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Install required libraries

install.packages(c(“ISLR”, “caret”))

Load libraries

library(ISLR) library(caret)

Load Default data

data(“Default”, package = “ISLR”) set.seed(456)

Split data into training (70%) and validation (30%)

trainIndex <- createDataPartition(Default$default, p = 0.7, list = FALSE) train <- Default[trainIndex,] test <- Default[-trainIndex,]

Logistic Regression Model

logit_model <- glm(default ~ income + balance, data = train, family = binomial) logit_preds <- predict(logit_model, test, type = “response”) logit_class <- ifelse(logit_preds > 0.5, “Yes”, “No”)

Compute Validation Error

validation_error <- mean(logit_class != test$default) print(paste(“Validation Error:”, round(validation_error, 4)))

Repeat with different splits

set.seed(789) trainIndex2 <- createDataPartition(Default$default, p = 0.7, list = FALSE) train2 <- Default[trainIndex2,] test2 <- Default[-trainIndex2,]

logit_model2 <- glm(default ~ income + balance, data = train2, family = binomial) logit_preds2 <- predict(logit_model2, test2, type = “response”) logit_class2 <- ifelse(logit_preds2 > 0.5, “Yes”, “No”) validation_error2 <- mean(logit_class2 != test2$default)

print(paste(“Second Validation Error:”, round(validation_error2, 4)))

Adding Student Variable

logit_model_student <- glm(default ~ income + balance + student, data = train, family = binomial) logit_preds_student <- predict(logit_model_student, test, type = “response”) logit_class_student <- ifelse(logit_preds_student > 0.5, “Yes”, “No”) validation_error_student <- mean(logit_class_student != test$default)

print(paste(“Validation Error with Student:”, round(validation_error_student, 4)))