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# \$30.00A national trade association is concerned with increasing competition from foreign companies

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Q:

(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
1. Analyze the above output to determine the multiple regression equation. (5 points)
2. What conclusions are possible using the result of the global usefulness test (the F test and its associated p-value)? (5 points)
3. 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)
4. 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)

Tutorial

\$30.00
A national trade association is concerned with increasing competition from foreign companies
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• Posted on Feb. 23, 2012 at 12:57:15AM
A:
Preview: ... alternative hypothesis Â  This data provide significant evidence that sales are associated with market shareÂ  Â  Ho: b3 =0 Ha: b3 â‰  0 Â  t3 (model) =1.99828 t 0.05;21 = 1.721 (from t table, df = 25-4 = 21 and k=3 , n=25) We can reject the null hypothesis at level of 0.10 of significance and we can accept alternative hypothesis Â  This data provide significant evidence that sales are associated with market share changeÂ  Â  P-value for x1 = 0.028 P-value for x2 = 0.029 P-value for x3 = 0.059 Â  Lower the p-value is better model, there is a strong evidence that model is very good for advertising Â  95% CI = (3811.28, 5066.12) Interpretation of the 95% Confident Interval, for x1, Â we are 95% confident that , if we take many such advertising data, the mean sales will be between \$3811.28 and \$5066.12 Â  95% CI = (3811.28, 5066.12) Interpretation of the 95% Confident Interval, for x2, Â we are 95% confident that , if we take many such market share data, the mean sales will be between \$3811.28 and \$5066.12 Â  95% CI = (3811.28, 5066.12) Interpretation of the 95% Confident Inter ...

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