##### Question

# 1)The director of marketing at Vanguard Corporation believes the 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 riva

1)The director of marketing at

Vanguard Corporation believes the

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, 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:

Dependant Variable: S

Observations: 36

R-Square: 0.2247 F-Ratio: 4.781

P-value on F: 0.0150

Variable: Intercept

Parameter Est: 175086.0

Standard Error: 63821.0

T-Ratio: 2.74

P-Value: 0.0098

Variable: A

Paramter estimate: 0.8550

Standard Error: 0.3250

T-Ratio: 2.63

P-Value: 0.0128

Variable: R

Parameter Est: – 0.284

Standard Err: 0.164

T-ratio: – 1.73

P-Value: 0.0927

c) Does Vanguard’s advertising

expenditure have a statistical

significant effect on the sales of

Bright Side detergent? Explain,

using appropriate p-value……

d) Does the advertising by its three

largest rivals affect sales of

Bright Side detergent in a

statistical 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?