install.packages("devtools", dependencies = TRUE, repos = "https://cran.rstudio.com")## Installing package into '/home/liqiuy01/R/x86_64-redhat-linux-gnu-library/3.4'
## (as 'lib' is unspecified)library(devtools)
devtools::install_github("ayhandis/creditR")## Skipping install of 'creditR' from a github remote, the SHA1 (9c7d3301) has not changed since last install.
## Use `force = TRUE` to force installationlibrary(creditR)## Loading required package: magrittr## Loading required package: woeBinning## Loading required package: cluster## Loading required package: MLmetrics##
## Attaching package: 'MLmetrics'## The following object is masked from 'package:base':
##
## Recallls("package:creditR")## [1] "Adjusted.Binomial.test"
## [2] "Adjusted.Herfindahl.Hirschman.Index"
## [3] "Anchor.point"
## [4] "bayesian.calibration"
## [5] "Binomial.test"
## [6] "chisquare.test"
## [7] "correlation.cluster"
## [8] "Gini_elimination"
## [9] "Gini.univariate"
## [10] "Gini.univariate.data"
## [11] "Herfindahl.Hirschman.Index"
## [12] "IV_elimination"
## [13] "IV.calc"
## [14] "IV.calc.data"
## [15] "k.fold.cross.validation.glm"
## [16] "Kolmogorov.Smirnov"
## [17] "master.scale"
## [18] "missing_elimination"
## [19] "missing_ratio"
## [20] "na_checker"
## [21] "na_filler_contvar"
## [22] "PSI.calc"
## [23] "PSI.calc.data"
## [24] "regression.calibration"
## [25] "scaled.score"
## [26] "SSI.calc"
## [27] "SSI.calc.data"
## [28] "train_test_balanced_split"
## [29] "train_test_split"
## [30] "variable.clustering"
## [31] "variable.clustering.gini"
## [32] "vif.calc"
## [33] "woe.get.clear.data"
## [34] "woe.glm.feature.importance"
## [35] "woe.table.calc"# Attaching the library
library(creditR)
#Model data and data structure
data("germancredit")
str(germancredit)## 'data.frame': 1000 obs. of 21 variables:
## $ status.of.existing.checking.account : Factor w/ 4 levels "... < 0 DM","... >= 200 DM / salary assignments for at least 1 year",..: 1 3 4 1 1 4 4 3 4 3 ...
## $ duration.in.month : num 6 48 12 42 24 36 24 36 12 30 ...
## $ credit.history : Factor w/ 5 levels "all credits at this bank paid back duly",..: 2 4 2 4 3 4 4 4 4 2 ...
## $ purpose : Factor w/ 11 levels "business","car (new)",..: 8 8 5 6 2 5 6 3 8 2 ...
## $ credit.amount : num 1169 5951 2096 7882 4870 ...
## $ savings.account.and.bonds : Factor w/ 5 levels "... < 100 DM",..: 5 1 1 1 1 5 4 1 2 1 ...
## $ present.employment.since : Factor w/ 5 levels "... < 1 year",..: 2 3 4 4 3 3 2 3 4 5 ...
## $ installment.rate.in.percentage.of.disposable.income : num 4 2 2 2 3 2 3 2 2 4 ...
## $ personal.status.and.sex : Factor w/ 5 levels "female : divorced/separated/married",..: 3 1 3 3 3 3 3 3 1 2 ...
## $ other.debtors.or.guarantors : Factor w/ 3 levels "co-applicant",..: 3 3 3 2 3 3 3 3 3 3 ...
## $ present.residence.since : num 4 2 3 4 4 4 4 2 4 2 ...
## $ property : Factor w/ 4 levels "building society savings agreement/ life insurance",..: 3 3 3 1 4 4 1 2 3 2 ...
## $ age.in.years : num 67 22 49 45 53 35 53 35 61 28 ...
## $ other.installment.plans : Factor w/ 3 levels "bank","none",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ housing : Factor w/ 3 levels "for free","own",..: 2 2 2 1 1 1 2 3 2 2 ...
## $ number.of.existing.credits.at.this.bank : num 2 1 1 1 2 1 1 1 1 2 ...
## $ job : Factor w/ 4 levels "management/ self-employed/ highly qualified employee/ officer",..: 4 4 3 4 4 3 4 1 3 1 ...
## $ number.of.people.being.liable.to.provide.maintenance.for: num 1 1 2 2 2 2 1 1 1 1 ...
## $ telephone : Factor w/ 2 levels "none","yes, registered under the customers name": 2 1 1 1 1 2 1 2 1 1 ...
## $ foreign.worker : Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 2 ...
## $ creditability : Factor w/ 2 levels "bad","good": 2 1 2 2 1 2 2 2 2 1 ...#Preparing a sample data set
sample_data <- germancredit[,c("duration.in.month","credit.amount","installment.rate.in.percentage.of.disposable.income", "age.in.years","creditability")]
#Converting the ???Creditability??? (default flag) variable into numeric type
sample_data$creditability <- ifelse(sample_data$creditability == "bad",1,0)
#Calculating the missing ratios
missing_ratio(sample_data)## Variable Missing_Ratio
## 1 duration.in.month 0
## 2 credit.amount 0
## 3 installment.rate.in.percentage.of.disposable.income 0
## 4 age.in.years 0
## 5 creditability 0
## Completeness
## 1 1
## 2 1
## 3 1
## 4 1
## 5 1#Splitting the data into train and test sets
traintest <- train_test_split(sample_data,123,0.70)
train <- traintest$train
test <- traintest$test
#Applying WOE transformation on the variables
woerules <- woe.binning(df = train,target.var = "creditability",pred.var = train,event.class = 1)
train_woe <- woe.binning.deploy(train, woerules, add.woe.or.dum.var='woe')
#Creating a dataset with the transformed variables and default flag
train_woe <- woe.get.clear.data(train_woe,default_flag = "creditability",prefix = "woe")
#Applying the WOE rules used on the train data to the test data
test_woe <- woe.binning.deploy(test, woerules, add.woe.or.dum.var='woe')
test_woe <- woe.get.clear.data(test_woe,default_flag = "creditability",prefix = "woe")
#Performing the IV and Gini calculations for the whole data set
IV.calc.data(train_woe,"creditability")## Variable
## 1 woe.duration.in.month.binned
## 2 woe.age.in.years.binned
## 3 woe.installment.rate.in.percentage.of.disposable.income.binned
## 4 woe.credit.amount.binned
## IV
## 1 0.27427337093608
## 2 0.147911820594104
## 3 0.054182491677713
## 4 0.0151201567965826#Creating a new dataset by Gini elimination. IV elimination is also possible
eliminated_data <- Gini_elimination(train_woe,"creditability",0.10)## Warning: glm.fit: algorithm did not convergestr(eliminated_data)## 'data.frame': 702 obs. of 4 variables:
