Econometrics - Regression Analysis

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 10 percent level or better.

a. What sign does the marketing director expect a, b, and c to have?
b. Interpret the coefficients a, b, and c.

The regression output from the computer is as follows:
DEPENDENT VARIABLE: S R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS: 36 0.2247 4.781 0.0150
VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE
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. 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?
e. 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?

(a) "a" should be positive because even with no advertising some sales would be expected"b" should also be positive because if the company does any advertising (and the more it does) its sales should increase"c" should be negative since any advertising by the rivals will bring down the sales for Vanguard
(b) "a" is the sales assuming that neither Vanguard nor its rivals advertise"b" is the additional sales Vanguard gets per dollar of advertising cost"c" is the sales lost for each dollar used by the rivals for advertising
(c) Yes, because the p value (0.0128) < 0.10(d) 1 - R^2 = = 1 - 0.2247 = = 0.7753 is the fraction that remains unexplainedThey can increase the sample size to increase the power of the regression equation. They could add variables such as positive or negative reviews in newspapers and on television.
(e) The expected sales = 175086 + 0.855 * 40000 - 0.284 * 100000 = $180886.