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##### The director of marketing at Vanguard Corporation

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The director of marketing at Vanguard Corporation believes that sales of the com-;pany?s Bright Side laundry detergent (S) are related to Vanguard?s own advertising ex-;penditure (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 Rto 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 cto have?;b. Interpret the coefficients a, b, and c.;The regression output from the computer is as follows;Dependant variable: S R=Square F-Ration P-value F;P-Value on F;Observations: 36 0.2247 4.781 0.0150;Variable Parameter Standard T Ratio P-Value;Estimate Error;Intercept 175086.0 63821.0 2.74 0.0098;A 0.8550 0.3250 2.63 0.0128;R -0.284 0.164 -1.73 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;statistically 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 week;and the combined advertising expenditures for the three rivals are \$100,000 per week?

Paper#21371 | Written in 18-Jul-2015

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