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 expenditures (A), as well as 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 10 per cent level or better.
a. What sign does the marketing director expect a, b, and c to have?
The marketing director expects a, b, c to have appositive or a negative sign.
b. Interpret the coefficients a, b, c.
Coefficient a = 175086.0 when b and c are zero.
b- is greater than zero, therefore, we reject the null hypothesis (Ho: b = 0) and accept the alternative hypothesis (Ha : b < 0). At the 10 percent significance level, the t-statistic (2.63) is greater than the critical t-value (1.697).
c- co-efficient is negative and closer to and less than zero; the standard error is greater than the c-coefficient of the parameter estimate, R. The t-statistic/t-ratio (-1.73)) is smaller than the critical value (1.697) at 33 degrees of freedom.
c. Does Vanguard’s advertising expenditure have a statistically significant effect on sales of Bright Side detergent? Explain, using the appropriate p-value.
Yes, Vanguard’s advertising expenditure has a statistically significant effect on sales because: Given the t-ratio, 2.74, for advertising (b), the lowest level of significance for the co-efficient, b, is 1.28 % and it’s less than the 10% significance level. This means there is 1.28 chance that advertising expenditure does not affect sales of Bright Side laundry detergent.
d. Advertising by Vanguard’s three