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Regression analysis in Minitab

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 associationâ??s research director, with substantial input from member companiesâ?? 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 companyâ??s market share over the previous four years (Market Share)

x3 = change in the companyâ??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)

Solution Summary

Step by step method for regression analysis in Minitab is given in the answer.

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