Description
In the lending industry, investors provide loans to borrowers in exchange for the promise of repayment
with interest. If the borrower repays the loan, then the lender profits from the interest. However, if the
borrower is unable to repay the loan, then the lender loses money. Therefore, lenders would like to
minimize the risk of a borrower being unable to repay a loan.
In this exercise, we will use publicly available data from LendingClub, a website that connects
borrowers and investors over the internet. The dataset is in the file Loans.csv. There are 9,578
observations, each representing a 3-year loan that was funded through the LendingClub.com platform
between May 2007 and February 2010. There are 18 variables in the dataset, described in Table 1. We
will be trying to predict NotFullyPaid, using all of the other variables as independent variables.
(a) Let us start by building a logistic regression model.
(i) First, randomly split the dataset Loans.csv into a training set and a testing set. Put 70% of the data
in the training set. What is the accuracy on the test set of a simple baseline model that predicts that all
loans will be paid back in full (NotFullyPaid = 0)? Our goal will be to build a model that adds value over
this simple baseline method.
(ii) Now, build a logistic regression model that predicts the dependent variable NotFullyPaid using
all of the other variables as independent variables. Use the training set as the data for the model.
Describe
your resulting model. Which of the independent variables are significant in your model?
(iii) Consider two loan applications, which are identical other than the fact that the borrower in
Application A has a FICO credit score of 700 while the borrower in Application B has a FICO credit score
of 710. Let Logit (A) be the value of the linear logit function of loan A not being paid back in full, according
to our logistic regression model, and define Logit (B) similarly of loan B. What is the value of Logit (A)
minus Logit (B)?
(iv) Now predict the probability of the test set loans not being paid back in full. What is the accuracy
of the logistic regression model on the test set using a threshold of 0.5? How does this compare to the
baseline model?
(b) LendingClub assigns the interest rate to a loan based on their estimate of that loan’s risk. This
variable, IntRate, is an independent variable in our dataset. In this part, we will investigate just using the
loan’s interest rate as a “Smart baseline” to order the loans according to risk.
(i) Using the training set, build a logistic regression model that predicts the dependent variable
NotFullyPaid using IntRate as the only independent variable. Is IntRate significant in this model? Was it
significant in the first logistic regression model you built? How would you explain this difference?
(ii) Use the model you just built (with only one independent variable) to make predictions for the
observations in the test set. What is the highest predicted probability of a loan not being paid back in full
on the test set? How many loans would we predict would not be paid back in full if we used a threshold of
0.5 to make predictions?
Variable Description
CreditPolicy 1 if the customer meets the credit underwriting criteria of LendingClub.com, and
0 otherwise.
Purpose.CC 1 if the purpose of the loan is related to Credit Card, and 0 otherwise.
Purpose.DC 1 if the purpose of the loan is related to Debt Consolidation, and 0 otherwise.
Purpose.Edu 1 if the purpose of the loan is related to Education, and 0 otherwise.
Purpose.MP 1 if the purpose of the loan is related to Major Purchase, and 0 otherwise.
Purpose.SB 1 if the purpose of the loan is related to Small Business, and 0 otherwise.
IntRate The interest rate of the loan, as a proportion (a rate of 11% would be stored as
0.11). Note that borrowers judged by LendingClub to be more risky are assigned
higher interests.
Installment The monthly installments ($) owed by the borrower if the loan is funded.
LogAnnualInc The natural log of the self-reported annual income of the borrower.
Dti The debt-to-income ratio of the borrower (amount of debt divided by annual
income).
Fico The FICO credit score of the borrower.
DaysWithCrLine The number of days the borrower has had a credit line.
RevolBal The borrower’s revolving balance (amount unpaid at the end of the credit billing
cycle).
RevolUtil The borrower’s revolving line utilization rate (the amount of the credit line used
relative to total credit available).
InqLast6mths The borrower’s number of inquiries by creditors in the last 6 months.
Delinq2yrs The number of times the borrower had been 30+ days past due on a payment in
the past 2 years.
PubRec The borrower’s number of derogatory public records (bankruptcy fillings, tax
liens, or judgements).
NotFullyPaid 1 if the loan was not paid back in full, and 0 otherwise.
Table 1: Variables in the dataset Loans.csv.
