Question

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 0.10 level or better. The regression output from the computer is as follows:

DEPENDENT VARIABLE: S                             R-SQUARE                           F-RATIO               P-VALUE ON F

OBSERVATIONS: 36                                         0.2964                                   4.781                     0.0150

                                                PARAMETER       STANDARD        

VARIABLE                            ESTIMATE            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

a. Interpret the sign of coefficients a, b, and c.

b. Does Vanguard’s advertising expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value.

c. Does advertising by its three largest rivals affect sales of Bright Side detergent in a 1 statistically significant way? 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 $30,000 per week and the combined advertising expenditures for the three rivals are $200,000 per week?

Answer 1

a.

a = 175086 is the intercept team. It suggests the average sale when A and R are equal to 0.

b= 0.8550 tells us about the positive association of Sales with advertising expenditure

c = -0.284 indicates a negative relationship between Sales of Vanguard corporation with combined advertising expenditures of its three biggest rival detergents.

b.

At 10% level of significance, Vanguard’s advertising expenditure has a statistically significant effect on the sales of its detergent. This can be verified by looking at p-value which is 0.0128 and lower than 0.10.

The result holds true even at 5% level of significance.

c.

At 10% level of significance, Vanguard’s advertising by its three largest rivals has a statistically significant effect on the sales of its detergent. This can be verified by looking at p-value which is 0.0128 and lower than 0.10.

The result however doesn’t hold true even at 5% level of significance.

d. This model only explains 29.64% of the variation in sales. It implies that 70.36% of variation in sales is rather unexplained variation. To improve the model’s explanatory power, the director can add variables such as price of the detergent, competitor’s price, average consumer income or anything that gives us some information about the taste and preferences of the consumer

e.

A = 30,000

R= 200,000

E(S| A = 30,000 and R= 200,000) = 175086+0.855*30000-0.284*200000 =$143,936.00