Question 11.53

11.53 Bank auto loans, continued.

Table 11.4 gives the coefficients for the fitted model and the individual statistic for each explanatory variable in the study described in the previous exercise. The -values are given without the sign, assuming that all tests are two-sided.

Table 11.13: TABLE 11.4 Regression coefficients and statistics for Exercise 11.53
Variable
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 (, ) −0.009 3.02
Unsecured loan (, ) 0.034 2.19
Total payments (borrower’s monthly installment debt) 0.100 1.37
Total income (borrower’s total monthly income) −0.170 2.37
Bad credit report (, ) 0.012 1.99
Young borrower (, ) 0.027 2.85
Male borrower (, ) −0.001 0.89
Married (, ) −0.023 1.91
Own home (, ) −0.011 2.73
Years at current address −0.124 4.21

565

  1. State the null and alternative hypotheses tested by an individual statistic. What are the degrees of freedom for these statistics? What values of will lead to rejection of the null hypothesis at the 5% level?
  2. Which of the explanatory variables have coefficients that are significantly different from zero in this model? Explain carefully what you conclude when an individual statistic is not significant.
  3. The signs of many of the coefficients are what we might expect before looking at the data. For example, the negative coefficient for loan size means that larger loans get a smaller interest rate. This is reasonable. Examine the signs of each of the statistically significant coefficients and give a short explanation of what they tell us.

11.53

(a) . (b) Loan size, Length of loan, Percent down, Cosigner, Unsecured loan, Total income, Bad credit report, Young borrower, Own home, and Years at current address are significant. Those that aren’t significant only mean that the particular variable is not useful after all other variables are considered included in the model already. (c) Having a larger loan size gives a smaller interest rate. Having a longer loan gives a smaller interest rate. Having a larger percent down payment gives a smaller interest rate. Having a cosigner gives a smaller interest rate. Having an unsecured loan gives a larger interest rate. Having larger total income gives a smaller interest rate. Having a bad credit report gives a larger interest rate. Being a young borrower gives a larger interest rate. Owning a home gives a smaller interest rate. More years at current address gives a smaller interest rate.