
## 469 470 471 472 473 474 475 476 477 478 479 480 481
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "Yes"
## 482 483 484 485 486 487 488 489 490 491 492 493 494
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 495 496 497 498 499 500 501 502 503 504 505 506 507
## "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 508 509 510 511 512 513 514 515 516 517 518 519 520
## "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No"
## 521 522 523 524 525 526 527 528 529 530 531 532 533
## "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No"
## 534 535 536 537 538 539 540 541 542 543 544 545 546
## "No" "No" "No" "Yes" "No" "No" "No" "Yes" "No" "No" "No" "No" "No"
## 547 548 549 550 551 552 553 554 555 556 557 558 559
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 560 561 562 563 564 565 566 567 568 569 570 571 572
## "No" "No" "No" "No" "No" "Yes" "No" "Yes" "No" "No" "No" "No" "No"
## 573 574 575 576 577 578 579 580 581 582 583 584 585
## "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 586 587 588 589 590 591 592 593 594 595 596 597 598
## "No" "No" "No" "No" "Yes" "No" "Yes" "No" "No" "No" "No" "No" "No"
## 599 600 601 602 603 604 605 606 607 608 609 610 611
## "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 612 613 614 615 616 617 618 619 620 621 622 623 624
## "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 625 626 627 628 629 630 631 632 633 634 635 636 637
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes"
## 638 639 640 641 642 643 644 645 646 647 648 649 650
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 651 652 653 654 655 656 657 658 659 660 661 662 663
## "No" "No" "No" "No" "No" "No" "Yes" "No" "Yes" "No" "Yes" "No" "No"
## 664 665 666 667 668 669 670 671 672 673 674 675 676
## "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "Yes" "No" "No"
## 677 678 679 680 681 682 683 684 685 686 687 688 689
## "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "Yes"
## 690 691 692 693 694 695 696 697 698 699 700 701 702
## "Yes" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No"
## 703 704 705 706 707 708 709 710 711 712 713 714 715
## "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "Yes" "No" "No" "No"
## 716 717 718 719 720 721 722 723 724 725 726 727 728
## "No" "No" "Yes" "No" "No" "Yes" "No" "No" "No" "No" "Yes" "No" "No"
## 729 730 731 732 733 734 735 736 737 738 739 740 741
## "No" "No" "No" "Yes" "No" "No" "Yes" "No" "No" "No" "No" "No" "No"
## 742 743 744 745 746 747 748 749 750 751 752 753 754
## "No" "No" "No" "No" "No" "No" "Yes" "Yes" "No" "No" "No" "No" "No"
## 755 756 757 758 759 760 761 762 763 764 765 766 767
## "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No"
## 768 769 770 771 772 773 774 775 776 777 778 779 780
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "Yes" "No" "No"
## 781 782 783 784 785 786 787 788 789 790 791 792 793
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 794 795 796 797 798 799 800 801 802 803 804 805 806
## "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No"
## 807 808 809 810 811 812 813 814 815 816 817 818 819
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 820 821 822 823 824 825 826 827 828 829 830 831 832
## "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "Yes" "No" "No"
## 833 834 835 836 837 838 839 840 841 842 843 844 845
## "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No"
## 846 847 848 849 850 851 852 853 854 855 856 857 858
## "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 859 860 861 862 863 864 865 866 867 868 869 870 871
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 872 873 874 875 876 877 878 879 880 881 882 883 884
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 885 886 887 888 889 890 891 892 893 894 895 896 897
## "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No"
## 898 899 900 901 902 903 904 905 906 907 908 909 910
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 911 912 913 914 915 916 917 918 919 920 921 922 923
## "No" "Yes" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "Yes" "No"
## 924 925 926 927 928 929 930 931 932 933 934 935 936
## "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "Yes" "No" "No" "No"
## 937 938 939 940 941 942 943 944 945 946 947 948 949
## "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "Yes" "No"
## 950 951 952 953 954 955 956 957 958 959 960 961 962
## "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 963 964 965 966 967 968 969 970 971 972 973 974 975
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 976 977 978 979 980 981 982 983 984 985 986 987 988
## "Yes" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No"
## 989 990 991 992 993 994 995 996 997 998 999 1000 1001
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014
## "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "Yes" "No"
## 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027
## "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No"
## 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040
## "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "Yes" "No" "No" "No"
## 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066
## "No" "No" "No" "No" "Yes" "Yes" "No" "Yes" "No" "Yes" "No" "No" "No"
## 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079
## "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092
## "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No"
## 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No"
## 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No"
## 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170
## "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "Yes" "Yes" "No"
## 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183
## "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209
## "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No"
## 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235
## "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248
## "No" "Yes" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261
