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 file includes historical data for 400 customers including information on whether the customer defaulted and the corresponding loan-to-value ratio (LTV in %), FICO credit score (FICO), and age. Consider a logistic regression model for default using the predictor variables LTV, FICO, and Age.
a. Estimate the logistic regression model to find the predicted probability of default given the average values of LTV, FICO, and Age.
b. Extend the model to also include Age-squared to find the corresponding predicted probability of default.
c. Is the Age-squared variable statistically significant at the 5% level?

 

Default	LTV	FICO	Age
0	70.50	705	61
0	73.91	586	20
0	80.33	779	67
0	91.06	764	55
0	68.45	776	32
0	90.75	721	52
1	92.23	633	35
0	83.15	735	65
1	82.13	543	35
0	63.98	775	20
0	68.59	788	36
0	67.65	629	37
0	83.98	727	36
0	74.29	738	66
0	86.63	716	37
1	77.93	659	45
1	84.96	664	64
0	93.74	617	64
0	74.16	714	30
0	86.88	746	54
0	91.91	649	35
0	68.79	669	46
0	82.85	706	55
0	66.02	576	59
0	70.55	626	61
0	74.36	641	20
0	62.43	561	29
0	74.24	773	36
1	89.83	750	33