hw06

library(pROC)

## Type 'citation("pROC")' for a citation.

## 
## Attaching package: 'pROC'

## The following objects are masked from 'package:stats':
## 
##     cov, smooth, var

data <- read.csv("Default.csv")

data$default <- as.factor(data$default)
model1 <- glm(default ~ income + balance, data = data, family = "binomial")

model2 <- glm(default ~ income + balance + student, data = data, family = "binomial")

model3 <- glm(default ~ balance, data = data, family = "binomial")

prob1 <- predict(model1, type = "response")
prob2 <- predict(model2, type = "response")
prob3 <- predict(model3, type = "response")

roc1 <- roc(data$default, prob1)

## Setting levels: control = No, case = Yes

## Setting direction: controls < cases

roc2 <- roc(data$default, prob2)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

roc3 <- roc(data$default, prob3)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

plot(roc1, col="blue", main="ROC Curve Comparison")
plot(roc2, col="red", add=TRUE)
plot(roc3, col="green", add=TRUE)

legend("bottomright",
       legend=c("Model 1", "Model 2", "Model 3"),
       col=c("blue","red","green"),
       lwd=2)

auc(roc1)

## Area under the curve: 0.9491

auc(roc2)

## Area under the curve: 0.9496

auc(roc3)

## Area under the curve: 0.948

The ROC curve compares the classification performance of the three models. A model with a curve closer to the top-left corner has better predictive ability. Based on the AUC values, Model X performs the best because it has the highest AUC.