Question: Bank auto loans. Banks charge different interest rates for different loans. A random sample of 2229 loans made by banks for the purchase of new automobiles was studied to identify variables that explain the interest rate charged. A multiple regression was run with interest rate as the response variable and 13 explanatory variables.

Variable b t

Intercept 15.47

Loan size (in dollars) -0.0015 10.30

Length of loan (in months) -0.906 4.20

Percent down payment -0.522 8.35

Cosigner (0 = no, 1 = yes) -0.009 3.02

Unsecured loan (0 = no, 1 = yes) 0.034 2.19

Total payments (borrower’s total monthly installment debt) 0.100 1.37

Total income (borrower’s total monthly income) -0.170 2.37

Bad credit report (0 = no, 1 = yes) 0.012 1.99

Young borrower (0 = older than 25, 1 = 25 or younger) 0.027 2.85

Male borrower (0 = female, 1 = male) -0.001 0.89

Married (0 = no, 1 = yes) -0.023 1.91

Own home (0 = no, 1 = yes) -0.011 2.73

Years at current address -0.124 4.21

(a) The F statistic reported is 71.34. State the null and alternative hypotheses for this statistic. Give the degrees of freedom and the P-value for this test. What do you conclude?

(b) The value of R² is 0.297. What percent of the variation in interest is explained by the 13 explanatory variables?