MBS-ProblemSolutions-Ch15

MBS-ProblemSolutions-Ch15 - Chapter 15 Multiple Regression...

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Unformatted text preview: Chapter 15 Multiple Regression Learning Objectives 1. Understand how multiple regression analysis can be used to develop relationships involving one dependent variable and several independent variables. 2. Be able to interpret the coefficients in a multiple regression analysis. 3. Know the assumptions necessary to conduct statistical tests involving the hypothesized regression model. 4. Understand the role of Excel in performing multiple regression analysis. 5. Be able to interpret and use Excel's Regression tool output to develop the estimated regression equation. 6. Be able to determine how good a fit is provided by the estimated regression equation. 7. Be able to test for the significance of the regression equation. 8. Understand how multicollinearity affects multiple regression analysis. 15 - 1 Chapter 15 Solutions: 1. a. b 1 = .5906 is an estimate of the change in y corresponding to a 1 unit change in x 1 when x 2 is held constant. b 2 = .4980 is an estimate of the change in y corresponding to a 1 unit change in x 2 when x 1 is held constant. 2. a. The Excel output is shown below: Regression Statistics Multiple R 0.8124 R Square 0.6600 Adjusted R Square 0.6175 Standard Error 25.4009 Observations 10 ANOVA df SS MS F Significance F Regression 1 10021.24739 10021.25 15.5318 0.0043 Residual 8 5161.652607 645.2066 Total 9 15182.9 Coefficient s Standard Error t Stat P-value Intercept 45.0594 25.4181 1.7727 0.1142 X1 1.9436 0.4932 3.9410 0.0043 An estimate of y when x 1 = 45 is y = 45.0594 + 1.9436(45) = 132.52 b. The Excel output is shown below: Regression Statistics Multiple R 0.4707 R Square 0.2215 Adjusted R Square 0.1242 Standard Error 38.4374 Observations 10 ANOVA 15 - 2 Multiple Regression df SS MS F Significance F Regression 1 3363.4142 3363.414 2.2765 0.1698 Residual 8 11819.4858 1477.436 Total 9 15182.9 Coefficient s Standard Error t Stat P-value Intercept 85.2171 38.3520 2.2220 0.0570 X2 4.3215 2.8642 1.5088 0.1698 An estimate of y when x 2 = 15 is y = 85.2171 + 4.3215(15) = 150.04 c. The Excel output is shown below: Regression Statistics Multiple R 0.9620 R Square 0.9255 Adjusted R Square 0.9042 Standard Error 12.7096 Observations 10 ANOVA df SS MS F Significance F Regression 2 14052.15497 7026.077 43.4957 0.0001 Residual 7 1130.745026 161.535 Total 9 15182.9 Coefficients Standard Error t Stat P-value Intercept-18.3683 17.97150328-1.0221 0.3408 X1 2.0102 0.2471 8.1345 8.19E-05 X2 4.7378 0.9484 4.9954 0.0016 An estimate of y when x 1 = 45 and x 2 = 15 is y = -18.3683 + 2.0102(45) + 4.7378(15) = 143.16 3. a. b 1 = 3.8 is an estimate of the change in y corresponding to a 1 unit change in x 1 when x 2 , x 3 , and x 4 are held constant. b 2 = -2.3 is an estimate of the change in y corresponding to a 1 unit change in x 2 when x 1 , x 3 , and x 4 are held constant....
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MBS-ProblemSolutions-Ch15 - Chapter 15 Multiple Regression...

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