Question 11.55

11.55 Auto dealer loans, continued.

Table 11.5 gives the estimated regression coefficient and individual statistic for each explanatory variable in the setting of the previous exercise. The -values are given without the sign, assuming that all tests are two-sided.

  1. What are the degrees of freedom of any individual statistic for this model? What values of are significant at the 5% level? Explain carefully what significance tells us about an explanatory variable.
  2. Which of the explanatory variables have coefficients that are significantly different from zero in this model?
  3. The signs of many of these 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.

11.55

(a) . Any variable that is significant tells us that the particular variable is useful in predicting the response after all other variables are considered included in the model already. (b) Only Loan size, Length of loan, Percent down, and Unsecured loan are significant. (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 an unsecured loan gives a larger interest rate.