The director of marketing at Vanguard Corporation believes that sales of the com
ID: 1238516 • Letter: T
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 detergent (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 10% level or better.
DEPENDENT VARIABLE: S R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS: 36 0.2247 4.781 0.0150
VARIABLE PARAMETER STANDARD T-RATIO P-VALUE
ESTIMATE ERROR
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
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c. Does Vanguard's advertising expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value.
d. Does advertising by its three largest rivals affect sales of Bright Side detergent in a 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?
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?
Explanation / Answer
a)What sign does the marketing director expecta, b, and c to have?
ANSWER:
The director would expect his own advertising to have a positive effect and the competitor’s advertising to
have a negative effect. He should expect some level of brand loyalty, but his advertising should have a positive effect.
b)Interpret the coefficients a, b, and c?
ANSWER:
S = a + bA + cR
Here “a” will be the intercept parameter and b, along
with c, will be the slope parameter. Vanguard’s own advertising would be a positive effort and the competitor’s would be negative.
END
The regression output from the computer is as follows:
Dependent Variable: S
R-Square: 0.2247 F ratio: 4.781
P-Value on F: 0.0150
Observations: 36
Variable: Intercept
Parameter Estimate: 175086.0
Standard Error: 63821.0
T ratio: 2.74 P-Value: 0.0098
Variable: A
Parameter Estimate: 0.8550
Standard Error: 0.3250
T ratio: 2.63 P-Value: 0.0128
Variable: R
Parameter Estimate: - 0.284
Standard Error: 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?
ANSWER:
Yes, at the 5% level, there is statistical significance at the 5% level.
Explain, using appropriatep-value…
ANSWER:
A 0.0128 p-value means the exact level of significance for a T-Ratio of 2.63 is 1 % and the level of confidence
is 99%. Stating b is statistically significant.
d)Does the advertising by its three largest rivals affect sales of Bright Side detergent in a statistical
significant way?
ANSWER:
P-Value and T-Ratio show that the competitor’s advertising has a negative effect.
Explain using the appropriate p-value…
ANSWER:
The high P-value indicates that the negative T-ratio has a high probability of competitor’s advertising effecting sales of Bright Side negatively.
e)What fraction of the total variation in sales of Bright Side remains unexplained?
ANSWER:
22%
What can the marketing director do to increase the explanatory power of the sales equation?
ANSWER:
He could look at the prices charged by the competitor and Vanguard and add this to the equation as well as log variables on advertising expenses.
What other explanatory variables might be added to this equation?
ASNWER:
Other variables might include family size, loads of laundry done during the summer vs. the winter.
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?
ASNWER:
S = a + b($40,000) + c($100,000)
S = 175086.0 + 0.85550($40,000)
+ - 0.284($100,000)
S = 175086.0 + $34,000 + - $28,400
S = $209,306 + (- $28,400)
S = $180,906