Chapter B.3, Problem 67E

Home Sale Prices. Refer to Example B.18 on page B-67, regarding the relationship between the sale price of a home and its size in square feet. In that example, we used the presence/absence of a swimming pool as a qualitative predictor variable. Here we consider using the type of roof on the home as a predictor variable. The homes in this data set have either a tile roof or a non-tile roof. The data for the 88 homes are in the table on page B-89.

We introduced the indicator variable roof defined by

Roof = $\{\begin{array}{c}1,\text{If home has a tile roof;}\\ 0,\text{If home has a non-tile roof}\text{.}\end{array}$

1. a. Output B.52 on page B-90 shows a plot of price versus size, with the plot symbol being a solid black circle 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. We obtained the regression analysis of price on size and roof shown in Output B.53 on page B-90. 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 Output B.53, obtain the individual regression equations relating price to size for homes having tile roofs and for homes having non-tile roofs.
4. d. Outputs B.54(a)–(d) on page B-91 provide plots of residuals versus fitted values, residuals versus size, residuals versus roof, and a normal probability plot of residuals, respectively. 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. Output B.55 on page B-91 provides a plot of price versus size with the regression lines for homes with tile roofs and with non-tile roofs. Based on this output and your residual analysis in 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, we obtained the regression analysis of price on size, roof and roof size. The output is in Output B.56 on page B-92. 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.

Regression Analysis: PRICE versus SIXE, ROOF

OUTPUT B.53

Regression output for Exercise B.67

OUTPUT B.56 Regression output for Exercise B.67

Regression Analysis: PRICE versus SIZE, ROOF, ROOF*SIZE