$30.00 A national trade association is concerned with increasing competition from foreign companies
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(TCO E and F) A national trade association is concerned with increasing competition from foreign companies. They decide, in close consultation with their membership, to evaluate the sales performance of 25 randomly selected U.S. companies, so that all companies can benefit from their collective experience.
The association’s research director, with substantial input from member companies’ sales managers, has decided to measure the performance, y, of each company by using the yearly sales of the same product for all of the companies.
The research director and the sales managers believe that sales performance, y (measured in hundreds of units), substantially depends on three independent variables:
x1 = dollar advertising expenditures in the company (Advertising, in hundreds of dollars)
x2 = weighted average of the company’s market share over the previous four years (Market Share)
x3 = change in the company’s market share over the previous four years (Market share Change)
Refer to the Minitab output below to answer questions A through G.
Multiple Regression and Model Building: Minitab Output
Coefficients
|
Term |
Coef |
SE Coef |
T |
P |
95% CI |
|
Constant |
1060.13 |
643.589 |
1.64722 |
0.114 |
(-278.284, 2398.55) |
|
Advertising, x1 |
0.19 |
0.079 |
2.36297 |
0.028 |
(0.022, 0.35) |
|
Market Share, x2 |
189.56 |
80.646 |
2.35057 |
0.029 |
(21.852, 357.28) |
|
Market share Change, x3 |
664.45 |
332.514 |
1.99828 |
0.059 |
(-27.046, 1355.96) |
Summary of Model
|
S = 937.108 |
R-Sq = 55.43% |
R-Sq(adj) = 49.07% |
|
PRESS = 25785590 |
R-Sq(pred) = 37.69% |
Analysis of Variance
Error
|
Source |
DF |
Seq SS |
Adj SS |
Adj MS |
F |
|
Regression |
3 |
22937954 |
22937954 |
7645985 |
8.70671 |
|
Advertising, x1 |
1 |
14707456 |
4903392 |
4903392 |
5.58364 |
|
Market Share, x2 |
1 |
4723868 |
4852050 |
4852050 |
5.52518 |
|
Market share Change, x3 |
1 |
3506630 |
3506630 |
3506630 |
3.99311 |
|
Total |
21 |
18441595 |
18441595 |
878171 |
|
|
Error |
24 |
41379549 |
|
Source |
P |
|
Regression |
0.0006013 |
|
Advertising, x1 |
0.0278536 |
|
Market Share, x2 |
0.0285936 |
|
Market share Change, x3 |
0.0588001 |
|
Total |
|
|
Error |
Predicted Values for New Observations
|
New Obs |
Fit |
SE Fit |
95% CI |
95% PI |
|
1 |
4438.70 |
301.701 |
(3811.28, 5066.12) |
(2391.37, 6486.03) |
Values of Predictors for New Observations
|
New Obs |
Advertising, x1 |
Market Share, x2 |
Market Share Change, X3 |
|
1 |
7281.65 |
9.64 |
0.28 |
- Analyze the above output to determine the multiple regression equation. (5 points)
- What conclusions are possible using the result of the global usefulness test (the F test and its associated p-value)? (5 points)
- What conclusions are possible using the results of the t-tests of the independent variables (alpha = 0.10). Does this data provide significant evidence that Sales are associated with Time With Product and/or Market Potential and/or Advertising? Find the p-values and interpret. Interpret the 95% confidence interval of each of the regression coefficients, using the units of the variables. (20 points)
- Find and interpret the 95% Prediction interval for Sales, when Advertising = 7281.65, Market Share = 9.64, and Market share Change = 0.28. (10 points)
(Points : 40)
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- Posted on Feb. 23, 2012 at 12:57:15AM