1. Consider the Default dataset available in ISLR library. The Default dataset provides information on 10,000 customers. Furthermore, the dataset contains four variables as follows:

Table 1: Variable Description

Variables	Description
Default	A factor with levels No and Yes indicating whether the customer defaulted on their debt.
Student	A factor with levels No and Yes indicating whether the customer is a student.
Balance	The average balance that the customer has remaining on their credit card after making their monthly payment.
Income	Income of customer.

The objective is to predict whether an individual will default on his/her credit card payment. The data set is divided in two partsa training set consisting of 5000 observations and a test set consisting of the remaining 5000 observations. Following results are available:

Table 2: Logistic Regression Model (Model 1) for predicting default using student

based on the Training Data Set

	Estimate	Standard Error	value	-value
Intercept	3.482	0.099	35.312	0.000
studentYes	0.307	0.166	1.845	0.065

Note that studentYes is a dummy variable which takes the value 1 if the individual is a student and 0 otherwise. Furthermore, another logistic regression model using the variables student and balance is fitted based on the training data set. The details are provided below:

Table 3: Logistic Regression Model (Model 2) for predicting default using balance and student based on the Training Data Set

	Estimate	Standard Error	value	-value
Intercept	11.020	0.7130	15.446	0.000
balance	0.006	0.0003	17.383	0.000
studentYes	0.822	0.3401	2.416	0.016

Based on the fitted logistic regression model (Model 2), a confusion matrix is obtained for the test dataset. The confusion matrix is shown below.

Table 4: Confusion Matrix Based on Test Data Set for Logistic Regression

True Default Status
Predicted Default Status		No	Yes
	No	4808	120
	Yes	23	49

Based on the above output, answer the following questions (no need to fit any of the models):

1. Write the equation of the fitted Model 1 (summary provided in Table 2). Calculate the predicted default probabilities for an individual who is a student and for an individual who is not a student. Who is riskier for the credit card company? [3]

2. Consider the fitted Model 2 (summary provided in Table 3). Interpret the coefficients. Discuss the difference between Models 1 and 2. [4]

3. Suppose the credit card company wants to provide a credit card only to those customers who have the predicted default probability below 0.10. Recently, a student has approached the credit card company. Based on the fitted Model 2 (summary provided in Table 3), calculate the maximum allowed balance for such an individual. [3]

4. Based on the confusion matrix shown above (in Table 4), compute the sensitivity, specificity and total error rate for the logistic regression model. [3]

5. Discuss how the performance of the logistic regression model can be improved.

[3]

6. The logistic regression model uses here only a limited number of predictors. Identify at least 5 more predictors that can be useful in this context. [3]
7. How will you use such a logistic regression model for decision-making in this context?

[3]

What are the possible downsides of such a model? Discuss in detail.