## $ woe.duration.in.month.binned : num 142.9 -86.5 13 13 -86.5 ...
## $ woe.age.in.years.binned : num 38.5 -68.1 38.5 38.5 38.5 ...
## $ woe.installment.rate.in.percentage.of.disposable.income.binned: num -22.4 24.2 24.2 24.2 24.2 ...
## $ creditability : num 0 1 0 1 0 0 0 0 1 0 ...#A demonstration of the functions useful in performing Clustering
clustering_data <- variable.clustering(eliminated_data,"creditability", 2)
clustering_data## Group variable
## 1 1 woe.duration.in.month.binned
## 2 2 woe.age.in.years.binned
## 3 2 woe.installment.rate.in.percentage.of.disposable.income.binned# Returns the data for variables that have the maximum gini value in the dataset
selected_data <- variable.clustering.gini(eliminated_data,"creditability", 2)## Warning: glm.fit: algorithm did not convergecorrelation.cluster(eliminated_data,clustering_data,variables = "variable",clusters = "Group")## Clusters Correlation
## 1 1 NaN
## 2 2 -0.03818862#Creating a logistic regression model of the data
model= glm(formula = creditability ~ ., family = binomial(link = "logit"), data = eliminated_data)
summary(model)##
## Call:
## glm(formula = creditability ~ ., family = binomial(link = "logit"),
## data = eliminated_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5724 -0.8981 -0.7073 1.0510 2.4693
##
## Coefficients:
## Estimate
## (Intercept) -0.920051
## woe.duration.in.month.binned -0.010101
## woe.age.in.years.binned -0.010755
## woe.installment.rate.in.percentage.of.disposable.income.binned -0.009216
## Std. Error
## (Intercept) 0.088548
## woe.duration.in.month.binned 0.001801
## woe.age.in.years.binned 0.002269
## woe.installment.rate.in.percentage.of.disposable.income.binned 0.003782
## z value
## (Intercept) -10.390
## woe.duration.in.month.binned -5.607
## woe.age.in.years.binned -4.739
## woe.installment.rate.in.percentage.of.disposable.income.binned -2.437
## Pr(>|z|)
## (Intercept) < 2e-16
## woe.duration.in.month.binned 2.06e-08
## woe.age.in.years.binned 2.14e-06
## woe.installment.rate.in.percentage.of.disposable.income.binned 0.0148
##
## (Intercept) ***
## woe.duration.in.month.binned ***
## woe.age.in.years.binned ***
## woe.installment.rate.in.percentage.of.disposable.income.binned *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 840.75 on 701 degrees of freedom
## Residual deviance: 775.61 on 698 degrees of freedom
## AIC: 783.61
##
## Number of Fisher Scoring iterations: 4#Calculating variable weights
woe.glm.feature.importance(eliminated_data,model,"creditability")## Variables
## 1 woe.duration.in.month.binned
## 2 woe.age.in.years.binned
## 3 woe.installment.rate.in.percentage.of.disposable.income.binned
## beta_std importance
## 1 -0.5586544 0.4721259
## 2 -0.4093063 0.3459099
## 3 -0.2153136 0.1819642#Generating the PD values for the train and test data
ms_train_data <- cbind(eliminated_data,model$fitted.values)
ms_test_data <- cbind(test_woe[,colnames(eliminated_data)], predict(model,type = "response", newdata = test_woe))
colnames(ms_train_data) <- c("woe.duration.in.month.binned","woe.age.in.years.binned","woe.installment.rate.in.percentage.of.disposable.income.binned","creditability","PD")
colnames(ms_test_data) <- c("woe.duration.in.month.binned","woe.age.in.years.binned","woe.installment.rate.in.percentage.of.disposable.income.binned","creditability","PD")
#Generating the PD values for the train and test data
ms_train_data <- cbind(eliminated_data,model$fitted.values)
ms_test_data <- cbind(test_woe[,colnames(eliminated_data)], predict(model,type = "response", newdata = test_woe))
colnames(ms_train_data) <- c("woe.duration.in.month.binned","woe.age.in.years.binned","woe.installment.rate.in.percentage.of.disposable.income.binned","creditability","PD")
colnames(ms_test_data) <- c("woe.duration.in.month.binned","woe.age.in.years.binned","woe.installment.rate.in.percentage.of.disposable.income.binned","creditability","PD")
#Creating a master scale
master_scale <- master.scale(ms_train_data,"creditability","PD")
master_scale## Final.PD.Range Total.Observations Total.Distr Good.Count Bad.Count
## 1 <= 0.1559785868 164 23.4% 143 21
## 2 <= 0.2212992684 130 18.5% 100 30
## 3 <= 0.2441772337 106 15.1% 79 27
## 4 <= 0.3319088324 100 14.2% 68 32
## 5 <= 0.3353620015 22 3.1% 14 8
## 6 <= 0.3677802245 38 5.4% 26 12
## 7 <= 0.4369170215 37 5.3% 21 16
## 8 <= 0.4686697435 26 3.7% 16 10
## 9 <= 0.472177952 41 5.8% 22 19
## 10 <= Inf 38 5.4% 12 26
## Good.Distr Bad.Distr Bad.Rate PD Score
## 1 28.5% 10.4% 12.8% 0.12720 -1.9259458
## 2 20.0% 14.9% 23.1% 0.22088 -1.2605455
## 3 15.8% 13.4% 25.5% 0.24418 -1.1298976
## 4 13.6% 15.9% 32.0% 0.33191 -0.6995590
## 5 2.8% 4.0% 36.4% 0.33536 -0.6840410
## 6 5.2% 6.0% 31.6% 0.36778 -0.5417525
## 7 4.2% 8.0% 43.2% 0.43692 -0.2536716
## 8 3.2% 5.0% 38.5% 0.46867 -0.1254844
## 9 4.4% 9.5% 46.3% 0.47218 -0.1113950
## 10 2.4% 12.9% 68.4% 0.61282 0.4591816#Calibrating the master scale and the modeling data to the default rate of 5% using the bayesian calibration method
ms_train_data$Score = log(ms_train_data$PD/(1-ms_train_data$PD))
ms_test_data$Score = log(ms_test_data$PD/(1-ms_test_data$PD))
bayesian_method <- bayesian.calibration(data = master_scale,average_score ="Score",total_observations = "Total.Observations",PD = "PD",central_tendency = 0.05,calibration_data = ms_train_data,calibration_data_score ="Score")
#After calibration, the information and data related to the calibration process can be obtained as follows
bayesian_method$Calibration.model##
## Call:
## lm(formula = log(data$OddRatio) ~ data[, numberavg], data = data)
##
## Coefficients:
## (Intercept) data[, numberavg]
## 2.031 -1.000bayesian_method$Calibration.formula## [1] "Calibration method can be applied with: 1/(1+exp(Intercept + Score * Coefficient)) formula. Numerically : 1/(1+exp(2.03114364188451+Score *-1))"#The Scaled score can be created using the following function
scaled.score(bayesian_method$calibration_data, "calibrated_pd", 3000, 15)## woe.duration.in.month.binned woe.age.in.years.binned
## 1 142.85046 38.47006
## 2 -86.45110 -68.14996
## 3 12.98813 38.47006
## 5 12.98813 38.47006
## 6 -86.45110 38.47006
## 7 12.98813 38.47006
## 8 -86.45110 38.47006
## 9 12.98813 38.47006
## 12 -86.45110 -68.14996
## 13 12.98813 -68.14996
## 17 12.98813 38.47006
## 19 12.98813 38.47006
## 24 12.98813 38.47006
## 25 12.98813 -13.46318
## 26 142.85046 38.47006
## 28 12.98813 38.47006
## 29 12.98813 38.47006
## 30 -86.45110 38.47006
## 33 12.98813 -13.46318
## 35 12.98813 -13.46318
## 36 -86.45110 -13.46318
## 37 -86.45110 -13.46318
## 39 12.98813 38.47006
## 40 12.98813 -68.14996
## 43 12.98813 38.47006
## 44 12.98813 -68.14996
## 45 -86.45110 38.47006
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## 51 12.98813 -13.46318
## 52 12.98813 -13.46318
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## 788 -22.44737
## 790 -22.44737
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## 998 -22.44737