## "No" "Yes" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No"
## 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274
## "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No"
## 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326
## "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339
## "Yes" "No" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No"
## 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352
## "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365
## "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378
## "Yes" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "Yes" "No" "No"
## 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391
## "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404
## "Yes" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No"
## 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No"
## 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443
## "No" "No" "No" "No" "No" "No" "Yes" "No" "Yes" "No" "No" "No" "No"
## 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456
## "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469
## "No" "No" "No" "Yes" "No" "Yes" "No" "No" "No" "No" "No" "No" "No"
## 1470
## "No"ifelse(predict(logistic_mod, type = "response") > .5, "Yes", "No") == bi$attrition # observed labels## 1 2 3 4 5 6 7 8 9 10 11 12 13
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 14 15 16 17 18 19 20 21 22 23 24 25 26
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 27 28 29 30 31 32 33 34 35 36 37 38 39
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE FALSE
## 40 41 42 43 44 45 46 47 48 49 50 51 52
## TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## 53 54 55 56 57 58 59 60 61 62 63 64 65
## TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 66 67 68 69 70 71 72 73 74 75 76 77 78
## TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 79 80 81 82 83 84 85 86 87 88 89 90 91
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 92 93 94 95 96 97 98 99 100 101 102 103 104
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
## 105 106 107 108 109 110 111 112 113 114 115 116 117
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 118 119 120 121 122 123 124 125 126 127 128 129 130
## TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
## 131 132 133 134 135 136 137 138 139 140 141 142 143
## TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE
## 144 145 146 147 148 149 150 151 152 153 154 155 156
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 157 158 159 160 161 162 163 164 165 166 167 168 169
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 170 171 172 173 174 175 176 177 178 179 180 181 182
## TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE
## 183 184 185 186 187 188 189 190 191 192 193 194 195
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 196 197 198 199 200 201 202 203 204 205 206 207 208
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 209 210 211 212 213 214 215 216 217 218 219 220 221
## TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE TRUE
## 222 223 224 225 226 227 228 229 230 231 232 233 234
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE
## 235 236 237 238 239 240 241 242 243 244 245 246 247
## FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 248 249 250 251 252 253 254 255 256 257 258 259 260
## TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 261 262 263 264 265 266 267 268 269 270 271 272 273
## TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 274 275 276 277 278 279 280 281 282 283 284 285 286
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 287 288 289 290 291 292 293 294 295 296 297 298 299
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 300 301 302 303 304 305 306 307 308 309 310 311 312
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 313 314 315 316 317 318 319 320 321 322 323 324 325
## TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 326 327 328 329 330 331 332 333 334 335 336 337 338
## TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 339 340 341 342 343 344 345 346 347 348 349 350 351
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 352 353 354 355 356 357 358 359 360 361 362 363 364
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 365 366 367 368 369 370 371 372 373 374 375 376 377
## TRUE TRUE FALSE TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## 378 379 380 381 382 383 384 385 386 387 388 389 390
## TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 391 392 393 394 395 396 397 398 399 400 401 402 403
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 404 405 406 407 408 409 410 411 412 413 414 415 416
## TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE
## 417 418 419 420 421 422 423 424 425 426 427 428 429
## TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## 430 431 432 433 434 435 436 437 438 439 440 441 442
## TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE FALSE TRUE TRUE
## 443 444 445 446 447 448 449 450 451 452 453 454 455
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 456 457 458 459 460 461 462 463 464 465 466 467 468
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 469 470 471 472 473 474 475 476 477 478 479 480 481
## TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 482 483 484 485 486 487 488 489 490 491 492 493 494
## TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 495 496 497 498 499 500 501 502 503 504 505 506 507
## TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 508 509 510 511 512 513 514 515 516 517 518 519 520
## TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## 521 522 523 524 525 526 527 528 529 530 531 532 533
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE
## 534 535 536 537 538 539 540 541 542 543 544 545 546
## TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 547 548 549 550 551 552 553 554 555 556 557 558 559
## TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 560 561 562 563 564 565 566 567 568 569 570 571 572
## TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
## 573 574 575 576 577 578 579 580 581 582 583 584 585
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 586 587 588 589 590 591 592 593 594 595 596 597 598
## FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 599 600 601 602 603 604 605 606 607 608 609 610 611
## FALSE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
## 612 613 614 615 616 617 618 619 620 621 622 623 624
## TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 625 626 627 628 629 630 631 632 633 634 635 636 637
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 638 639 640 641 642 643 644 645 646 647 648 649 650
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE
## 651 652 653 654 655 656 657 658 659 660 661 662 663
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE FALSE
## 664 665 666 667 668 669 670 671 672 673 674 675 676
## FALSE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 677 678 679 680 681 682 683 684 685 686 687 688 689
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 690 691 692 693 694 695 696 697 698 699 700 701 702
## TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 703 704 705 706 707 708 709 710 711 712 713 714 715
## TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 716 717 718 719 720 721 722 723 724 725 726 727 728
## TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 729 730 731 732 733 734 735 736 737 738 739 740 741
## TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## 742 743 744 745 746 747 748 749 750 751 752 753 754
## TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE TRUE
## 755 756 757 758 759 760 761 762 763 764 765 766 767
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 768 769 770 771 772 773 774 775 776 777 778 779 780
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE
## 781 782 783 784 785 786 787 788 789 790 791 792 793
## FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE
## 794 795 796 797 798 799 800 801 802 803 804 805 806
## TRUE TRUE TRUE FALSE FALSE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
## 807 808 809 810 811 812 813 814 815 816 817 818 819
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 820 821 822 823 824 825 826 827 828 829 830 831 832
## TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE FALSE
## 833 834 835 836 837 838 839 840 841 842 843 844 845
## TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 846 847 848 849 850 851 852 853 854 855 856 857 858
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE
## 859 860 861 862 863 864 865 866 867 868 869 870 871
## TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## 872 873 874 875 876 877 878 879 880 881 882 883 884
## FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 885 886 887 888 889 890 891 892 893 894 895 896 897
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 898 899 900 901 902 903 904 905 906 907 908 909 910
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 911 912 913 914 915 916 917 918 919 920 921 922 923
## TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 924 925 926 927 928 929 930 931 932 933 934 935 936
## TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## 937 938 939 940 941 942 943 944 945 946 947 948 949
## TRUE FALSE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 950 951 952 953 954 955 956 957 958 959 960 961 962
## TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 963 964 965 966 967 968 969 970 971 972 973 974 975
## TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 976 977 978 979 980 981 982 983 984 985 986 987 988
## TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 989 990 991 992 993 994 995 996 997 998 999 1000 1001
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
## 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014
## TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027
## TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040
## TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE
## 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066
## TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
## 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092
## TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118
## TRUE FALSE TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144
## TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170
## TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE FALSE TRUE
## 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196
## TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE
## 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222
## TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235
## FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
## 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE
## 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287
## TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300
## TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE
## 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE
## 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE FALSE
## 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365
## TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE
## 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404
## FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
## 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443
## TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE
## 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456
## TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
## 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469
## TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 1470
## TRUE(ifelse(predict(logistic_mod, type = "response") > .5, "Yes", "No") == bi$attrition) %>%
mean # 0.89## [1] 0.892517bi %>%
summarize(attrition = mean(attrition=="No")) # 0.839## # A tibble: 1 × 1
## attrition
## <dbl>
## 1 0.839Majority class is “No”. The baseline rate of the majority class was .839, and hence, the logistic regression model at accuracy of .89 is doing slightly better than the majority class prediction.
