Chapter B, Problem 1CSD

At the beginning of this module on page B-l, we discussed the problem of examining the effects of various predictor variables on the average automobile insurance rate in a state. From the Statistical Abstract of the United States, we obtained data on the response variable (automobile insurance rate) and 15 predictor variables for each of the 50 states.

  The data for average automobile insurance rate and five predictor variables are shown in Table A.3 (see Case Study of Module A). The data for the other 10 predictor variables are presented in Tables B.23 and B.24. Using the technology of your choice, answer the following questions.

1. a. Plot insurance rate against each predictor variable. What do these scatterplots tell you about the relationship between insurance rate and each predictor variable?
2. b. Does a multiple linear regression equation relating insurance rate to the 15 predictor variables seem appropriate for these data? Explain your answer.
3. c. Obtain the linear correlation coefficient between each pair of predictor variables. Are any of the predictor variables highly intercorrelated?
4. d. Find the variance inflation factor for each predictor variable.
5. e. Assess the severity of multicollinearity for this set of predictor variables.
6. f. Obtain the multiple linear regression equation relating insurance rate to the 15 predictor variables.
7. g. Find the proportion of the variation in the observed insurance rates that can be accounted for by the multiple linear regression equation.
8. h. Decide which predictor variables are considered useful for predicting insurance rate based on the t-tests for the individual utility of the predictor variables. Use α = 0.05.
9. i. Do you consider the t-tests in part (h) reliable for assessing the individual utility of the predictor variables? Explain your answer.
10. j. Use the stepwise regression method to obtain a subset of the predictor variables to predict insurance rates.
11. k. Find the variance inflation factors for each predictor variable in the subset obtained from the stepwise regression, and assess the severity of multicollinearity for this subset of predictor variables.
12. l. Use all-subsets regression with Mallows’ C_p criterion to select possible subsets of the predictor variables for predicting insurance rate.
13. m. Compare the subset obtained from stepwise regression with the subsets obtained from the all-subsets regression.
14. n. For the subset with the smallest value of Mallows’ C_p, perform a residual analysis to assess the appropriateness of the multiple linear regression equation, the equal-standard-deviations assumption, and the normality assumption.
15. o. Referring to the subset of predictor variables found in part (n), do you think that this subset does a good job of predicting insurance rate? Explain your answer.
16. p. Is it possible that one of the other subsets of predictor variables fits the data as well as or better than the subset with the smallest value of C_P? Explain your answer.