Refer to Examples 1–4. Suppose the collector of grandfather clocks, having observed many auctions, believes that the rate of increase in the auction price with age will be driven upward by a large number of bidders. Thus, instead of a relationship like that shown in Figure 10a , in which the rate of increase in price with age is the same for any number of bidders, the collector believes that the relationship is like that shown in Figure 10b . Note that as the number of bidders increases from 5 to 15, the slope of the price-versus-age line increases.

Consequently, the following interaction model is proposed:

y = b0 + b1 x1 + b2 x2 + b3 x1 x2 + e The 32 data points listed in Table 1 were used to fit the model with interaction. A portion of the MINITAB printout is shown in Figure 11 .

a. Use the global F -test at a = .05 to test the overall utility of the model.

b. Test the hypothesis (at a = .05 ) that the price–age slope increases as the number of bidders increases—that is, that age and number of bidders, x2, interact positively.

c. Estimate the change in auction price y of a 150-year-old grandfather clock for each additional bidder.

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Price x = 15 bidders x = 10 bidders x=5 bidders Note: All lines have Age of clock the same slope x a. No interaction between x, and x Price x= 15 bidders x = 10 bidders X = 5 bidders Age of clock b. Interaction between .x, and x