The upside of standardizing inputs by centering and scaling is that it allows you to compare coefficient effect sizes easily—they are all on the same scale. (The downside is that they are no longer scaled in the original units, and interpretation changes.) Even though the coefficients are expressed in log odds in this case, after standardization they can still be compared for effect sizes on a relative basis.
There are a lot of coefficients to type into the model formula. A shortcut to automatically include all the predictors in the dataset is ., as in: glm(target ~ ., family = binomial, data = …). However, this shortcut doesn’t allow you to standardize also. The easiest solution to create a new dataset in which all the continuous variables are centered. For this a version of mutate() is useful: mutate_if(). The code would go like this:
data %>% mutate_if(is.numeric, scale)
In English: if the variable is numeric, then scale it.
Notice that some of the standard errors and coefficients in the model above have exploded. (You can see this more easily if you adjust the number of digits printed in the output with options(scipen = 3).) The SEs for some of the department and job_role coefficients are over 380. Why has this happened? Multicolinearity! Some of the levels of the department variable are correlated with levels in job_role. For example, since most of the people in the Human Resources department also have a job title of Human Resources, the information from department is redundant: by definition, if we know job_role we also know department and vice versa. This is a textbook example of how multicollinearity makes inference difficult—we can’t compare the coefficients because some of them are wacky. The solution? Remove the redundant variable. Refit the model without department
Which of the centered and scaled predictors has the largest effect size?
Interpret the coefficient with the largest effect size. Since you are working with standardized coefficients, the interpretation for continuous predictors will be: a 1 unit (that is, after scaling, a 1 standard deviation) increase in x is associated with a coefficient-sized change in the log odds of y, on average, while holding the other predictors constant. The coefficient represents the change in the log odds of the outcome associated with an increase from the reference level in the categorical variable.
# Standardization
bi_scaled <- bi %>%
mutate_if(is.numeric, function(x) scale(x) %>% as.vector())
