Figure 14.22 presents the Excel output of a regression analysis of the Fresh demand data using the model
y = β0 + β1x1 + β2x2 + β3x3 + β4D4 + β5DC + β5DC + β6x3DB + β7x3DC + ε
FIGURE 14.22
Excel Output of a Regression Analysis of the Fresh Demand Data Using the Model y = β0 + β1x1 + β2x2 + β3x3 + β4D4 + β5DC + β5DC + β6x3DB + β7x3DC + ε

where the dummy variables DB and DC are defined as in Exercise 14.32.
a. This model assumes that there is interaction between advertising expenditure x3 and type of advertising campaign. What do the p-values related to the significance of the cross-product terms x3DB and x3DC say about the need for these interaction terms and about whether there is interaction between x3 and type of advertising campaign?
b. The prediction results at the bottom of Figure 14.22 are for a future sales period in which x1 = 3.70, x2 = 3.90, x3 = 6.50, and advertising campaign C will be used. Use the output to find and report a point prediction of and a 95 percent prediction interval for Fresh demand in such a sales period. Is the 95 percent prediction interval given by this model shorter or longer than the 95 percent prediction interval given by the model that utilizes DH and DC in Exercise 14.32? What are the implications of this comparison?

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intercept Price (X1) Ind Price (X2) AdvExp (X3) DB DC X3DB X3DC Coefficients 8.7619 2.7895 1.6365 0.5160 0.2539 0.8435 0.0030 0.0629 Standard Error 1.7071 0.4339 0.2062 0.1288 0.8722 0.9739 0.1334 0.1502 t Stat 5.1327 6.4284 7.9376 4.0069 0.2911 0.8661 0.0226 0.4189 P-value 3.82E-05 1.81E-06 6.72E-08 0.0006 0.7737 0.3958 0.9822 0.6794 Lower 95% 5.2217 3.6894 1.2089 0.2489 -1.5550 1.1762 0.2736 0.3744 Upper 95% 12.3021 -1.8895 2.0641 0.7831 2.0628 2.8631 0.2797 0.2486 R2 0.960 Adjusted R 0.948 R 0.980 Std, Error 0.156 Predicted values for: Demand using an Excel add-in (MegaStat) Predicted 8.61178 95% Confidence Interval upper 8.71984 lower 8.50372 95% Prediction Interval upper 8.95266 lower 8.27089 Leverage 0.112