Analysis of Variance

(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 = sales of the product and all competing products in the company (Market Potential, in hundreds of units)
x2 = dollar advertising expenditures in the company (Advertising, in hundreds of dollars)
x3 = weighted average of the company’s market share over the previous four years (Market Share)
 

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 -1603.58 505.550 -3.17195 0.005 (-2654.93, -552.231)
Market Potential, x1 0.05 0.007 7.26321 0.000 (0.04, 0.070)
Advertising, x2 0.17 0.044 3.78288 0.001 (0.08, 0.260)
Market Share, x3 282.75 48.756 5.79927 0.000 (181.35, 384.139)
 

Summary of Model
 

S = 545.515 R-Sq = 84.90% R-Sq(adj) = 82.74%
RESS = 8616510 P R-Sq(pred) = 79.18%
 

Analysis of Variance
 

Source DF Seq SS Adj SS Adj MS F P
Regression 3 35130240 35130240 11710080 39.3502 0.0000000
Market Potential, x1 1 14788185 15698916 15698916 52.7542 0.0000004
Advertising, x2 1 10333786 4258521 4258521 14.3102 0.0010905
Market Share, x3 1 10008270 10008270 10008270 33.6315 0.0000093
Error 21 6249309 6249309 297586
Total 24 41379549
 

Predicted Values for New Observations
 

New Obs Fit SE Fit 95% CI 95% PI
1 4251.56 178.023 (3881.34, 4621.78) (3058.22, 5444.90)
 

Values of Predictors for New Observations
 

New Obs Marketing Potential, x1 Advertising, x2 Market Share, x3
1 35182.7 7281.65 9.64
 

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 = 0.05). Does this data provide significant evidence that Sales are associated with Market Potential and/or Advertising and/or Market Share? 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 Market Potential = 35182.7, Advertising = 7281.65, and Market Share = 9.64. (10 points)