glimpse(bi_scaled)## Rows: 1,470
## Columns: 28
## $ age <dbl> 0.44619856, 1.32191535, 0.00834016, -0.4295…
## $ business_travel <chr> "Travel_Rarely", "Travel_Frequently", "Trav…
## $ department <chr> "Sales", "Research & Development", "Researc…
## $ distance_from_home <dbl> -1.01056544, -0.14709966, -0.88721318, -0.7…
## $ education <dbl> -0.89138490, -1.86779013, -0.89138490, 1.06…
## $ education_field <chr> "Life Sciences", "Life Sciences", "Other", …
## $ environment_satisfaction <dbl> -0.6603060, 0.2545383, 1.1693826, 1.1693826…
## $ gender <chr> "Female", "Male", "Male", "Female", "Male",…
## $ job_involvement <dbl> 0.379543, -1.025818, -1.025818, 0.379543, 0…
## $ job_level <dbl> -0.05776789, -0.05776789, -0.96115930, -0.9…
## $ job_role <chr> "Sales Executive", "Research Scientist", "L…
## $ job_satisfaction <dbl> 1.1528613, -0.6606284, 0.2461164, 0.2461164…
## $ marital_status <chr> "Single", "Married", "Single", "Married", "…
## $ monthly_income <dbl> -0.1083127, -0.2916193, -0.9373347, -0.7633…
## $ num_companies_worked <dbl> 2.1244130, -0.6778187, 1.3237753, -0.677818…
## $ over_time <chr> "Yes", "No", "Yes", "Yes", "No", "No", "Yes…
## $ percent_salary_hike <dbl> -1.15016269, 2.12858163, -0.05724792, -1.15…
## $ performance_rating <dbl> -0.426085, 2.345353, -0.426085, -0.426085, …
## $ relationship_satisfaction <dbl> -1.5836393, 1.1910327, -0.6587487, 0.266142…
## $ stock_option_level <dbl> -0.9316973, 0.2419060, -0.9316973, -0.93169…
## $ total_working_years <dbl> -0.42149902, -0.16445544, -0.55002081, -0.4…
## $ training_times_last_year <dbl> -2.1712429, 0.1556541, 0.1556541, 0.1556541…
## $ work_life_balance <dbl> -2.4929720, 0.3379811, 0.3379811, 0.3379811…
## $ years_at_company <dbl> -0.164557109, 0.488341541, -1.143905083, 0.…
## $ years_in_current_role <dbl> -0.06327437, 0.76473737, -1.16729002, 0.764…
## $ years_since_last_promotion <dbl> -0.67891464, -0.36858985, -0.67891464, 0.25…
## $ years_with_curr_manager <dbl> 0.2457504, 0.8062671, -1.1555415, -1.155541…
## $ attrition <fct> Yes, No, Yes, No, No, No, No, No, No, No, N…# Fitting Model
(scaled_mod <- glm(ifelse(attrition=="Yes", 1, 0) ~.,
data = bi_scaled,
family = binomial)) %>%
summary##
## Call:
## glm(formula = ifelse(attrition == "Yes", 1, 0) ~ ., family = binomial,
## data = bi_scaled)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6316 -0.4902 -0.2510 -0.0909 3.4150
##
## Coefficients:
## Estimate Std. Error z value
## (Intercept) -17.91144 383.60550 -0.047
## age -0.28617 0.12348 -2.317
## business_travelTravel_Frequently 1.92453 0.41015 4.692
## business_travelTravel_Rarely 1.04066 0.37812 2.752
## departmentResearch & Development 12.78573 383.60484 0.033
## departmentSales 12.60973 383.60508 0.033
## distance_from_home 0.37163 0.08701 4.271
## education 0.00326 0.08957 0.036
## education_fieldLife Sciences -0.79101 0.80298 -0.985
## education_fieldMarketing -0.36664 0.85225 -0.430
## education_fieldMedical -0.89387 0.80254 -1.114
## education_fieldOther -0.87160 0.86138 -1.012
## education_fieldTechnical Degree 0.11824 0.82073 0.144
## environment_satisfaction -0.47377 0.09038 -5.242
## genderMale 0.38791 0.18393 2.109
## job_involvement -0.37798 0.08693 -4.348
## job_level -0.08404 0.34839 -0.241
## job_roleHuman Resources 14.02195 383.60514 0.037
## job_roleLaboratory Technician 