To compare the effectiveness of advertising campaigns A , B , and C , we define

Question

     To compare the effectiveness of advertising campaigns A, B, and C, we define two dummy variables. Specifically, we define the dummy variable DB to equal 1 if campaign B is used in a sales period and 0 otherwise. Furthermore, we define the dummy variable DC to equal 1 if campaign C is used in a sales period and 0 otherwise. The table presents the Excel and Excel add-in (MegaStat) output of a regression analysis of the Fresh demand data by using the model

Enterprise Industries produces Fresh, a brand of liquid laundry detergent. In order to manage its inventory more effectively and make revenue projections, the company would like to better predict demand for Fresh. To develop a prediction model, the company has gathered data concerning demand for Fresh over the last 30 sales periods (each sales period is defined to be a four-week period). The demand data are presented in table concerning y (demand for Fresh liquid laundry detergent), (the price of Fresh), (the average industry price of competitors' similar detergents), and (Enterprise Industries’ advertising expenditure for Fresh). To ultimately increase the demand for Fresh, Enterprise Industries’ marketing department is comparing the effectiveness of three different advertising campaigns. These campaigns are denoted as campaigns A, B, and C. Campaign A consists entirely of television commercials, campaign B consists of a balanced mixture of television and radio commercials, and campaign C consists of a balanced mixture of television, radio, newspaper, and magazine ads. To conduct the study, Enterprise Industries has randomly selected one advertising campaign to be used in each of the 30 sales periods in table below. Although logic would indicate that each of campaigns A, B, and C should be used in 10 of the 30 sales periods, Enterprise Industries has made previous commitments to the advertising media involved in the study. As a result, campaigns A, B, and C were randomly assigned to, respectively, 9, 11, and 10 sales periods. Furthermore, advertising was done in only the first three weeks of each sales period, so that the carryover effect of the campaign used in a sales period to the next sales period would be minimized. Table below lists the campaigns used in the sales periods.

Explanation / Answer

From Excel

The fitted Regression is

y=6.37 -1.92(X1) +1.43(X2) +0.55(X3)

SUMMARY OUTPUT Regression Statistics Multiple R 0.931789 R Square 0.868231 Adjusted R Square 0.853027 Standard Error 0.258399 Observations 30 ANOVA df SS MS F Significance F Regression 3 11.43876 3.81292 57.1051 1.42E-11 Residual 26 1.736026 0.06677 Total 29 13.17479 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 6.368597 2.456492 2.592557 0.015431 1.319205 11.41799 1.319205 11.41799 Fresh, x1 -1.91691 0.643542 -2.97868 0.006198 -3.23973 -0.59409 -3.23973 -0.59409 Price, x2 1.435205 0.304904 4.707079 7.28E-05 0.808467 2.061944 0.808467 2.061944 for Fresh, x3 0.546461 0.127865 4.273744 0.000228 0.283631 0.809291 0.283631 0.809291

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