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# Statistics

e. State the conclusion of the test in part (d).

Review of the previous exercise and answers:
12.1 A manufacturer of industrial chemicals investigates the effects on its sales of promotion activities (primarily direct contact and trade show), direct development expenditures, and short-range research effort. Data are assembled for 24 quarters (6 years) and analyzed by Minitab as shown (in \$100,000 per quarter).
Regression Analysis: Sales versus Promotion, Development, Research.

The regression equation is:
Sales = 326 + 136 Promotion - 61.2 Development - 43.7 Research

Predictor Coef SE Coef T P
Constant 326.4 241.6 1.35 0.192
Promotion 136.1 28.11 4.84 0.000
Development -61.18 50.94 -1.20 0.244
Research -43.70 48.32 -0.90 0.377

S = 25.6282 R-Sq = 77.0% R-Sq (adj) = 73.5%

Analysis of Variance
Source DF SS MS F P
Regression 3 43902 14634 22.28 0.000
Residual Error 20 13136 657
Total 23 57038

a. Write the estimated regression equation.
Sales = 326 + 136 Promotion - 61.2 Development - 43.7 Research

b. Locate MS(Residual) and its square root, the residual standard deviation.
MS (Residual) = 657 and its square root = 25.63.
c. Locate SS (Residual) and the coefficient of determination R2.
The SS (Residual) = 13136 and the coefficient of determination R2 = 77.0%.

12.2 State the interpretation of ?1, the estimated coefficient of promotion expense, of Exercise 12.1.
Coefficient of promotion expense is 136.1

This means sales increase by \$136.11 * 100000 = \$136110000 for every one million dollar more spent on promotion
12.7 Refer to Minitab computer output of Exercise 12.1

a. Locate the F statistic.
The F statistic = 22.28
b. Can the hypothesis of no overall predictive value be rejected at ± = .01?
p- value for the F- test is 0. This means at least one of the three predictor variables is significant in the regression.

Therefore, the hypothesis of no overall predictive value can be rejected at a = 0.01.

c. Locate the t statistic for the coefficient of promotion ?1.
T = 4.84

d. Test the research hypothesis that ?1 â?  0. Use ± = .05.
Since p- value for promotion expense is 0, we reject the hypothesis that the coefficient is 0, and conclude that promotion expense is a significant predictor of sales.

e. State the conclusion of the test in part (d).

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(e) From (d), we observe that the p- value for the independent ...

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