1.49185 0.48331 3.087
## job_roleManager 0.39092 0.88674 0.441
## job_roleManufacturing Director 0.25836 0.53005 0.487
## job_roleResearch Director -1.05126 1.00181 -1.049
## job_roleResearch Scientist 0.55346 0.49426 1.120
## job_roleSales Executive 1.20223 1.12559 1.068
## job_roleSales Representative 2.14437 1.18037 1.817
## job_satisfaction -0.46147 0.08953 -5.154
## marital_statusMarried 0.32126 0.26569 1.209
## marital_statusSingle 1.15955 0.34385 3.372
## monthly_income 0.03868 0.38212 0.101
## num_companies_worked 0.48327 0.09662 5.002
## over_timeYes 1.97011 0.19294 10.211
## percent_salary_hike -0.08023 0.14301 -0.561
## performance_rating 0.03855 0.14310 0.269
## relationship_satisfaction -0.27797 0.08909 -3.120
## stock_option_level -0.17783 0.13357 -1.331
## total_working_years -0.47701 0.22873 -2.085
## training_times_last_year -0.24730 0.09417 -2.626
## work_life_balance -0.25666 0.08721 -2.943
## years_at_company 0.57850 0.23844 2.426
## years_in_current_role -0.54984 0.16381 -3.357
## years_since_last_promotion 0.57369 0.13551 4.234
## years_with_curr_manager -0.48016 0.16796 -2.859
## Pr(>|z|)
## (Intercept) 0.962758
## age 0.020478 *
## business_travelTravel_Frequently 0.000002702 ***
## business_travelTravel_Rarely 0.005919 **
## departmentResearch & Development 0.973411
## departmentSales 0.973777
## distance_from_home 0.000019469 ***
## education 0.970961
## education_fieldLife Sciences 0.324577
## education_fieldMarketing 0.667048
## education_fieldMedical 0.265365
## education_fieldOther 0.311602
## education_fieldTechnical Degree 0.885452
## environment_satisfaction 0.000000159 ***
## genderMale 0.034939 *
## job_involvement 0.000013748 ***
## job_level 0.809386
## job_roleHuman Resources 0.970841
## job_roleLaboratory Technician 0.002024 **
## job_roleManager 0.659319
## job_roleManufacturing Director 0.625962
## job_roleResearch Director 0.294010
## job_roleResearch Scientist 0.262804
## job_roleSales Executive 0.285482
## job_roleSales Representative 0.069265 .
## job_satisfaction 0.000000255 ***
## marital_statusMarried 0.226602
## marital_statusSingle 0.000746 ***
## monthly_income 0.919373
## num_companies_worked 0.000000568 ***
## over_timeYes < 0.0000000000000002 ***
## percent_salary_hike 0.574786
## performance_rating 0.787631
## relationship_satisfaction 0.001808 **
## stock_option_level 0.183054
## total_working_years 0.037031 *
## training_times_last_year 0.008633 **
## work_life_balance 0.003249 **
## years_at_company 0.015257 *
## years_in_current_role 0.000789 ***
## years_since_last_promotion 0.000023005 ***
## years_with_curr_manager 0.004253 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1298.58 on 1469 degrees of freedom
## Residual deviance: 860.85 on 1428 degrees of freedom
## AIC: 944.85
##
## Number of Fisher Scoring iterations: 14options(scipen = 3)
# Remove Redundant Variable
bi_scaled <- bi_scaled %>%
select(-department)
# Refitting
(scaled_mod <- glm(ifelse(attrition=="Yes", 1, 0) ~.,
data = bi_scaled,
family = binomial)) %>%
summary##
## Call:
## glm(formula = ifelse(attrition == "Yes", 1, 0) ~ ., family = binomial,
## data = bi_scaled)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6383 -0.4920 -0.2548 -0.0938 3.4097
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.255992 0.965177 -5.446 5.16e-08 ***
