1)The director of marketing at

Question

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?

Thanks,
EY

I find it interesting that the Vanguard director doesnt even consider price as a determinent of sales. Hummmm. While good economic reasoning should be a part of any econometric analyses, you are given what you are given.
a) I would expect own advertising would have a positive effect and competitor advertising have a negitive effect. Because of some level of brand-loyality, I would expect the intercept term to be positive.
b) ta da, the model meets my priors.
c) I would answer: Significant at the 5% level, but not at the 1% level.
d) what does the T-ratio (and accompaning P-value) tell you?
e) what does the R^2 statistic tell you? In addition to adding Prices (own and competitors) to the equation, I would consider adding lag variable(s) on advertising expenses. I would also test some seasonal dummy variables (are more loads of laundry done in the summer vs winter?)
f) Plug the values into your estimated equation. What do you get.

Your suggestions were a trendous help, can I e-mail them to you to check? I need them back by Sunday at 6pm.