Recall from Exercise 14.32 (page 616) that Enterprise Industries has advertised Fresh liquid laundry detergent by using three different advertising campaigns-advertising campaign A (television commercials), advertising campaign B (a balanced mixture of television and radio commercials) and advertising campaign C (a balanced mixture of television, radio, newspaper, and magazine ads). To compare the effectiveness of these advertising campaigns, consider the model
y = β0 + β1x4 + β2x3 + β3x23 + β4x4x3 + β5DB + B6DC + ε
Here, y is demand for Fresh; x4 is the price difference; x3 is Enterprise Industries' advertising expenditure for Fresh; DB equals 1 if advertising campaign B is used in a sales period and 0 otherwise; and DC equals 1 if advertising campaign C is used in a sales period and 0 otherwise. If we use this model to perform a regression analysis of the data in Tables 14.12 (page 616) and 15.2 (page 639) we obtain the following Excel and Excel add-in (MegaStat) output:
(a) The Excel output

(b) Prediction using an Excel add-in (MegaStat)

a. In the above model the parameter β5 represents the effect on mean demand of advertising campaign B compared to advertising campaign A, and the parameter β6 represents the effect on mean demand of advertising campaign C compared to advertising campaign A. Use the regression output to And a point estimate of each of the above effects and to test the significance of each of the above effects. Also, find a 95 percent confidence interval for each of the above effects. Interpret your results.
b. Consider the alternative model
y = β0 + β1x4 + β2x3 + β3x23 + β4x4x3 + β5DA + B6DC + ε
Here DA equals l if advertising campaign A is used and 0 otherwise. The Excel output of the least squares point estimates of the parameters of this model is as follows:

Noting that represents the effect on mean demand of advertising campaign C compared to advertising campaign B, find a point estimate of and a 95 percent confidence interval for this effect. Also, test the significance of this effect. Interpret your results.
c. Consider the alternative model
y = β0 + β1x4 + β2x3 + β3x23 + β4x4x3 + β5DB + β6DB + β7x3DB + β8x3DC + ε
The Excel and Excel add-in (MegaStat) output of the least squares point estimates of the parameters of this model is as follows:

Let µ[d,a,A], µ[d,a,B], and µ[d,a,C] denote the mean demands for Fresh when the price difference is d, the advertising expenditure is d, and we use advertising campaigns A, B, and C, respectively. The model of this part implies that

Using these equations, verify that µ[d,a,C] - µ[d,a,A] equals β6 + β8a. Then, using the least squares point estimates, show that a point estimate of µ[d,a,C] - µ[d,a,A] equals .3266 when α = 6.2 and equals .4080 when α = 6.6. Also, verify that µ[d,a,C] - µ[d,a,B] equals β6 - β5 + β8a - β7a. Using the least squares point estimates, show that a point estimate µ[d,a,C] - µ[d,a,B] equals .14266 when a = 6.2 and equals .18118 when a = 6.6. Discuss why these results imply that the larger that advertising expenditure a is. then the larger is the improvement in mean sales that is obtained by using advertising campaign C rather than advertising campaign A or B.
d. The prediction results given at the bottom of the first and third Excel outputs of this exercise correspond to a future period when the price difference will be x4 = .20, the advertising expenditure will be x3 = 6.50, and campaign C will be used. Which model-the first model or the third model of this exercise-gives the shortest 95 percent prediction interval for Fresh demand? Using all of the results in this exercise, discuss why there might be a small amount of interaction between advertising expenditure and advertising campaign.

Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.9853 0.9708 0.9631 0.1308 ANOVA Significance F 1.83E-16 Regressiorn Residual 13.0650 0.3936 13.4586 2.1775 0.0171 127.2527 2 Coefficients 25.612696 9.0587 -6.5377 0.5844 -1.1565 0.2137 0.3818 Lower 95% 15.6960 2.7871 -9.8090 0.3158 Standard Error 4.7938 3.0317 t StatP-value 2.00E-05 Upper 95% 5.3429 2.9880 1.5814 4.1342 4.5001 -2.5376 3.4380 6.2328 35.5294 15.3302 3.2664 0.8531 -0.2137 0.3423 0.5085 Intercept 0.1299 0.4557 0.0622 0.0613 0.0066 0.0002 0.0022 -2.0992 0.0851 0.2551 2.33E-06 95% Confidence Interval 95% Prediction Interval Predicted 8.50068 lower 8.40370 upper 8.59765 lower 8.21322 upper 8.78813 Leverage 0.128 Coefficients 25.8264 9.05868 -6.5377 0.58444 -1.1565 0.2137 0.16809 Standard Error 4.7946 3.0317 1.5814 0.1299 0.4557 0.0622 0.0637 t Stat 5.3866 2.9880 -4.1342 4.5001 -2.5376 -3.4380 2.6385 p-value 1.80E-05 0.0066 0.0004 0,0002 0.0184 0.0022 0.0147 Lower 95% Upper 95% Intercept X4 X3 X350 X4X3 DA DC 15.9081 2.7871 9.8090 0.3158 2.0992 0.3423 0.0363 35.7447 15.3302 -3.2664 0.8531 -0.2137 0.0851 0.2999 (a) The Excel output Coefficients 28.6873 10.8253 -7.4115 0.6458 14156 0.4807 -0.9351 0.10722 0.20349 P-value 1.5E-05 0.0036 0.0002 4.79849.66E-05 Upper 95% 9.3526 17.6855 -3.9558 0.9257 0.3907 1.0393 0.8029 0.3395 0.4714 Standard Error tStat 5.5937 3.2816 Intercept X4 X3 X3SQ X4X3 DB DC X3DB X3DC 5.1285 3.2988 1.6617 4.4602 0.1346 0.4929 2.8722 0.00912 0.7309 0.6577 0.517904 0.8357 1.1189 Lower 95% 18.0221 3.9651 -10.8671 0.3659 2.4406 2.0007 -2.6731 -0.1251 -0.0644 0.9600 1.5797 0.2758 0.3480 0.1291 0.1288 (b) Prediction using an Excel add-in (MegaStat) 95% Confidence Interval 95% Prediction Interval Predicted 8.51183 lower 8.41229 upper 8.61136 lower 8.22486 upper 8.79879 Leverage 0.137 Id.aAl lda.C Po