National Trade Association

(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 Sales, 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 = number of months the company has been selling the product (Time with Product)
x2 = sales of the product and all competing products in the company (Market Potential, measured in hundreds of units)
x3 = dollar advertising expenditures in the company (Advertising, in hundreds of dollars)
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 787.217 462.766 1.70111 0.104 (-175.158, 1749.59)
Time with Product, x1 5.251 2.072 2.53464 0.019 (0.943, 9.56)
Market Potential, x2 0.030 0.011 2.69180 0.014 (0.007, 0.05)
Advertising, x3 0.218 0.060 3.60435 0.002 (0.092, 0.34)
 

Summary of Model
S = 769.944 R-Sq = 69.91% R-Sq(adj) = 65.62%
PRESS = 18030073 R-Sq(pred) = 56.43%
 

Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 3 28930450 28930450 9643483 16.2673 0.0000107
Time with Product, x1 1 16056475 3808479 3808479 6.4244 0.0192765
Market Potential, x2 1 5172530 4295406 4295406 7.2458 0.0136558
Advertising, x3
1 7701445 7701445 7701445 12.9913 0.0016663
Error 21 12449099 12449099 592814
Total 24 41379549
 

Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 3889.25 240.686 (3388.71, 4389.78) (2211.65, 5566.85)
 

Values and Predictors for New Observations
New Obs Time with Product, x1 Market Potential, x2 Advertising, x3
1 85.42 35182.7 7281.65
 

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 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 Time with Product = 85.42, Market Potential = 35182.7, and Advertising = 7281.65. (10 points)