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 0.01 level or better. The regression output from the computer is as follows: DEPENDENT VARIABLE: S OBSERVATIONS: 36 VARIABLE INTERCEPT A R PARAMETER ESTIMATE 105086.0 0.4550 -0.284 R- SQUARE 0.3364 STANDARD ERROR 63821.0 0.3250 0.164 F-RATIO 4.781 T-RATIO 2.74 2.63 -1.73 P-VALUE ON F 0.0150 P-VALUE 0.0098 0.0228 0.0927 a. Does Vanguard's advertising expenditure (A) have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value. b. What fraction of the total variation in sales of Bright Side remains unexplained (undetermined)? What other explanatory variables might be added to this equation? c. What is the expected level of sales each week when Vanguard spends $20,000 per week and the combined advertising expenditures for the three rivals are $300,000 per week?
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 0.01 level or better. The regression output from the computer is as follows: DEPENDENT VARIABLE: S OBSERVATIONS: 36 VARIABLE INTERCEPT A R PARAMETER ESTIMATE 105086.0 0.4550 -0.284 R- SQUARE 0.3364 STANDARD ERROR 63821.0 0.3250 0.164 F-RATIO 4.781 T-RATIO 2.74 2.63 -1.73 P-VALUE ON F 0.0150 P-VALUE 0.0098 0.0228 0.0927 a. Does Vanguard's advertising expenditure (A) have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value. b. What fraction of the total variation in sales of Bright Side remains unexplained (undetermined)? What other explanatory variables might be added to this equation? c. What is the expected level of sales each week when Vanguard spends $20,000 per week and the combined advertising expenditures for the three rivals are $300,000 per week?
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
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Transcribed Image Text: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 0.01 level or better. The regression output from
the computer is as follows:
DEPENDENT VARIABLE: S
OBSERVATIONS: 36
VARIABLE
INTERCEPT
A
R
PARAMETER
ESTIMATE
105086.0
0.4550
-0.284
R- SQUARE
0.3364
STANDARD
ERROR
63821.0
0.3250
0.164
F-RATIO
4.781
T-RATIO
2.74
2.63
-1.73
P-VALUE ON F
0.0150
P-VALUE
0.0098
0.0228
0.0927
a. Does Vanguard's advertising expenditure (A) have a statistically significant effect on the sales of Bright
Side detergent? Explain, using the appropriate p-value. b. What fraction of the total variation in sales of
Bright Side remains unexplained (undetermined)? What other explanatory variables might be added to this
equation? c. What is the expected level of sales each week when Vanguard spends $20,000 per week and
the combined advertising expenditures for the three rivals are $300,000 per week?
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