## 999 -22.44737
## 1000 24.24695
## creditability PD Score calibrated_pd scaled_score
## 1 0 0.07110493 -2.5698391 0.0099 3041.057
## 2 1 0.61364871 0.4626756 0.1724 2975.344
## 3 0 0.15597859 -1.6884591 0.0237 3021.862
## 5 1 0.15597859 -1.6884591 0.0237 3021.862
## 6 0 0.33536200 -0.6840320 0.0621 3000.148
## 7 0 0.15597859 -1.6884591 0.0237 3021.862
## 8 0 0.33536200 -0.6840320 0.0621 3000.148
## 9 0 0.15597859 -1.6884591 0.0237 3021.862
## 12 1 0.61364871 0.4626756 0.1724 2975.344
## 13 0 0.36778022 -0.5417515 0.0709 2997.076
## 17 0 0.22129927 -1.2581109 0.0359 3012.604
## 19 1 0.22129927 -1.2581109 0.0359 3012.604
## 24 0 0.15597859 -1.6884591 0.0237 3021.862
## 25 0 0.24417723 -1.1299126 0.0407 3009.780
## 26 0 0.04741741 -3.0001874 0.0065 3050.236
## 28 0 0.15597859 -1.6884591 0.0237 3021.862
## 29 0 0.15597859 -1.6884591 0.0237 3021.862
## 30 1 0.33536200 -0.6840320 0.0621 3000.148
## 33 0 0.24417723 -1.1299126 0.0407 3009.780
## 35 0 0.33190883 -0.6995643 0.0612 3000.485
## 36 1 0.57563085 0.3048628 0.1511 2978.748
## 37 0 0.46866974 -0.1254854 0.1037 2988.070
## 39 0 0.15597859 -1.6884591 0.0237 3021.862
## 40 0 0.47217795 -0.1114033 0.1050 2987.769
## 43 0 0.15597859 -1.6884591 0.0237 3021.862
## 44 0 0.36778022 -0.5417515 0.0709 2997.076
## 45 1 0.43691702 -0.2536837 0.0924 2990.838
## 46 0 0.22129927 -1.2581109 0.0359 3012.604
## 49 0 0.15597859 -1.6884591 0.0237 3021.862
## 50 0 0.33190883 -0.6995643 0.0612 3000.485
## 51 0 0.33190883 -0.6995643 0.0612 3000.485
## 52 0 0.24417723 -1.1299126 0.0407 3009.780
## 54 0 0.24417723 -1.1299126 0.0407 3009.780
## 55 1 0.43691702 -0.2536837 0.0924 2990.838
## 56 0 0.08005199 -2.4416409 0.0113 3038.164
## 57 1 0.15597859 -1.6884591 0.0237 3021.862
## 58 0 0.46866974 -0.1254854 0.1037 2988.070
## 60 1 0.70951380 0.8930239 0.2427 2966.022
## 61 0 0.24417723 -1.1299126 0.0407 3009.780
## 63 1 0.43691702 -0.2536837 0.0924 2990.838
## 64 1 0.46866974 -0.1254854 0.1037 2988.070
## 65 0 0.33190883 -0.6995643 0.0612 3000.485
## 67 0 0.24417723 -1.1299126 0.0407 3009.780
## 69 1 0.43691702 -0.2536837 0.0924 2990.838
## 70 0 0.57563085 0.3048628 0.1511 2978.748
## 71 0 0.46866974 -0.1254854 0.1037 2988.070
## 73 0 0.15597859 -1.6884591 0.0237 3021.862
## 75 1 0.43691702 -0.2536837 0.0924 2990.838
## 77 1 0.43691702 -0.2536837 0.0924 2990.838
## 79 0 0.33536200 -0.6840320 0.0621 3000.148
## 83 0 0.36778022 -0.5417515 0.0709 2997.076
## 84 0 0.22129927 -1.2581109 0.0359 3012.604
## 87 0 0.33190883 -0.6995643 0.0612 3000.485
## 89 0 0.33190883 -0.6995643 0.0612 3000.485
## 90 1 0.33190883 -0.6995643 0.0612 3000.485
## 91 0 0.22129927 -1.2581109 0.0359 3012.604
## 92 0 0.22129927 -1.2581109 0.0359 3012.604
## 93 1 0.33190883 -0.6995643 0.0612 3000.485
## 94 0 0.47217795 -0.1114033 0.1050 2987.769
## 95 0 0.22129927 -1.2581109 0.0359 3012.604
## 98 0 0.22129927 -1.2581109 0.0359 3012.604
## 99 0 0.43691702 -0.2536837 0.0924 2990.838
## 100 0 0.15597859 -1.6884591 0.0237 3021.862
## 102 0 0.70951380 0.8930239 0.2427 2966.022
## 103 0 0.13546484 -1.8534798 0.0201 3025.507
## 104 0 0.22129927 -1.2581109 0.0359 3012.604
## 105 0 0.24417723 -1.1299126 0.0407 3009.780
## 106 1 0.15597859 -1.6884591 0.0237 3021.862
## 108 0 0.24417723 -1.1299126 0.0407 3009.780
## 109 0 0.24417723 -1.1299126 0.0407 3009.780
## 110 0 0.15597859 -1.6884591 0.0237 3021.862
## 112 0 0.47217795 -0.1114033 0.1050 2987.769
## 114 1 0.57563085 0.3048628 0.1511 2978.748
## 115 0 0.15597859 -1.6884591 0.0237 3021.862
## 116 0 0.43691702 -0.2536837 0.0924 2990.838
## 117 1 0.57563085 0.3048628 0.1511 2978.748
## 120 0 0.15597859 -1.6884591 0.0237 3021.862
## 121 1 0.24417723 -1.1299126 0.0407 3009.780
## 124 0 0.22129927 -1.2581109 0.0359 3012.604
## 125 1 0.33190883 -0.6995643 0.0612 3000.485
## 127 0 0.22129927 -1.2581109 0.0359 3012.604
## 128 1 0.33190883 -0.6995643 0.0612 3000.485
## 129 0 0.22129927 -1.2581109 0.0359 3012.604
## 130 1 0.24417723 -1.1299126 0.0407 3009.780
## 133 0 0.24417723 -1.1299126 0.0407 3009.780
## 134 0 0.22129927 -1.2581109 0.0359 3012.604
## 135 0 0.61364871 0.4626756 0.1724 2975.344
## 136 0 0.22129927 -1.2581109 0.0359 3012.604
## 138 1 0.22129927 -1.2581109 0.0359 3012.604
## 139 0 0.22129927 -1.2581109 0.0359 3012.604
## 140 0 0.15597859 -1.6884591 0.0237 3021.862
## 141 0 0.08005199 -2.4416409 0.0113 3038.164
## 142 0 0.57563085 0.3048628 0.1511 2978.748
## 143 0 0.24417723 -1.1299126 0.0407 3009.780
## 144 1 0.36778022 -0.5417515 0.0709 2997.076
## 145 0 0.47217795 -0.1114033 0.1050 2987.769
## 146 0 0.57563085 0.3048628 0.1511 2978.748
## 147 0 0.04741741 -3.0001874 0.0065 3050.236
## 148 0 0.22129927 -1.2581109 0.0359 3012.604
## 152 0 0.15597859 -1.6884591 0.0237 3021.862
## 153 0 0.70951380 0.8930239 0.2427 2966.022
## 154 0 0.24417723 -1.1299126 0.0407 3009.780
## 155 0 0.22129927 -1.2581109 0.0359 3012.604
## 156 1 0.36778022 -0.5417515 0.0709 2997.076
## 157 0 0.15597859 -1.6884591 0.0237 3021.862
## 158 0 0.22129927 -1.2581109 0.0359 3012.604
## 160 0 0.04741741 -3.0001874 0.0065 3050.236
## 162 0 0.33190883 -0.6995643 0.0612 3000.485
## 163 0 0.22129927 -1.2581109 0.0359 3012.604
## 165 0 0.43691702 -0.2536837 0.0924 2990.838
## 166 0 0.08005199 -2.4416409 0.0113 3038.164
## 167 1 0.33190883 -0.6995643 0.0612 3000.485
## 169 0 0.24417723 -1.1299126 0.0407 3009.780
## 170 1 0.33190883 -0.6995643 0.0612 3000.485
## 172 0 0.33190883 -0.6995643 0.0612 3000.485
## 175 1 0.24417723 -1.1299126 0.0407 3009.780
## 176 1 0.22129927 -1.2581109 0.0359 3012.604
## 177 0 0.15597859 -1.6884591 0.0237 3021.862
## 178 0 0.07110493 -2.5698391 0.0099 3041.057
## 179 0 0.33190883 -0.6995643 0.0612 3000.485
## 180 0 0.22129927 -1.2581109 0.0359 3012.604
## 182 1 0.46866974 -0.1254854 0.1037 2988.070
## 183 1 0.22129927 -1.2581109 0.0359 3012.604
## 184 0 0.22129927 -1.2581109 0.0359 3012.604
## 185 1 0.22129927 -1.2581109 0.0359 3012.604
## 186 0 0.33190883 -0.6995643 0.0612 3000.485
## 187 1 0.15597859 -1.6884591 0.0237 3021.862
## 188 0 0.15597859 -1.6884591 0.0237 3021.862
## 189 1 0.47217795 -0.1114033 0.1050 2987.769
## 190 0 0.24417723 -1.1299126 0.0407 3009.780
## 191 1 0.15597859 -1.6884591 0.0237 3021.862
## 193 1 0.22129927 -1.2581109 0.0359 3012.604
## 194 0 0.08005199 -2.4416409 0.0113 3038.164
## 195 1 0.70951380 0.8930239 0.2427 2966.022
## 196 1 0.15597859 -1.6884591 0.0237 3021.862
## 198 1 0.33190883 -0.6995643 0.0612 3000.485
## 200 1 0.22129927 -1.2581109 0.0359 3012.604
## 203 0 0.24417723 -1.1299126 0.0407 3009.780
## 204 1 0.47217795 -0.1114033 0.1050 2987.769
## 205 0 0.22129927 -1.2581109 0.0359 3012.604
## 206 0 0.15597859 -1.6884591 0.0237 3021.862
## 207 0 0.22129927 -1.2581109 0.0359 3012.604
## 208 0 0.33190883 -0.6995643 0.0612 3000.485
## 209 0 0.36778022 -0.5417515 0.0709 2997.076
## 210 0 0.15597859 -1.6884591 0.0237 3021.862
## 211 0 0.24417723 -1.1299126 0.0407 3009.780
## 214 1 0.22129927 -1.2581109 0.0359 3012.604
## 215 0 0.43691702 -0.2536837 0.0924 2990.838
## 216 0 0.04741741 -3.0001874 0.0065 3050.236
## 217 0 0.24417723 -1.1299126 0.0407 3009.780
## 218 0 0.61364871 0.4626756 0.1724 2975.344
## 219 0 0.36778022 -0.5417515 0.0709 2997.076
## 220 0 0.15597859 -1.6884591 0.0237 3021.862
## 223 0 0.33190883 -0.6995643 0.0612 3000.485
## 224 0 0.33190883 -0.6995643 0.0612 3000.485
## 225 0 0.24417723 -1.1299126 0.0407 3009.780
## 226 0 0.57563085 0.3048628 0.1511 2978.748
## 227 1 0.46866974 -0.1254854 0.1037 2988.070
## 228 1 0.22129927 -1.2581109 0.0359 3012.604
## 229 1 0.47217795 -0.1114033 0.1050 2987.769
## 230 0 0.47217795 -0.1114033 0.1050 2987.769
## 231 1 0.57563085 0.3048628 0.1511 2978.748
## 232 0 0.15597859 -1.6884591 0.0237 3021.862
## 233 0 0.15597859 -1.6884591 0.0237 3021.862
## 234 0 0.33190883 -0.6995643 0.0612 3000.485
## 236 1 0.33190883 -0.6995643 0.0612 3000.485
## 237 1 0.13546484 -1.8534798 0.0201 3025.507
## 238 1 0.22129927 -1.2581109 0.0359 3012.604
## 239 0 0.22129927 -1.2581109 0.0359 3012.604
## 241 1 0.33190883 -0.6995643 0.0612 3000.485
## 242 0 0.04741741 -3.0001874 0.0065 3050.236
## 243 1 0.61364871 0.4626756 0.1724 2975.344
## 245 0 0.22129927 -1.2581109 0.0359 3012.604
## 249 0 0.24417723 -1.1299126 0.0407 3009.780
## 250 1 0.36778022 -0.5417515 0.0709 2997.076
## 252 0 0.15597859 -1.6884591 0.0237 3021.862
## 253 1 0.47217795 -0.1114033 0.1050 2987.769
## 254 0 0.15597859 -1.6884591 0.0237 3021.862
## 255 0 0.36778022 -0.5417515 0.0709 2997.076
## 257 0 0.22129927 -1.2581109 0.0359 3012.604
## 260 0 0.22129927 -1.2581109 0.0359 3012.604
## 261 0 0.24417723 -1.1299126 0.0407 3009.780
## 262 0 0.22129927 -1.2581109 0.0359 3012.604
## 263 0 0.15597859 -1.6884591 0.0237 3021.862
## 264 0 0.15597859 -1.6884591 0.0237 3021.862
## 265 0 0.24417723 -1.1299126 0.0407 3009.780
## 267 0 0.43691702 -0.2536837 0.0924 2990.838
## 270 0 0.33190883 -0.6995643 0.0612 3000.485
## 271 0 0.33190883 -0.6995643 0.0612 3000.485
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## 275 1 0.15597859 -1.6884591 0.0237 3021.862
