Interpreting regression coefficients as well as explaining their Statistical Significance.
The director of marketing at vanguard corporation believe 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 utilizing parameter estimates that are statistically significant at the 10% level or better.
1) What sign does the marketing director expect a, b, and c to have?
2) Interpret the coefficients a, b and c.
The regression outcomes from the computer is as follows-
|
DEPENDENT VARIABLE-
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S
|
R-SQUARE
|
F-RATIO
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P-VALUE ON F
|
|
OBSERVATIONS-
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36
|
0.2247
|
4.781
|
0.0150
|
|
|
Parameter
|
Standard
|
|
|
|
Variable
|
Estimate
|
Error
|
T-Ratio
|
P-Value
|
3) Does Vanguard's advertising expenditures have a statistically significant effect on the sale of Brightside detergent? Explain using the appropriate p-value
4) Does advertising by its three largest rivals affect sales of Bright Side detergent in a statistically way? Explain using the appropriate p-value.
5) What fraction of the total variation in sales of Bright Side remains unexplained and what can the marketing director do to increase the explanatory power of sales equation and what other explanatory variables might be added to this equation?
6) What is the expected level of sales each week when Vanguard spends $40,000 per week as well as the combined advertising expenditures for the three rivals are $100,000 per week?