## age -0.286685 0.123481 -2.322 0.020250 *
## business_travelTravel_Frequently 1.916549 0.409938 4.675 2.94e-06 ***
## business_travelTravel_Rarely 1.029756 0.377867 2.725 0.006427 **
## distance_from_home 0.373074 0.086912 4.293 1.77e-05 ***
## education 0.001838 0.089633 0.021 0.983637
## education_fieldLife Sciences -0.636669 0.756292 -0.842 0.399883
## education_fieldMarketing -0.210456 0.805873 -0.261 0.793975
## education_fieldMedical -0.745371 0.756263 -0.986 0.324331
## education_fieldOther -0.728186 0.822241 -0.886 0.375827
## education_fieldTechnical Degree 0.263370 0.777694 0.339 0.734870
## environment_satisfaction -0.472694 0.090303 -5.235 1.65e-07 ***
## genderMale 0.384540 0.183942 2.091 0.036569 *
## job_involvement -0.380629 0.086838 -4.383 1.17e-05 ***
## job_level -0.091126 0.348695 -0.261 0.793834
## job_roleHuman Resources 1.300441 0.674242 1.929 0.053762 .
## job_roleLaboratory Technician 1.482158 0.483232 3.067 0.002161 **
## job_roleManager 0.184607 0.786224 0.235 0.814362
## job_roleManufacturing Director 0.253002 0.529989 0.477 0.633097
## job_roleResearch Director -1.030455 0.998159 -1.032 0.301905
## job_roleResearch Scientist 0.543235 0.494240 1.099 0.271710
## job_roleSales Executive 1.018424 0.446029 2.283 0.022412 *
## job_roleSales Representative 1.956923 0.551146 3.551 0.000384 ***
## job_satisfaction -0.463738 0.089445 -5.185 2.16e-07 ***
## marital_statusMarried 0.318912 0.265685 1.200 0.230008
## marital_statusSingle 1.144697 0.343560 3.332 0.000863 ***
## monthly_income 0.042897 0.381930 0.112 0.910572
## num_companies_worked 0.486656 0.096599 5.038 4.71e-07 ***
## over_timeYes 1.973530 0.193041 10.223 < 2e-16 ***
## percent_salary_hike -0.079948 0.142665 -0.560 0.575212
## performance_rating 0.037690 0.142885 0.264 0.791949
## relationship_satisfaction -0.276487 0.088957 -3.108 0.001883 **
## stock_option_level -0.185089 0.133146 -1.390 0.164491
## total_working_years -0.481526 0.228213 -2.110 0.034860 *
## training_times_last_year -0.243712 0.094064 -2.591 0.009572 **
## work_life_balance -0.257597 0.087273 -2.952 0.003161 **
## years_at_company 0.553308 0.235679 2.348 0.018889 *
## years_in_current_role -0.538649 0.163006 -3.304 0.000952 ***
## years_since_last_promotion 0.579743 0.134794 4.301 1.70e-05 ***
## years_with_curr_manager -0.469430 0.168172 -2.791 0.005249 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1298.58 on 1469 degrees of freedom
## Residual deviance: 862.21 on 1430 degrees of freedom
## AIC: 942.21
##
## Number of Fisher Scoring iterations: 7options(scipen = 3)Among all the centered and scaled predictors, ‘over_time’ has the largest effect size. An increase of one unit in centered and scaled ‘over_time’ (i.e. one standard deviation) is associated with a change of 1.97 in the log odds of attrition rate.
Based on the above logistic regression model (and, specifically, on the coefficient with the largest effect size that you identified above), how might company policy be changed to reduce employee attrition?
Describe your proposed policy change.
Estimate and explain the change in churn probability associated with that policy change.
# Churn Probability
predict(logistic_mod,
type = "response") %>%
mean # .161## [1] 0.1612245# Churn Probability with Policy Change
predict(logistic_mod,
newdata = mutate(bi, over_time = "No",
business_travel = "Travel_Rarely"),
type = "response") %>%
mean # .095## [1] 0.09509158# Change in Churn Probability
.161 - .095## [1] 0.066Based on the above logistic regression model, BI can reduce employee’s overtime and business trip frequency. With such policy change, the churn probability can reduce from .161 to .095 with a difference of .066.
What should Angelica say in her report? Please include quantitative details from your answers to the questions above.
# Cost to Rehire a Position Saved
60000 * 1000 * .21 * .066 # 831600## [1] 831600Angelica should recommend a policy change of reducing the amount of overtime as well as business trip frequency in order to prevent employee turnover. Currently, the company-side attrition rate is at 16.1%. Attrition varies by department and position. Employee turnover is a more severe problem in the Sales Department than Research and Development Department and Human Resources Deparment with the churn rates differ by approximately 15%. Besides, generally speaking, attrition rate is much lower on the management level, compared to the other employees. Within the Sales Deparment, sales representative has an attrition rate of 39.8%, whereas, the manager has an attrition rate of 5.4%, giving a difference of 34.4%. Using a logistic regression model, we are able to find out that the amount of overtime is the strongest predictors of attrition, following by the frequent business trips. With the policy change, the churn probability can be reduced by 6.6%. In other words, out of 100 employees we would expect roughly 6 fewer employees to resign under the new policy. In terms of the cost saveing from rehiring a replacement, Bioimplants is able to save $831,600 per year by changing the policy to keep 1000 employees whose annual salary is at $60000.