## 276 0 0.24417723 -1.1299126 0.0407 3009.780
## 278 0 0.15597859 -1.6884591 0.0237 3021.862
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## 280 0 0.33190883 -0.6995643 0.0612 3000.485
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## 283 0 0.22129927 -1.2581109 0.0359 3012.604
## 284 0 0.22129927 -1.2581109 0.0359 3012.604
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## 292 1 0.46866974 -0.1254854 0.1037 2988.070
## 293 0 0.15597859 -1.6884591 0.0237 3021.862
## 294 0 0.43691702 -0.2536837 0.0924 2990.838
## 295 0 0.43691702 -0.2536837 0.0924 2990.838
## 296 1 0.46866974 -0.1254854 0.1037 2988.070
## 297 0 0.36778022 -0.5417515 0.0709 2997.076
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## 299 0 0.15597859 -1.6884591 0.0237 3021.862
## 300 0 0.24417723 -1.1299126 0.0407 3009.780
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## 304 0 0.22129927 -1.2581109 0.0359 3012.604
## 305 1 0.33536200 -0.6840320 0.0621 3000.148
## 307 0 0.36778022 -0.5417515 0.0709 2997.076
## 308 1 0.33190883 -0.6995643 0.0612 3000.485
## 309 1 0.36778022 -0.5417515 0.0709 2997.076
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## 312 0 0.33190883 -0.6995643 0.0612 3000.485
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## 317 0 0.15597859 -1.6884591 0.0237 3021.862
## 318 0 0.15597859 -1.6884591 0.0237 3021.862
## 320 0 0.24417723 -1.1299126 0.0407 3009.780
## 322 1 0.33190883 -0.6995643 0.0612 3000.485
## 325 0 0.22129927 -1.2581109 0.0359 3012.604
## 326 0 0.15597859 -1.6884591 0.0237 3021.862
## 327 0 0.15597859 -1.6884591 0.0237 3021.862
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## 331 0 0.15597859 -1.6884591 0.0237 3021.862
## 332 1 0.33190883 -0.6995643 0.0612 3000.485
## 333 1 0.70951380 0.8930239 0.2427 2966.022
## 334 1 0.61364871 0.4626756 0.1724 2975.344
## 336 1 0.04741741 -3.0001874 0.0065 3050.236
## 338 1 0.47217795 -0.1114033 0.1050 2987.769
## 339 0 0.33190883 -0.6995643 0.0612 3000.485
## 340 0 0.33190883 -0.6995643 0.0612 3000.485
## 341 0 0.36778022 -0.5417515 0.0709 2997.076
## 342 0 0.24417723 -1.1299126 0.0407 3009.780
## 344 0 0.24417723 -1.1299126 0.0407 3009.780
## 347 0 0.47217795 -0.1114033 0.1050 2987.769
## 348 0 0.36778022 -0.5417515 0.0709 2997.076
## 349 0 0.04741741 -3.0001874 0.0065 3050.236
## 350 1 0.33190883 -0.6995643 0.0612 3000.485
## 351 0 0.36778022 -0.5417515 0.0709 2997.076
## 354 1 0.33190883 -0.6995643 0.0612 3000.485
## 355 0 0.22129927 -1.2581109 0.0359 3012.604
## 356 1 0.47217795 -0.1114033 0.1050 2987.769
## 357 0 0.15597859 -1.6884591 0.0237 3021.862
## 358 1 0.57563085 0.3048628 0.1511 2978.748
## 359 0 0.33190883 -0.6995643 0.0612 3000.485
## 360 1 0.47217795 -0.1114033 0.1050 2987.769
## 362 0 0.15597859 -1.6884591 0.0237 3021.862
## 363 0 0.15597859 -1.6884591 0.0237 3021.862
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## 365 1 0.33190883 -0.6995643 0.0612 3000.485
## 367 0 0.24417723 -1.1299126 0.0407 3009.780
## 368 0 0.36778022 -0.5417515 0.0709 2997.076
## 370 0 0.15597859 -1.6884591 0.0237 3021.862
## 371 0 0.43691702 -0.2536837 0.0924 2990.838
## 372 0 0.24417723 -1.1299126 0.0407 3009.780
## 376 1 0.33536200 -0.6840320 0.0621 3000.148
## 378 0 0.15597859 -1.6884591 0.0237 3021.862
## 379 1 0.43691702 -0.2536837 0.0924 2990.838
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## 381 0 0.22129927 -1.2581109 0.0359 3012.604
## 382 1 0.15597859 -1.6884591 0.0237 3021.862
## 383 0 0.33190883 -0.6995643 0.0612 3000.485
## 384 0 0.33190883 -0.6995643 0.0612 3000.485
## 385 0 0.24417723 -1.1299126 0.0407 3009.780
## 386 0 0.24417723 -1.1299126 0.0407 3009.780
## 389 0 0.24417723 -1.1299126 0.0407 3009.780
## 390 0 0.24417723 -1.1299126 0.0407 3009.780
## 391 0 0.24417723 -1.1299126 0.0407 3009.780
## 392 0 0.36778022 -0.5417515 0.0709 2997.076
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## 395 0 0.24417723 -1.1299126 0.0407 3009.780
## 396 0 0.46866974 -0.1254854 0.1037 2988.070
## 397 0 0.15597859 -1.6884591 0.0237 3021.862
## 398 0 0.33536200 -0.6840320 0.0621 3000.148
## 400 0 0.22129927 -1.2581109 0.0359 3012.604
## 401 0 0.15597859 -1.6884591 0.0237 3021.862
## 402 0 0.33190883 -0.6995643 0.0612 3000.485
## 403 1 0.24417723 -1.1299126 0.0407 3009.780
## 404 0 0.33190883 -0.6995643 0.0612 3000.485
## 405 0 0.22129927 -1.2581109 0.0359 3012.604
## 407 0 0.22129927 -1.2581109 0.0359 3012.604
## 409 0 0.24417723 -1.1299126 0.0407 3009.780
## 410 1 0.33190883 -0.6995643 0.0612 3000.485
## 412 0 0.33536200 -0.6840320 0.0621 3000.148
## 413 1 0.22129927 -1.2581109 0.0359 3012.604
## 417 1 0.33190883 -0.6995643 0.0612 3000.485
## 419 0 0.24417723 -1.1299126 0.0407 3009.780
## 420 1 0.33190883 -0.6995643 0.0612 3000.485
## 421 0 0.36778022 -0.5417515 0.0709 2997.076
## 422 0 0.33190883 -0.6995643 0.0612 3000.485
## 423 0 0.15597859 -1.6884591 0.0237 3021.862
## 425 1 0.24417723 -1.1299126 0.0407 3009.780
## 427 0 0.33190883 -0.6995643 0.0612 3000.485
## 428 0 0.22129927 -1.2581109 0.0359 3012.604
## 431 0 0.04741741 -3.0001874 0.0065 3050.236
## 432 1 0.24417723 -1.1299126 0.0407 3009.780
## 434 0 0.33190883 -0.6995643 0.0612 3000.485
## 435 0 0.24417723 -1.1299126 0.0407 3009.780
## 436 1 0.24417723 -1.1299126 0.0407 3009.780
## 439 0 0.43691702 -0.2536837 0.0924 2990.838
## 441 0 0.22129927 -1.2581109 0.0359 3012.604
## 444 1 0.22129927 -1.2581109 0.0359 3012.604
## 446 0 0.22129927 -1.2581109 0.0359 3012.604
## 447 1 0.43691702 -0.2536837 0.0924 2990.838
## 448 0 0.15597859 -1.6884591 0.0237 3021.862
## 449 0 0.15597859 -1.6884591 0.0237 3021.862
## 450 1 0.15597859 -1.6884591 0.0237 3021.862
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## 454 0 0.22129927 -1.2581109 0.0359 3012.604
## 456 0 0.33190883 -0.6995643 0.0612 3000.485
## 460 0 0.24417723 -1.1299126 0.0407 3009.780
## 461 0 0.33536200 -0.6840320 0.0621 3000.148
## 463 0 0.15597859 -1.6884591 0.0237 3021.862
## 465 0 0.22129927 -1.2581109 0.0359 3012.604
## 467 1 0.33190883 -0.6995643 0.0612 3000.485
## 468 0 0.46866974 -0.1254854 0.1037 2988.070
## 469 0 0.46866974 -0.1254854 0.1037 2988.070
## 471 1 0.36778022 -0.5417515 0.0709 2997.076
## 472 1 0.19417113 -1.4231315 0.0306 3016.179
## 473 1 0.33190883 -0.6995643 0.0612 3000.485
## 474 0 0.07110493 -2.5698391 0.0099 3041.057
## 476 1 0.24417723 -1.1299126 0.0407 3009.780
## 477 0 0.70951380 0.8930239 0.2427 2966.022
## 478 0 0.33190883 -0.6995643 0.0612 3000.485
## 482 0 0.33190883 -0.6995643 0.0612 3000.485
## 484 0 0.24417723 -1.1299126 0.0407 3009.780
## 485 0 0.22129927 -1.2581109 0.0359 3012.604
## 487 0 0.15597859 -1.6884591 0.0237 3021.862
## 488 0 0.22129927 -1.2581109 0.0359 3012.604
## 489 0 0.15597859 -1.6884591 0.0237 3021.862
## 490 0 0.08005199 -2.4416409 0.0113 3038.164
## 491 0 0.24417723 -1.1299126 0.0407 3009.780
## 492 1 0.15597859 -1.6884591 0.0237 3021.862
## 493 0 0.08005199 -2.4416409 0.0113 3038.164
## 494 0 0.07110493 -2.5698391 0.0099 3041.057
## 495 0 0.15597859 -1.6884591 0.0237 3021.862
## 497 1 0.57563085 0.3048628 0.1511 2978.748
## 498 0 0.22129927 -1.2581109 0.0359 3012.604
## 499 0 0.33190883 -0.6995643 0.0612 3000.485
## 500 0 0.08005199 -2.4416409 0.0113 3038.164
## 503 0 0.15597859 -1.6884591 0.0237 3021.862
## 505 1 0.47217795 -0.1114033 0.1050 2987.769
## 506 1 0.33190883 -0.6995643 0.0612 3000.485
## 507 0 0.15597859 -1.6884591 0.0237 3021.862
## 508 1 0.15597859 -1.6884591 0.0237 3021.862
## 509 0 0.33190883 -0.6995643 0.0612 3000.485
## 510 0 0.43691702 -0.2536837 0.0924 2990.838
## 512 0 0.46866974 -0.1254854 0.1037 2988.070
## 513 0 0.24417723 -1.1299126 0.0407 3009.780
## 515 0 0.22129927 -1.2581109 0.0359 3012.604
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## 517 0 0.04741741 -3.0001874 0.0065 3050.236
