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?
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.
a) Based on the information provided, the marketing director would expect the coefficients a, b, and c to have the following signs:
- The intercept term (a) is expected to be positive, indicating a base level of sales for the Bright Side laundry detergent.
- The coefficient for Vanguard's own advertising expenditure (b) is expected to be positive, indicating that an increase in advertising expenditure by Vanguard would lead to an increase in sales.
- The coefficient for the combined advertising expenditures of its three biggest rival detergents (c) is expected to be negative, indicating that an increase in competitor advertising expenditure would lead to a decrease in sales.
b) The interpretation of the coefficients is as follows:
- The intercept term (a) represents the base level of sales for the Bright Side laundry detergent when there is no advertising expenditure from Vanguard or its competitors.
- The coefficient for Vanguard's own advertising expenditure (b) represents the effect of a one-unit increase in Vanguard's advertising expenditure on the sales of the Bright Side laundry detergent.
- The coefficient for the combined advertising expenditures of its three biggest rival detergents (c) represents the effect of a one-unit increase in competitor advertising expenditure on the sales of the Bright Side laundry detergent.
c) based on the p-value provided in the regression output for Vanguard's advertising expenditure (A), which is 0.0128, the marketing director can conclude that Vanguard's advertising expenditure has a statistically significant effect on the sales of the Bright Side detergent. This means that there is strong evidence to suggest that an increase in Vanguard's advertising expenditure leads to an increase in sales.
d) Based on the p-value provided in the regression output for the combined advertising expenditures of the three largest rivals (R), which is 0.0927, the marketing director cannot conclude with statistical significance that competitor advertising has a significant effect on the sales of the Bright Side detergent. This means that there is not enough evidence to suggest that an increase in competitor advertising expenditure leads to a decrease in sales.
e) The fraction of the total variation in sales of the Bright Side detergent that remains unexplained can be determined by looking at the R-Square value. The R-Square value in the regression output is 0.2247, which means that approximately 22.47% of the total variation in sales of the Bright Side detergent is explained by the variables included in the regression equation. To increase the explanatory power of the sales equation, the marketing director can consider adding other explanatory variables such as prices of the detergent, lag variables on advertising expenses, and seasonal dummy variables.
f) To calculate 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, plug these values into the estimated regression equation:
S = a + bA + cR
S = 175086.0 + 0.8550 * 40000 + (-0.284) * 100000
By calculating this equation, you can find the expected level of sales each week.