QI: Ch 4 (20%) The director of marketing at Vanguard Corporation believes that s
ID: 3370308 • Letter: Q
Question
QI: Ch 4 (20%) 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: 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 R-SQUARE 0.2964 F- RATIO 4.781 P. VALUE ON F 0.0150 STANDARD TRATIO0.0098 VARIABLE ESTIMATEERROR 638210 0.3250 0.164 T- RATIOP-VALUE 2.74 2.63 INTERCEPT 175086.0 0.4550 -0.284 0.0228 0.0927 a. Does Vanguard's advertising expenditure (A) have a statistically significant effect on b. Does advertising by its three largest rivals affect sales of Bright Side detergent in a c. What fraction of the total variation in sales of Bright Side remains unexplained d. What is the expected level of sales each week when Vanguard spends $20,000 per the sales of Bright Side detergent? Explain, using the appropriate p-value. statistically significant way? Explain, using the appropriate p-value. (undetermined)? What other explanatory variables might be added to this equation? week and the combined advertising expenditures for the three rivals are $300,000 por week?Explanation / Answer
Answer a) P value of coefficient of Vanguard's advertising expenditure (A) is 0.0228. Since P value (0.0228) is greater than level significance (0.01), Vanguard's advertising expenditure does not have a statistically significant effect on the sales of Bright Side detergent.
Answer b) P value of coefficient of advertising by its 3 largest rivals (B) is 0.0927. Since P value (0.0927) is greater than level significance (0.01), advertising by its 3 largest rivals does not have a statistically significant effect on the sales of Bright Side detergent.
Answer c) R squared value is 0.2964. This means that 29.64% variance in sales of Bright Side detergent is explained by Vanguard's advertising expenditure and advertising by its 3 largest rivals. Therefore, percentage of variance unexplained is 70.36%.
Answer d)
Regression Equation
S = 175086.0 0.4550*A -0.284*B
A = 20000
B = 300000
S = 175086.0 0.4550*20000 -0.284*300000
S = $ 98986
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