## 519 0 0.04741741 -3.0001874 0.0065 3050.236
## 520 0 0.07110493 -2.5698391 0.0099 3041.057
## 521 0 0.15597859 -1.6884591 0.0237 3021.862
## 522 1 0.36778022 -0.5417515 0.0709 2997.076
## 523 1 0.33536200 -0.6840320 0.0621 3000.148
## 524 0 0.36778022 -0.5417515 0.0709 2997.076
## 526 0 0.24417723 -1.1299126 0.0407 3009.780
## 527 0 0.33190883 -0.6995643 0.0612 3000.485
## 528 0 0.04741741 -3.0001874 0.0065 3050.236
## 529 1 0.57563085 0.3048628 0.1511 2978.748
## 530 0 0.04741741 -3.0001874 0.0065 3050.236
## 532 1 0.24417723 -1.1299126 0.0407 3009.780
## 533 0 0.22129927 -1.2581109 0.0359 3012.604
## 536 1 0.24417723 -1.1299126 0.0407 3009.780
## 537 0 0.07110493 -2.5698391 0.0099 3041.057
## 539 1 0.43691702 -0.2536837 0.0924 2990.838
## 540 0 0.15597859 -1.6884591 0.0237 3021.862
## 541 1 0.36778022 -0.5417515 0.0709 2997.076
## 542 0 0.22129927 -1.2581109 0.0359 3012.604
## 543 1 0.33190883 -0.6995643 0.0612 3000.485
## 544 1 0.15597859 -1.6884591 0.0237 3021.862
## 545 0 0.22129927 -1.2581109 0.0359 3012.604
## 547 0 0.22129927 -1.2581109 0.0359 3012.604
## 548 0 0.24417723 -1.1299126 0.0407 3009.780
## 549 1 0.47217795 -0.1114033 0.1050 2987.769
## 550 0 0.33536200 -0.6840320 0.0621 3000.148
## 551 0 0.47217795 -0.1114033 0.1050 2987.769
## 552 0 0.04741741 -3.0001874 0.0065 3050.236
## 553 1 0.33536200 -0.6840320 0.0621 3000.148
## 554 0 0.33190883 -0.6995643 0.0612 3000.485
## 555 0 0.22129927 -1.2581109 0.0359 3012.604
## 556 1 0.36778022 -0.5417515 0.0709 2997.076
## 557 1 0.24417723 -1.1299126 0.0407 3009.780
## 558 1 0.24417723 -1.1299126 0.0407 3009.780
## 559 1 0.24417723 -1.1299126 0.0407 3009.780
## 560 1 0.24417723 -1.1299126 0.0407 3009.780
## 562 1 0.47217795 -0.1114033 0.1050 2987.769
## 563 0 0.08005199 -2.4416409 0.0113 3038.164
## 565 0 0.22129927 -1.2581109 0.0359 3012.604
## 566 0 0.36778022 -0.5417515 0.0709 2997.076
## 568 0 0.15597859 -1.6884591 0.0237 3021.862
## 569 0 0.43691702 -0.2536837 0.0924 2990.838
## 572 0 0.15597859 -1.6884591 0.0237 3021.862
## 573 0 0.24417723 -1.1299126 0.0407 3009.780
## 574 0 0.47217795 -0.1114033 0.1050 2987.769
## 575 0 0.33190883 -0.6995643 0.0612 3000.485
## 576 0 0.36778022 -0.5417515 0.0709 2997.076
## 577 0 0.24417723 -1.1299126 0.0407 3009.780
## 578 0 0.24417723 -1.1299126 0.0407 3009.780
## 579 1 0.57563085 0.3048628 0.1511 2978.748
## 580 0 0.33190883 -0.6995643 0.0612 3000.485
## 583 0 0.33190883 -0.6995643 0.0612 3000.485
## 585 0 0.22129927 -1.2581109 0.0359 3012.604
## 586 1 0.36778022 -0.5417515 0.0709 2997.076
## 587 0 0.15597859 -1.6884591 0.0237 3021.862
## 588 0 0.47217795 -0.1114033 0.1050 2987.769
## 589 1 0.22129927 -1.2581109 0.0359 3012.604
## 590 1 0.15597859 -1.6884591 0.0237 3021.862
## 591 0 0.22129927 -1.2581109 0.0359 3012.604
## 592 0 0.22129927 -1.2581109 0.0359 3012.604
## 595 1 0.22129927 -1.2581109 0.0359 3012.604
## 597 1 0.47217795 -0.1114033 0.1050 2987.769
## 598 1 0.15597859 -1.6884591 0.0237 3021.862
## 599 1 0.24417723 -1.1299126 0.0407 3009.780
## 600 0 0.24417723 -1.1299126 0.0407 3009.780
## 601 0 0.15597859 -1.6884591 0.0237 3021.862
## 603 1 0.22129927 -1.2581109 0.0359 3012.604
## 605 0 0.47217795 -0.1114033 0.1050 2987.769
## 606 0 0.47217795 -0.1114033 0.1050 2987.769
## 607 0 0.15597859 -1.6884591 0.0237 3021.862
## 608 1 0.43691702 -0.2536837 0.0924 2990.838
## 609 0 0.33190883 -0.6995643 0.0612 3000.485
## 611 1 0.47217795 -0.1114033 0.1050 2987.769
## 612 1 0.15597859 -1.6884591 0.0237 3021.862
## 616 0 0.33536200 -0.6840320 0.0621 3000.148
## 617 0 0.46866974 -0.1254854 0.1037 2988.070
## 618 0 0.04741741 -3.0001874 0.0065 3050.236
## 621 0 0.24417723 -1.1299126 0.0407 3009.780
## 624 0 0.47217795 -0.1114033 0.1050 2987.769
## 626 0 0.22129927 -1.2581109 0.0359 3012.604
## 627 0 0.04741741 -3.0001874 0.0065 3050.236
## 629 0 0.43691702 -0.2536837 0.0924 2990.838
## 630 0 0.15597859 -1.6884591 0.0237 3021.862
## 631 0 0.24417723 -1.1299126 0.0407 3009.780
## 632 1 0.22129927 -1.2581109 0.0359 3012.604
## 633 0 0.47217795 -0.1114033 0.1050 2987.769
## 634 1 0.36778022 -0.5417515 0.0709 2997.076
## 635 1 0.24417723 -1.1299126 0.0407 3009.780
## 637 0 0.33190883 -0.6995643 0.0612 3000.485
## 640 1 0.46866974 -0.1254854 0.1037 2988.070
## 641 1 0.33190883 -0.6995643 0.0612 3000.485
## 642 0 0.22129927 -1.2581109 0.0359 3012.604
## 644 0 0.33190883 -0.6995643 0.0612 3000.485
## 646 1 0.57563085 0.3048628 0.1511 2978.748
## 647 0 0.24417723 -1.1299126 0.0407 3009.780
## 650 1 0.22129927 -1.2581109 0.0359 3012.604
## 652 1 0.22129927 -1.2581109 0.0359 3012.604
## 654 1 0.33536200 -0.6840320 0.0621 3000.148
## 655 0 0.22129927 -1.2581109 0.0359 3012.604
## 656 0 0.36778022 -0.5417515 0.0709 2997.076
## 657 1 0.22129927 -1.2581109 0.0359 3012.604
## 658 0 0.43691702 -0.2536837 0.0924 2990.838
## 659 0 0.24417723 -1.1299126 0.0407 3009.780
## 660 0 0.15597859 -1.6884591 0.0237 3021.862
## 661 0 0.36778022 -0.5417515 0.0709 2997.076
## 662 1 0.47217795 -0.1114033 0.1050 2987.769
## 663 0 0.22129927 -1.2581109 0.0359 3012.604
## 665 0 0.04741741 -3.0001874 0.0065 3050.236
## 666 0 0.33190883 -0.6995643 0.0612 3000.485
## 667 0 0.22129927 -1.2581109 0.0359 3012.604
## 668 0 0.46866974 -0.1254854 0.1037 2988.070
## 670 0 0.22129927 -1.2581109 0.0359 3012.604
## 672 0 0.46866974 -0.1254854 0.1037 2988.070
## 673 0 0.33536200 -0.6840320 0.0621 3000.148
## 674 0 0.13546484 -1.8534798 0.0201 3025.507
## 675 1 0.22129927 -1.2581109 0.0359 3012.604
## 676 0 0.33190883 -0.6995643 0.0612 3000.485
## 677 0 0.33190883 -0.6995643 0.0612 3000.485
## 678 1 0.61364871 0.4626756 0.1724 2975.344
## 679 0 0.22129927 -1.2581109 0.0359 3012.604
## 680 0 0.24417723 -1.1299126 0.0407 3009.780
## 681 0 0.04741741 -3.0001874 0.0065 3050.236
## 682 0 0.22129927 -1.2581109 0.0359 3012.604
## 684 0 0.15597859 -1.6884591 0.0237 3021.862
## 686 0 