Chapter B.5, Problem 106E

Home Sale Prices. In Example B.18 on page B-67, we considered the regression analysis of sale price of a home based on its size and the presence of a swimming pool for 88 homes in northeast Phoenix. In this exercise, we add information on seven additional predictor variables for each home: area of the lot, age of the home, number of baths, number of stories, number of garage stalls, whether or not the home is on a street with busy traffic, and whether or not the home has a tile roof. The data, which were provided by T. Helmer, are displayed in the table on pages B-142–B-143. Use the technology of your choice to do the following.

a. Use the forward selection method to obtain a regression equation for the data. (Take t_enter = 2.00, α_enter = 0.05.)

b. Use the backward elimination method to obtain a regression equation for the data. (Take t_remove = 2.00, α_remove = 0.05.)

c. Use stepwise regression to obtain a regression equation for the data. (Take t_enter = t_remove = 2.00, α_enter = α_remove = 0.05.)

d. Are the regression equations obtained in parts (a), (b), and (c) the same?

e. For the regression equation selected by stepwise regression in part (c), obtain plots of residuals versus fitted values, residuals versus the included predictor variables, 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.