Question

DEPENDENT VARIABLE: S R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 36 0.2247 4.781 0.0150 PARAMETER ESTIMATE STANDARD ERROR VARIABLE T-RATIO P- VALUE INTERCEPT 175086.0 0.8550 63821.0 0.3250 0.164 2.74 2.63 0.0098 0.0128 0.0927 0.284 1.73

1. The director of marketing at Vanguard Corporationbelieves 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 weeklyobservations 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 levelor better.

1. What sign does the marketing director expect a, b, and c to have?
2. Interpret the coefficients a, b, and c.
   The regression output from the computer is as follows:

3. Does Vanguard’s advertising expenditurehave a statistically significant effect on the salesof Bright Side detergent? Explain, using the appropriate p-value.

4. Does advertising by its three largest rivals affect sales of Bright Side detergent in a statistically significant way? Explain, using the appropriate p-value.
5. 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?

Answer 1

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