0.43691702 -0.2536837 0.0924 2990.838
## 687 0 0.33190883 -0.6995643 0.0612 3000.485
## 688 0 0.57563085 0.3048628 0.1511 2978.748
## 689 0 0.15597859 -1.6884591 0.0237 3021.862
## 690 0 0.24417723 -1.1299126 0.0407 3009.780
## 691 0 0.24417723 -1.1299126 0.0407 3009.780
## 692 0 0.24417723 -1.1299126 0.0407 3009.780
## 693 0 0.24417723 -1.1299126 0.0407 3009.780
## 694 0 0.04741741 -3.0001874 0.0065 3050.236
## 695 0 0.33190883 -0.6995643 0.0612 3000.485
## 697 0 0.33190883 -0.6995643 0.0612 3000.485
## 700 0 0.22129927 -1.2581109 0.0359 3012.604
## 702 1 0.43691702 -0.2536837 0.0924 2990.838
## 703 0 0.22129927 -1.2581109 0.0359 3012.604
## 704 0 0.22129927 -1.2581109 0.0359 3012.604
## 705 0 0.33190883 -0.6995643 0.0612 3000.485
## 709 0 0.33190883 -0.6995643 0.0612 3000.485
## 711 0 0.33190883 -0.6995643 0.0612 3000.485
## 713 0 0.22129927 -1.2581109 0.0359 3012.604
## 714 0 0.33190883 -0.6995643 0.0612 3000.485
## 715 1 0.57563085 0.3048628 0.1511 2978.748
## 716 0 0.15597859 -1.6884591 0.0237 3021.862
## 717 0 0.15597859 -1.6884591 0.0237 3021.862
## 718 0 0.33190883 -0.6995643 0.0612 3000.485
## 719 0 0.24417723 -1.1299126 0.0407 3009.780
## 720 0 0.24417723 -1.1299126 0.0407 3009.780
## 721 1 0.22129927 -1.2581109 0.0359 3012.604
## 722 1 0.19417113 -1.4231315 0.0306 3016.179
## 726 0 0.04741741 -3.0001874 0.0065 3050.236
## 728 1 0.33190883 -0.6995643 0.0612 3000.485
## 729 1 0.43691702 -0.2536837 0.0924 2990.838
## 730 0 0.15597859 -1.6884591 0.0237 3021.862
## 732 1 0.36778022 -0.5417515 0.0709 2997.076
## 735 0 0.04741741 -3.0001874 0.0065 3050.236
## 736 0 0.46866974 -0.1254854 0.1037 2988.070
## 738 0 0.15597859 -1.6884591 0.0237 3021.862
## 739 0 0.04741741 -3.0001874 0.0065 3050.236
## 742 0 0.47217795 -0.1114033 0.1050 2987.769
## 743 0 0.22129927 -1.2581109 0.0359 3012.604
## 744 0 0.47217795 -0.1114033 0.1050 2987.769
## 745 0 0.57563085 0.3048628 0.1511 2978.748
## 746 0 0.24417723 -1.1299126 0.0407 3009.780
## 747 0 0.36778022 -0.5417515 0.0709 2997.076
## 750 0 0.24417723 -1.1299126 0.0407 3009.780
## 751 0 0.04741741 -3.0001874 0.0065 3050.236
## 752 1 0.36778022 -0.5417515 0.0709 2997.076
## 753 0 0.36778022 -0.5417515 0.0709 2997.076
## 754 0 0.33190883 -0.6995643 0.0612 3000.485
## 755 1 0.22129927 -1.2581109 0.0359 3012.604
## 756 1 0.33190883 -0.6995643 0.0612 3000.485
## 757 0 0.04741741 -3.0001874 0.0065 3050.236
## 758 1 0.15597859 -1.6884591 0.0237 3021.862
## 759 0 0.24417723 -1.1299126 0.0407 3009.780
## 760 1 0.22129927 -1.2581109 0.0359 3012.604
## 761 0 0.15597859 -1.6884591 0.0237 3021.862
## 762 1 0.47217795 -0.1114033 0.1050 2987.769
## 763 0 0.47217795 -0.1114033 0.1050 2987.769
## 764 1 0.33190883 -0.6995643 0.0612 3000.485
## 765 0 0.33190883 -0.6995643 0.0612 3000.485
## 766 0 0.15597859 -1.6884591 0.0237 3021.862
## 767 1 0.24417723 -1.1299126 0.0407 3009.780
## 768 0 0.24417723 -1.1299126 0.0407 3009.780
## 769 0 0.24417723 -1.1299126 0.0407 3009.780
## 771 0 0.24417723 -1.1299126 0.0407 3009.780
## 772 1 0.46866974 -0.1254854 0.1037 2988.070
## 774 0 0.22129927 -1.2581109 0.0359 3012.604
## 775 0 0.15597859 -1.6884591 0.0237 3021.862
## 776 1 0.33190883 -0.6995643 0.0612 3000.485
## 777 0 0.43691702 -0.2536837 0.0924 2990.838
## 778 0 0.33190883 -0.6995643 0.0612 3000.485
## 779 0 0.43691702 -0.2536837 0.0924 2990.838
## 780 0 0.15597859 -1.6884591 0.0237 3021.862
## 782 0 0.22129927 -1.2581109 0.0359 3012.604
## 783 0 0.24417723 -1.1299126 0.0407 3009.780
## 784 1 0.47217795 -0.1114033 0.1050 2987.769
## 785 0 0.15597859 -1.6884591 0.0237 3021.862
## 786 0 0.22129927 -1.2581109 0.0359 3012.604
## 788 0 0.43691702 -0.2536837 0.0924 2990.838
## 790 1 0.57563085 0.3048628 0.1511 2978.748
## 797 1 0.15597859 -1.6884591 0.0237 3021.862
## 799 0 0.22129927 -1.2581109 0.0359 3012.604
## 801 0 0.22129927 -1.2581109 0.0359 3012.604
## 802 0 0.15597859 -1.6884591 0.0237 3021.862
## 803 0 0.36778022 -0.5417515 0.0709 2997.076
## 806 1 0.61364871 0.4626756 0.1724 2975.344
## 807 0 0.08005199 -2.4416409 0.0113 3038.164
## 808 0 0.22129927 -1.2581109 0.0359 3012.604
## 809 0 0.33536200 -0.6840320 0.0621 3000.148
## 811 0 0.24417723 -1.1299126 0.0407 3009.780
## 813 1 0.70951380 0.8930239 0.2427 2966.022
## 815 1 0.43691702 -0.2536837 0.0924 2990.838
## 820 1 0.33190883 -0.6995643 0.0612 3000.485
## 821 0 0.24417723 -1.1299126 0.0407 3009.780
## 822 0 0.36778022 -0.5417515 0.0709 2997.076
## 823 1 0.33536200 -0.6840320 0.0621 3000.148
## 824 0 0.22129927 -1.2581109 0.0359 3012.604
## 826 0 0.33190883 -0.6995643 0.0612 3000.485
## 827 1 0.24417723 -1.1299126 0.0407 3009.780
## 829 1 0.33536200 -0.6840320 0.0621 3000.148
## 830 0 0.43691702 -0.2536837 0.0924 2990.838
## 832 1 0.47217795 -0.1114033 0.1050 2987.769
## 834 0 0.15597859 -1.6884591 0.0237 3021.862
## 835 1 0.24417723 -1.1299126 0.0407 3009.780
## 837 0 0.47217795 -0.1114033 0.1050 2987.769
## 838 0 0.13546484 -1.8534798 0.0201 3025.507
## 839 0 0.22129927 -1.2581109 0.0359 3012.604
## 840 0 0.22129927 -1.2581109 0.0359 3012.604
## 841 1 0.57563085 0.3048628 0.1511 2978.748
## 842 0 0.24417723 -1.1299126 0.0407 3009.780
## 843 1 0.47217795 -0.1114033 0.1050 2987.769
## 844 0 0.22129927 -1.2581109 0.0359 3012.604
## 848 0 0.33190883 -0.6995643 0.0612 3000.485
## 849 0 0.15597859 -1.6884591 0.0237 3021.862
## 850 1 0.22129927 -1.2581109 0.0359 3012.604
## 852 0 0.15597859 -1.6884591 0.0237 3021.862
## 853 0 0.22129927 -1.2581109 0.0359 3012.604
## 854 1 0.33190883 -0.6995643 0.0612 3000.485
## 855 0 0.33536200 -0.6840320 0.0621 3000.148
## 856 0 0.33190883 -0.6995643 0.0612 3000.485
## 858 0 0.33190883 -0.6995643 0.0612 3000.485
## 859 1 0.24417723 -1.1299126 0.0407 3009.780
## 861 0 0.33190883 -0.6995643 0.0612 3000.485
## 862 1 0.33190883 -0.6995643 0.0612 3000.485
## 864 0 0.33190883 -0.6995643 0.0612 3000.485
## 865 1 0.24417723 -1.1299126 