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