ch 13. 3: 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 below concerning y (demand for Fresh liquid laundry detergent), x1 (the price of Fresh), x2 (the average industry price of competitors' similar detergents), and x3 (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 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 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. Table presents the JMP output of a regression analysis of the Fresh demand data by using the model Historical Data Concerning Demand for Fresh Detergent Sales Period Price for Fresh, x1 Average Industry Price, x2 Advertising Expenditure for Fresh, x3 Demand for Fresh, y 1 3.99 3.87 5.55 7.33 2 3.75 4.04 6.73 8.56 3 3.72 4.34 7.22 9.27 4 3.74 3.70 5.51 7.51 5 3.67 3.82 7.02 9.34 6 3.64 3.81 6.59 8.29 7 3.61 3.74 6.71 8.77 8 3.84 3.81 5.27 7.87 9 3.82 3.67 5.27 7.10 10 3.89 4.04 6.01 8.02 11 3.98 4.13 6.54 7.84 12 3.99 4.02 6.28 8.10 13 3.72 4.18 7.09 9.16 14 3.76 4.29 6.95 8.87 15 3.72 4.14 6.89 8.92 16 3.80 4.11 6.85 8.87 17 3.79 4.25 7.13 9.21 18 3.83 4.38 7.02 9.07 19 3.79 4.12 6.82 8.72 20 3.83 3.72 6.57 7.92 21 3.86 3.75 6.23 7.62 22 3.77 3.62 6.02 7.28 23 3.76 3.95 6.57 8.01 24 3.58 3.69 7.02 8.57 25 3.69 4.17 6.88 8.77 26 3.64 4.24 6.81 9.29 27 3.71 3.61 6.54 8.20 28 3.75 3.70 5.70 7.66 29 3.80 3.83 5.85 7.92 30 3.75 4.25 6.83 9.25 Advertising Campaigns Used by Enter prise Industries Sales Period Advertising Campaign 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 22 A 23 A 24 A 25 A 26 B 27 C 28 B 29 C 30 C

ch 13. 3: 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 below concerning y (demand for Fresh liquid laundry detergent), x1 (the price of Fresh), x2 (the average industry price of competitors' similar detergents), and x3 (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 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 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. Table presents the JMP output of a regression analysis of the Fresh demand data by using the model Historical Data Concerning Demand for Fresh Detergent Sales Period Price for Fresh, x1 Average Industry Price, x2 Advertising Expenditure for Fresh, x3 Demand for Fresh, y 1 3.99 3.87 5.55 7.33 2 3.75 4.04 6.73 8.56 3 3.72 4.34 7.22 9.27 4 3.74 3.70 5.51 7.51 5 3.67 3.82 7.02 9.34 6 3.64 3.81 6.59 8.29 7 3.61 3.74 6.71 8.77 8 3.84 3.81 5.27 7.87 9 3.82 3.67 5.27 7.10 10 3.89 4.04 6.01 8.02 11 3.98 4.13 6.54 7.84 12 3.99 4.02 6.28 8.10 13 3.72 4.18 7.09 9.16 14 3.76 4.29 6.95 8.87 15 3.72 4.14 6.89 8.92 16 3.80 4.11 6.85 8.87 17 3.79 4.25 7.13 9.21 18 3.83 4.38 7.02 9.07 19 3.79 4.12 6.82 8.72 20 3.83 3.72 6.57 7.92 21 3.86 3.75 6.23 7.62 22 3.77 3.62 6.02 7.28 23 3.76 3.95 6.57 8.01 24 3.58 3.69 7.02 8.57 25 3.69 4.17 6.88 8.77 26 3.64 4.24 6.81 9.29 27 3.71 3.61 6.54 8.20 28 3.75 3.70 5.70 7.66 29 3.80 3.83 5.85 7.92 30 3.75 4.25 6.83 9.25 Advertising Campaigns Used by Enter prise Industries Sales Period Advertising Campaign 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 22 A 23 A 24 A 25 A 26 B 27 C 28 B 29 C 30 C

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

ch 13. 3:

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 below concerning y (demand for Fresh liquid laundry detergent), x₁ (the price of Fresh), x₂ (the average industry price of competitors' similar detergents), and x₃ (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 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 D_C to equal 1 if campaign C is used in a sales period and 0 otherwise. Table presents the JMP output of a regression analysis of the Fresh demand data by using the model

