EMS 1. The director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergents (R). The marketing director collects 36 weekly observations on S, A, and R to estimate the following multiple regression equation: S = a + bA + CR where S, A, and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better. a. What sign does the marketing director expect a, b, and c to have? b. Interpret the coefficients a, b, and c. The regression output from the computer is as follows: DEPENDENT VARIABLE: S A R OBSERVATIONS: 36 VARIABLE INTERCEPT PARAMETER ESTIMATE 175086.0 0.8550 -0.284 R-SQUARE 0.2247 STANDARD ERROR 63821.0 F-RATIO 4.781 0.3250 0.164 T-RATIO 2.74 2.63 -1.73 P-VALUE ON F 0.0150 P-VALUE 0.0098 0.0128 0.0927 c. Does Vanguard's advertising expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value. d. Does advertising by its three largest rivals affect sales of Bright Side detergent in a sta- tistically significant way? Explain, using the appropriate p-value. e. What fraction of the total variation in sales of Bright Side remains unexplained? What can the marketing director do to increase the explanatory power of the sales equation? What other explanatory variables might be added to this equation? f. What is the expected level of sales each week when Vanguard spends $40,000 per and the combined advertising expenditures for the three rivals are $100,000 per week week?
EMS 1. The director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergents (R). The marketing director collects 36 weekly observations on S, A, and R to estimate the following multiple regression equation: S = a + bA + CR where S, A, and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better. a. What sign does the marketing director expect a, b, and c to have? b. Interpret the coefficients a, b, and c. The regression output from the computer is as follows: DEPENDENT VARIABLE: S A R OBSERVATIONS: 36 VARIABLE INTERCEPT PARAMETER ESTIMATE 175086.0 0.8550 -0.284 R-SQUARE 0.2247 STANDARD ERROR 63821.0 F-RATIO 4.781 0.3250 0.164 T-RATIO 2.74 2.63 -1.73 P-VALUE ON F 0.0150 P-VALUE 0.0098 0.0128 0.0927 c. Does Vanguard's advertising expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value. d. Does advertising by its three largest rivals affect sales of Bright Side detergent in a sta- tistically significant way? Explain, using the appropriate p-value. e. What fraction of the total variation in sales of Bright Side remains unexplained? What can the marketing director do to increase the explanatory power of the sales equation? What other explanatory variables might be added to this equation? f. What is the expected level of sales each week when Vanguard spends $40,000 per and the combined advertising expenditures for the three rivals are $100,000 per week week?
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter4: Estimating Demand
Section: Chapter Questions
Problem 9E
Related questions
Question
Transcribed Image Text:EMS
1. The director of marketing at Vanguard Corporation believes that sales of the company's
Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditure
(A), as well as the combined advertising expenditures of its three biggest rival detergents
(R). The marketing director collects 36 weekly observations on S, A, and R to estimate the
following multiple regression equation:
S = a + bA + CR
where S, A, and R are measured in dollars per week. Vanguard's marketing director is
comfortable using parameter estimates that are statistically significant at the 10 percent
level or better.
a. What sign does the marketing director expect a, b, and c to have?
b. Interpret the coefficients a, b, and c.
The regression output from the computer is as follows:
DEPENDENT VARIABLE: S
A
R
OBSERVATIONS: 36
VARIABLE
INTERCEPT
PARAMETER
ESTIMATE
175086.0
0.8550
-0.284
R-SQUARE
0.2247
STANDARD
ERROR
63821.0
F-RATIO
4.781
0.3250
0.164
T-RATIO
2.74
2.63
-1.73
P-VALUE ON F
0.0150
P-VALUE
0.0098
0.0128
0.0927
c. Does Vanguard's advertising expenditure have a statistically significant effect on the
sales of Bright Side detergent? Explain, using the appropriate p-value.
d. Does advertising by its three largest rivals affect sales of Bright Side detergent in a sta-
tistically significant way? Explain, using the appropriate p-value.
e. What fraction of the total variation in sales of Bright Side remains unexplained? What
can the marketing director do to increase the explanatory power of the sales equation?
What other explanatory variables might be added to this equation?
f. What is the expected level of sales each week when Vanguard spends $40,000 per
and the combined advertising expenditures for the three rivals are $100,000 per
week
week?
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