We concluded in Exercise 15.3 that the model
y = β0 + β1xl + β2x2 + β1x22 + ε
might appropriately relate y to x1 and x2. To investigate whether interaction exists between x1 and x2, we consider the model
y = β0 + β1xl + β2x2 + β3x22 + β4x1x2 + ε
Figure 15.11 on the next page presents the MINITAB output of a regression analysis of the real estate sales price data using this model.
FIGURE 15.11
MINITAB Output of a Regression Analysis of the Real Estate Sales Price Data Using the Model y = β0 + β1xl + β2x2 + β3x22 + β4x1x2 + ε

a. Does the p-value for x1x2 indicate that this interaction variable is important? Do the p-values for the other independent variables in the model indicate that these variables are important?
b. Report and interpret a point prediction of and a 95 percent prediction interval for the sales price of an individual house having 2.000 square feet and a rating of 8 (see the bottom of the MINITAB output in Figure 15.11). Is the 95 percent prediction interval given by the model
y = β0 + β1xl + β2x2 + β3x22 + β4x1x2 + ε
shorter than the 95 percent prediction interval given by the model
y = β0 + β1xl + β2x2 + β3x22 + ε
(see the MINITAB output in Figure 15.5 on page 641). If so. what does this mean?

The regression equation is salesprice = 27.4 + 5.08 x1 + 7.29 x2-0.531 x2sq + 0.115 x1x2 Predictor Constant cl x2 x2sq x1x2 E SE Coef 27.438 3.059 8.97 0.000 5.0813 0.1476 34.42 0.000 7.2899 0.9089 8.02 0.000 -0.53110 006978-7.61 0.001 0.11473 0.03103 3.70 0.014 S- 1.00404 R-Sq 99.9% R-Sq (adj ) 99.9% = = Analysis of Variance Source Regression Residual Err 55.1.0 Total DF sS MS 4 7442.5 1860.6 1845.66 0.000 9 7447.5 Values of Predictors for New Obs Predicted Values for New Observations New Obs l 2x2x1x2 New Obs 95% cr 1 171.751 0.527 (170.396, 173.105) (168.836, 174.665) Fit SE Fit 95% PI 1 20.0 8.00 64.0 160