5. Automobiles, including cars and light trucks, are the most held nonfinancial assets among americans, which are often financed through loans. Peter Firsov works in the car loan division of a major commercial bank. He wants to use a data-driven strategy to identify borrowers who are likely to default on the automobile loan. The accompanying data file (Default) includes historical data for 400 customers including information on whether the customer defaulted and the corresponding loan-to-value ration (LTV in %), FICO credit score (FICO), and age.
a. Estimate the linear probability model to find the predicted probability of default given the average values of LTV, FICO and Age,
b. What is the probability of default given LTV = 70, FICO = 600 and Age = 50.
c. Estimate the logistic regression model to find the predicted probability of default given the average values of LTV, FICO and Age.
Consider the logistic regression mode for default for the following questions.
d. Extend the model to also include Age-squared to find the corresponding predicted probability of default.
e. Is the Age-squared variable statistically significant at the 5% level?
f. What is the probability and odds of default given LTV = 70, FICO = 600 and Age = 50.
g. Find the corresponding probability and odds if FICO = 700.
h. Interpret the percentage change in the default odds when each predictor variable increases by one unit, holding the other