0.0407 3009.780
## 866 0 0.36778022 -0.5417515 0.0709 2997.076
## 868 0 0.15597859 -1.6884591 0.0237 3021.862
## 870 0 0.47217795 -0.1114033 0.1050 2987.769
## 871 0 0.33536200 -0.6840320 0.0621 3000.148
## 872 0 0.04741741 -3.0001874 0.0065 3050.236
## 873 0 0.33190883 -0.6995643 0.0612 3000.485
## 874 0 0.47217795 -0.1114033 0.1050 2987.769
## 875 0 0.24417723 -1.1299126 0.0407 3009.780
## 876 0 0.22129927 -1.2581109 0.0359 3012.604
## 877 0 0.15597859 -1.6884591 0.0237 3021.862
## 880 0 0.15597859 -1.6884591 0.0237 3021.862
## 882 0 0.15597859 -1.6884591 0.0237 3021.862
## 883 0 0.22129927 -1.2581109 0.0359 3012.604
## 884 0 0.22129927 -1.2581109 0.0359 3012.604
## 886 1 0.22129927 -1.2581109 0.0359 3012.604
## 887 0 0.22129927 -1.2581109 0.0359 3012.604
## 889 0 0.43691702 -0.2536837 0.0924 2990.838
## 890 0 0.15597859 -1.6884591 0.0237 3021.862
## 891 0 0.22129927 -1.2581109 0.0359 3012.604
## 892 0 0.22129927 -1.2581109 0.0359 3012.604
## 893 0 0.22129927 -1.2581109 0.0359 3012.604
## 896 0 0.46866974 -0.1254854 0.1037 2988.070
## 897 0 0.33190883 -0.6995643 0.0612 3000.485
## 898 0 0.15597859 -1.6884591 0.0237 3021.862
## 899 0 0.24417723 -1.1299126 0.0407 3009.780
## 902 0 0.15597859 -1.6884591 0.0237 3021.862
## 903 0 0.33536200 -0.6840320 0.0621 3000.148
## 904 0 0.22129927 -1.2581109 0.0359 3012.604
## 905 0 0.22129927 -1.2581109 0.0359 3012.604
## 906 0 0.36778022 -0.5417515 0.0709 2997.076
## 910 0 0.24417723 -1.1299126 0.0407 3009.780
## 911 0 0.43691702 -0.2536837 0.0924 2990.838
## 912 1 0.24417723 -1.1299126 0.0407 3009.780
## 913 0 0.24417723 -1.1299126 0.0407 3009.780
## 914 0 0.24417723 -1.1299126 0.0407 3009.780
## 915 1 0.33190883 -0.6995643 0.0612 3000.485
## 916 1 0.46866974 -0.1254854 0.1037 2988.070
## 917 0 0.24417723 -1.1299126 0.0407 3009.780
## 919 1 0.24417723 -1.1299126 0.0407 3009.780
## 921 0 0.33190883 -0.6995643 0.0612 3000.485
## 922 0 0.43691702 -0.2536837 0.0924 2990.838
## 924 0 0.24417723 -1.1299126 0.0407 3009.780
## 925 1 0.15597859 -1.6884591 0.0237 3021.862
## 926 1 0.22129927 -1.2581109 0.0359 3012.604
## 927 0 0.47217795 -0.1114033 0.1050 2987.769
## 928 1 0.43691702 -0.2536837 0.0924 2990.838
## 930 0 0.22129927 -1.2581109 0.0359 3012.604
## 932 1 0.47217795 -0.1114033 0.1050 2987.769
## 933 0 0.24417723 -1.1299126 0.0407 3009.780
## 936 1 0.33190883 -0.6995643 0.0612 3000.485
## 938 0 0.11802236 -2.0112926 0.0173 3028.815
## 939 1 0.43691702 -0.2536837 0.0924 2990.838
## 940 0 0.15597859 -1.6884591 0.0237 3021.862
## 942 0 0.24417723 -1.1299126 0.0407 3009.780
## 943 0 0.33190883 -0.6995643 0.0612 3000.485
## 944 0 0.04741741 -3.0001874 0.0065 3050.236
## 945 0 0.22129927 -1.2581109 0.0359 3012.604
## 946 0 0.46866974 -0.1254854 0.1037 2988.070
## 949 1 0.22129927 -1.2581109 0.0359 3012.604
## 950 1 0.24417723 -1.1299126 0.0407 3009.780
## 951 0 0.15597859 -1.6884591 0.0237 3021.862
## 952 1 0.61364871 0.4626756 0.1724 2975.344
## 953 1 0.24417723 -1.1299126 0.0407 3009.780
## 954 1 0.57563085 0.3048628 0.1511 2978.748
## 955 0 0.33190883 -0.6995643 0.0612 3000.485
## 956 0 0.22129927 -1.2581109 0.0359 3012.604
## 957 0 0.22129927 -1.2581109 0.0359 3012.604
## 960 0 0.33190883 -0.6995643 0.0612 3000.485
## 962 0 0.15597859 -1.6884591 0.0237 3021.862
## 963 0 0.24417723 -1.1299126 0.0407 3009.780
## 965 0 0.13546484 -1.8534798 0.0201 3025.507
## 967 1 0.47217795 -0.1114033 0.1050 2987.769
## 968 0 0.22129927 -1.2581109 0.0359 3012.604
## 969 0 0.46866974 -0.1254854 0.1037 2988.070
## 970 0 0.15597859 -1.6884591 0.0237 3021.862
## 971 0 0.47217795 -0.1114033 0.1050 2987.769
## 973 1 0.24417723 -1.1299126 0.0407 3009.780
## 974 1 0.43691702 -0.2536837 0.0924 2990.838
## 975 0 0.33190883 -0.6995643 0.0612 3000.485
## 976 0 0.15597859 -1.6884591 0.0237 3021.862
## 977 0 0.04741741 -3.0001874 0.0065 3050.236
## 978 0 0.22129927 -1.2581109 0.0359 3012.604
## 980 1 0.24417723 -1.1299126 0.0407 3009.780
## 982 1 0.46866974 -0.1254854 0.1037 2988.070
## 984 1 0.46866974 -0.1254854 0.1037 2988.070
## 985 0 0.24417723 -1.1299126 0.0407 3009.780
## 988 0 0.15597859 -1.6884591 0.0237 3021.862
## 990 0 0.22129927 -1.2581109 0.0359 3012.604
## 991 0 0.15597859 -1.6884591 0.0237 3021.862
## 994 0 0.57563085 0.3048628 0.1511 2978.748
## 997 0 0.22129927 -1.2581109 0.0359 3012.604
## 998 0 0.22129927 -1.2581109 0.0359 3012.604
## 999 1 0.70951380 0.8930239 0.2427 2966.022
## 1000 0 0.46866974 -0.1254854 0.1037 2988.070#Calculating the Vif values of the variables.
vif.calc(model)## woe.duration.in.month.binned
## 1.008253
## woe.age.in.years.binned
## 1.013963
## woe.installment.rate.in.percentage.of.disposable.income.binned
## 1.007966#Calculating the Gini for the model
Gini(model$fitted.values,ms_train_data$creditability)## [1] 0.3577422#Performing the 5 Fold cross validation
k.fold.cross.validation.glm(ms_train_data,"creditability",5,1)## Warning in predict.lm(object, newdata, se.fit, scale = 1, type =
## ifelse(type == : prediction from a rank-deficient fit may be misleading## Warning in predict.lm(object, newdata, se.fit, scale = 1, type =
## ifelse(type == : prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type =
## ifelse(type == : prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type =
## ifelse(type == : prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type =
## ifelse(type == : prediction from a rank-deficient fit may be misleading## Fold GiniTrain GiniTest
## 1 1 0.400376911152315 0.151181968114349
## 2 2 0.376178390137781 0.260832625318607
## 3 3 0.315072535038112 0.505598621877692
## 4 4 0.347456161044271 0.332859848484848
## 5 5 0.355831037649219 0.328042328042328
## 6 Average 0.35898300700434 0.315703078367565#The KS test is performed on the distributions of the estimates for good and bad observations
Kolmogorov.Smirnov(ms_train_data,"creditability","PD")## Warning in ks.test(as.vector(t(Events[1])), as.vector(t(NonEvents[1]))): p-
