Chapter A, Problem 1CSD

At the beginning of this module on page A-0, we discussed studying the effect various factors might have on the average automobile insurance rate in a state. Data were obtained from the Statistical Abstract of the United States for each of the 50 states on the response variable, average automobile insurance rate, and five predictor variables: population density, automobile theft rate, automobile death rate per 100 million miles driven, average drive time to work, and average cost of a day's stay in a hospital. The data are shown in Table A3. Using the technology of your choice, answer the following questions. The data are on the WeissStats site.

1. a. Draw a scatterplot matrix of the data for the six variables. What do these scatterplots tell you about the relationship among the variables?
2. b. Does a multiple linear regression equation relating insurance rate to the five predictor variables seem appropriate for these data? Explain your answer.
3. c. Find the multiple linear regression equation relating the response variable of insurance rate to the five predictor variables.
4. d. Interpret the sample regression coefficients.
5. e. Determine the proportion of variation in the observed insurance rates that can be accounted for by the multiple linear regression equation in the five predictor variables.
6. f. Should all of the predictors remain in the regression equation?
7. g. Construct residual plots and assess the appropriateness of the multiple linear regression equation.
8. h. Construct residual plots to assess the assumptions of constant conditional standard deviation and normality.
9. i. Identify potential outliers and influential observations.
10. j. Do you think these predictor variables do a good job of predicting the response?
11. k. Suggest other possible variables that should be considered as predictors in this regression model.