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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?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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?
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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