The trend in home building in recent years has been to emphasize open spaces and great rooms, rather than smaller living rooms and family rooms. A builder of speculative homes in the college community of Oxford, Ohio, had been building such homes, but his homes had been taking many months to sell and selling for substantially less than the asking price. In order to determine what types of homes would attract residents of the community the builder contacted a statistician at a local college. The statistician went to a local real estate agency and obtained the data in Table. This table presents the sales price y, square footage x1, number of rooms x2, number of bedrooms x3, and age x4 for each of 63 single-family residences recently sold in the community. When we perform a regression analysis of these data using the model
y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε
We find that the least squares point estimates of the model parameters and their associated p-values (given in parentheses) are as shown in Table 14.17. Discuss why the estimates b2 = 6.3218 and b3 = – 11.1032 suggest that it might be more profitable when building a house of a specified square footage (1) to include both a (smaller) living room and family room rather than a (larger) great room and (2) to not increase the number of bedrooms (at the cost of another type of room) that would normally be included in a house of the specified square footage.