Historical Data Concerning Demand for Fresh Detergent
Sales Period	Price for Fresh, x₁	Average Industry Price, x₂	Advertising Expenditure for Fresh, x₃	Demand for Fresh, y
1	3.99	3.87	5.55	7.33
2	3.75	4.04	6.73	8.56
3	3.72	4.34	7.22	9.27
4	3.74	3.70	5.51	7.51
5	3.67	3.82	7.02	9.34
6	3.64	3.81	6.59	8.29
7	3.61	3.74	6.71	8.77
8	3.84	3.81	5.27	7.87
9	3.82	3.67	5.27	7.10
10	3.89	4.04	6.01	8.02
11	3.98	4.13	6.54	7.84
12	3.99	4.02	6.28	8.10
13	3.72	4.18	7.09	9.16
14	3.76	4.29	6.95	8.87
15	3.72	4.14	6.89	8.92
16	3.80	4.11	6.85	8.87
17	3.79	4.25	7.13	9.21
18	3.83	4.38	7.02	9.07
19	3.79	4.12	6.82	8.72
20	3.83	3.72	6.57	7.92
21	3.86	3.75	6.23	7.62
22	3.77	3.62	6.02	7.28
23	3.76	3.95	6.57	8.01
24	3.58	3.69	7.02	8.57
25	3.69	4.17	6.88	8.77
26	3.64	4.24	6.81	9.29
27	3.71	3.61	6.54	8.20
28	3.75	3.70	5.70	7.66
29	3.80	3.83	5.85	7.92
30	3.75	4.25	6.83	9.25

Advertising Campaigns Used by Enter prise Industries
Sales Period	Advertising Campaign
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
22	A
23	A
24	A
25	A
26	B
27	C
28	B
29	C
30	C

(b) The prediction results at the bottom of the output correspond to a future period when Fresh's price will be T, = 3.76, the average
price of similar detergents will be 12 = 3.95, Fresh's advertising expenditure will be æ3 = 6.57, and advertising campaign C will be
used. Show how ý = 8.65454 is calculated. Then find, report, and interpret a 95 percent confidence interval for mean demand and a
95 percent prediction interval for an individual demand when #1 = 3.76, x2 = 3.95, r3 = 6.57, and campaign Cis used. (Round your
answers to 5 decimal places.)
y-hat
Confidence interval
Prediction interval

Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.945798
0.934505
0.17458
8.382667
30
Analysis of Variance
Sum of
Mean
Source
DF
Squares
F Ratio
Square
2.55290
Model
12.764512
83.7569
Error
24
0.731518
0.03048
Prob > F
C. Total
29
13.496030
<.0001*
Term
Estimate
Std Error
t Ratio
Prob>|t|
Lower 95%
Upper 95%
Intercept
Price(X1)
IndPrice(X2)
AdvExp(X3)
8.892705
1.643365
5.41
<0.0001*
5.5009662
12.284445
-2.658980
0.430584
-6.18
<0.0001*
-3.54766
-1.770297
0.202070
0.088002
1.4657013
7.25
<0.0001*
1.0486491
1.8827536
0.5335372
6.06
<0.0001*
0.351910
0.715165
DB
0.203502
0.079320
2.57
0.0169719*
0.0397930
0.3672100
DC
0.4647419
0.081841
5.68
<0.0001*
0.2958299
0.6336539
Predicted
Upper 95%
Indiv Demand
Lower 95%
Upper 95%
Lower 95%
Demand
Mean Demand
Mean Demand
Indiv Demand
31
8.654543531
8.538000205
8.771086856
8.275839247
9.033247814
y = 6g + 61 Ti + 82 2 + 83 3 + 84DB + e5Dc + E
%3D
Click here for the Excel Data File
(a) In this model the parameter 64 represents the effect on mean demand of advertising campaign B compared to advertising
campaign A, and the parameter 65 represents the effect on mean demand of advertising campaign C compared to advertising
campaign A. Use the regression output to find and report a point estimate of each of the above effects and to test the significance of
each of the above effects. Also, find and report a 95 percent confidence interval for each of the above effects. Interpret your results.
(Round your answers to 4 decimal places.)
The point estimate of the effect on the mean of campaign B compared to campaign A is b4 =
The 95% confidence interval = [
The point estimate of the effect on the mean of campaign C compared to campaign A is b5 =
The 95% confidence interval = [
J.
Campaign
is probably most effective even though intervals overlap.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here