Chapter B.3, Problem 70E

Home Sale Prices. Refer to Exercise B.67 regarding the relationship between the sale price of a home and the predictor variables size in square feet and type of roof (tile or non-tile). In that exercise, we considered the regression of price on size and roof, the indicator variable for type of roof. Use the technology of your choice to obtain output similar to that in Outputs B.52–B.56 on pages B–9G–B-92.

1. a. Obtain a plot of price versus size with different plot symbols for homes having a tile roof and for homes having a non-tile roof. Based on this plot, does it appear that roof is a useful predictor variable? Explain your answer.
2. b. Obtain the regression analysis of price on size and roof. Conduct the t-tests for the individual utility of the two predictor variables at the 5% level of significance. Interpret your results.
3. c. Based on the output in part (b), obtain the individual regression equations relating price to size for homes having tile roofs and for homes having non-tile roofs.
4. d. Obtain plots of residuals versus fitted values, residuals versus size, residuals versus roof and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.
5. e. Provide a scatterplot of price versus size with the individual regression lines for homes with the roofs and homes with non-tile roofs. Based on this plot and your residual analysis from part (d), do you feel that this model fits the data well? Explain your answer.
6. f. To check for possible interaction between the two predictor variables, perform the regression analysis of price on size, roof and roof-size. Is there an interaction between size and roof that is, is the cross-product term roof-size a useful predictor variable in the regression equation that also contains size and roof? Use α = 0.05.