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$20.00 (TCO E and F) A national trade association is concerned with increasing competition from foreign companies. They decide,

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Chapter 1, # 4
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volcanblack
 
 
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
 
$20.00
(TCO E and F) A national trade association is concerned with increasing competition from foreign companies. They decide,
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  • Posted on Dec 13, 2011 at 3:23:19PM
A:
Preview: ... (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)  a) Y= 1060.13 +0.19x1 + 189.56x2 + 664.45x3 b) F(model)= 8.70671 P-value = 0.0006013 This tell us that we have extremely strong evidence that sales peformance are related to at least one of the independent variables, ...

The full tutorial is about 713 words long .