Mathematics
Mathematics, 02.06.2020 23:58, SmokeyRN

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 Freshliquid laundry detergent), (the price of Fresh), (the average industry price of competitors' similar detergents), and (Enterprise Industriesâ advertising expenditure for Fresh). To ultimately increase the demand for Fresh, Enterprise Industriesâ marketing department is comparing the effectiveness of three different advertising campaigns. These campaigns are denoted ascampaignsA, B, and C. CampaignAconsists 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 the30 sales periods in the 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. The table below lists the campaigns used in the sales periods.

To compare the effectiveness of advertising campaigns A, B, and C, we define two dummy variables. Specifically, we define the dummy variable D_B 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 Exceladd-in (MegaStat) output of a regression analysis of the Fresh demand data by using the model:

Historical Data Concerning Demand for Fresh Detergent
Sales Price Average Advertising Demand
Period forFresh, x1 Industry Expenditure for Fresh, y
Price, x2 for Fresh, x3
1 3.85 3.87 5.59 7.39
2 3.72 4.07 6.72 8.52
3 3.77 4.39 7.22 9.21
4 3.74 3.77 5.57 7.55
5 3.68 3.85 7.02 9.33
6 3.65 3.87 6.57 8.23
7 3.62 3.73 6.79 8.78
8 3.82 3.83 5.20 7.81
9 3.89 3.60 5.27 7.14
10 3.84 4.03 6.08 8.05
11 3.97 4.13 6.57 7.85
12 3.92 4.05 6.23 8.16
13 3.75 4.18 7.08 9.15
14 3.75 4.20 6.90 8.84
15 3.78 4.14 6.82 8.94
16 3.86 4.11 6.84 8.87
17 3.72 4.20 7.11 9.29
18 3.86 4.38 7.04 9.06
19 3.73 4.17 6.82 8.75
20 3.83 3.77 6.54 7.98
21 3.80 3.78 6.26 7.66
22 3.79 3.65 6.02 7.26
23 3.75 3.97 6.57 8.05
24 3.54 3.68 7.08 8.55
25 3.64 4.16 6.82 8.78
26 3.64 4.21 6.84 9.22
27 3.71 3.68 6.55 8.25
28 3.70 3.73 5.70 7.60
29 3.82 3.87 5.85 7.95
30 3.79 4.25 6.84 9.29

Advertising Campaigns Used
by Enterprise Industries
SalesPeriod AdvertisingCampaign
1 B
2 B
3 B
4 A
5 C
6 A
7 C
8 C
9 B
10 C
11 A
12 C
13 C
14 A
15 B
16 B
17 B
18 A
19 B
20 B
21 C

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