## value will be approximate in the presence of ties## KS Statistic (%) P-Value
## D 25.46549 1.663272e-08##
## Two-sample Kolmogorov-Smirnov test
##
## data: as.vector(t(Events[1])) and as.vector(t(NonEvents[1]))
## D = 0.25465, p-value = 1.663e-08
## alternative hypothesis: two-sidedKolmogorov.Smirnov(ms_test_data,"creditability","PD")## Warning in ks.test(as.vector(t(Events[1])), as.vector(t(NonEvents[1]))): p-
## value will be approximate in the presence of ties## KS Statistic (%) P-Value
## D 12.30902 0.2691131##
## Two-sample Kolmogorov-Smirnov test
##
## data: as.vector(t(Events[1])) and as.vector(t(NonEvents[1]))
## D = 0.12309, p-value = 0.2691
## alternative hypothesis: two-sided#Variable stabilities are measured
SSI.calc.data(train_woe,test_woe,"creditability")## Variable
## 1 woe.duration.in.month.binned
## 2 woe.age.in.years.binned
## 3 woe.installment.rate.in.percentage.of.disposable.income.binned
## 4 woe.credit.amount.binned
## SSI
## 1 0.000439898132479022
## 2 0.00923101380175131
## 3 0.0151877872027667
## 4 0.00272853164681345#The HHI test is performed to measure the concentration of the master scale
Herfindahl.Hirschman.Index(master_scale,"Total.Observations")## Final.PD.Range Total.Observations Total.Distr Good.Count Bad.Count
## 1 <= 0.1559785868 164 23.4% 143 21
## 2 <= 0.2212992684 130 18.5% 100 30
## 3 <= 0.2441772337 106 15.1% 79 27
## 4 <= 0.3319088324 100 14.2% 68 32
## 5 <= 0.3353620015 22 3.1% 14 8
## 6 <= 0.3677802245 38 5.4% 26 12
## 7 <= 0.4369170215 37 5.3% 21 16
## 8 <= 0.4686697435 26 3.7% 16 10
## 9 <= 0.472177952 41 5.8% 22 19
## 10 <= Inf 38 5.4% 12 26
## Good.Distr Bad.Distr Bad.Rate PD Score SumTotal concentration
## 1 28.5% 10.4% 12.8% 0.12720 -1.9259458 702 0.23361823
## 2 20.0% 14.9% 23.1% 0.22088 -1.2605455 702 0.18518519
## 3 15.8% 13.4% 25.5% 0.24418 -1.1298976 702 0.15099715
## 4 13.6% 15.9% 32.0% 0.33191 -0.6995590 702 0.14245014
## 5 2.8% 4.0% 36.4% 0.33536 -0.6840410 702 0.03133903
## 6 5.2% 6.0% 31.6% 0.36778 -0.5417525 702 0.05413105
## 7 4.2% 8.0% 43.2% 0.43692 -0.2536716 702 0.05270655
## 8 3.2% 5.0% 38.5% 0.46867 -0.1254844 702 0.03703704
## 9 4.4% 9.5% 46.3% 0.47218 -0.1113950 702 0.05840456
## 10 2.4% 12.9% 68.4% 0.61282 0.4591816 702 0.05413105
## HHI
## 1 0.0545774791
## 2 0.0342935528
## 3 0.0228001396
## 4 0.0202920431
## 5 0.0009821349
## 6 0.0029301710
## 7 0.0027779807
## 8 0.0013717421
## 9 0.0034110924
## 10 0.0029301710## [1] 0.1463665#Performing the Anchor point test
Anchor.point(master_scale,"PD","Total.Observations",0.30)## central_tendency avg_pd lower_r lower_g upper_g upper_r
## 1 0.3 0.286326 0.2004282 0.2290608 0.3435912 0.3722238
## test_result
## 1 Green#The Chi-square test is applied on the master scale
chisquare.test(master_scale,"PD","Bad.Count","Total.Observations",0.90)## $data
## Final.PD.Range Total.Observations Total.Distr Good.Count Bad.Count
## 1 <= 0.1559785868 164 23.4% 143 21
## 2 <= 0.2212992684 130 18.5% 100 30
## 3 <= 0.2441772337 106 15.1% 79 27
## 4 <= 0.3319088324 100 14.2% 68 32
## 5 <= 0.3353620015 22 3.1% 14 8
## 6 <= 0.3677802245 38 5.4% 26 12
## 7 <= 0.4369170215 37 5.3% 21 16
## 8 <= 0.4686697435 26 3.7% 16 10
## 9 <= 0.472177952 41 5.8% 22 19
## 10 <= Inf 38 5.4% 12 26
## Good.Distr Bad.Distr Bad.Rate PD Score expected.bad
## 1 28.5% 10.4% 12.8% 0.12720 -1.9259458 20.86080
## 2 20.0% 14.9% 23.1% 0.22088 -1.2605455 28.71440
## 3 15.8% 13.4% 25.5% 0.24418 -1.1298976 25.88308
## 4 13.6% 15.9% 32.0% 0.33191 -0.6995590 33.19100
## 5 2.8% 4.0% 36.4% 0.33536 -0.6840410 7.37792
## 6 5.2% 6.0% 31.6% 0.36778 -0.5417525 13.97564
## 7 4.2% 8.0% 43.2% 0.43692 -0.2536716 16.16604
## 8 3.2% 5.0% 38.5% 0.46867 -0.1254844 12.18542
## 9 4.4% 9.5% 46.3% 0.47218 -0.1113950 19.35938
## 10 2.4% 12.9% 68.4% 0.61282 0.4591816 23.28716
## chi.square
## 1 0.0009288541
## 2 0.0575588332
## 3 0.0481979071
## 4 0.0427369166
## 5 0.0524515753
## 6 0.2792826239
## 7 0.0017053825
## 8 0.3919487860
## 9 0.0066713905
## 10 0.3160325632
##
## $p_value
## [1] 0.7261811
##
## $result
## [1] "The rating scale did not pass the test 0.726 > 0.1"#The Binomial test is applied on the master scale
master_scale$DR <- master_scale$Bad.Count/master_scale$Total.Observations
Binomial.test(master_scale,"Total.Observations","PD","DR",0.90,"one")## Final.PD.Range Total.Observations Total.Distr Good.Count Bad.Count
## 1 <= 0.1559785868 164 23.4% 143 21
## 2 <= 0.2212992684 130 18.5% 100 30
## 3 <= 0.2441772337 106 15.1% 79 27
## 4 <= 0.3319088324 100 14.2% 68 32
## 5 <= 0.3353620015 22 3.1% 14 8
## 6 <= 0.3677802245 38 5.4% 26 12
## 7 <= 0.4369170215 37 5.3% 21 16
## 8 <= 0.4686697435 26 3.7% 16 10
## 9 <= 0.472177952 41 5.8% 22 19
## 10 <= Inf 38 5.4% 12 26
## Good.Distr Bad.Distr Bad.Rate PD Score DR BadObs
## 1 28.5% 10.4% 12.8% 0.12720 -1.9259458 0.1280488 21
## 2 20.0% 14.9% 23.1% 0.22088 -1.2605455 0.2307692 30
## 3 15.8% 13.4% 25.5% 0.24418 -1.1298976 0.2547170 27
## 4 13.6% 15.9% 32.0% 0.33191 -0.6995590 0.3200000 32
## 5 2.8% 4.0% 36.4% 0.33536 -0.6840410 0.3636364 8
## 6 5.2% 6.0% 31.6% 0.36778 -0.5417525 0.3157895 12
## 7 4.2% 8.0% 43.2% 0.43692 -0.2536716 0.4324324 16
## 8 3.2% 5.0% 38.5% 0.46867 -0.1254844 0.3846154 10
## 9 4.4% 9.5% 46.3% 0.47218 -0.1113950 0.4634146 19
## 10 2.4% 12.9% 68.4% 0.61282 0.4591816 0.6842105 26
## BadEstimations TestEstimation Test_Result
## 1 20.86080 26.32918 Target Value Correct
## 2 28.71440 34.77601 Target Value Correct
## 3 25.88308 31.55139 Target Value Correct
## 4 33.19100 39.22581 Target Value Correct
## 5 7.37792 10.21581 Target Value Correct
## 6 13.97564 17.78504 Target Value Correct
## 7 16.16604 20.03258 Target Value Correct
## 8 12.18542 15.44633 Target Value Correct
## 9 19.35938 23.45599 Target Value Correct
## 10 23.28716 27.13530 Target Value Correct