# Ch15 - Chapter 15 Multiple Regression Learning Objectives 1...

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15 - 1 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 computer packages in performing multiple regression analysis. 5. Be able to interpret and use computer 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. 9. Know how residual analysis can be used to make a judgement as to the appropriateness of the model, identify outliers, and determine which observations are influential. 10. Understand how logistic regression is used for regression analyses involving a binary dependent variable.

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Chapter 15 15 - 2 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 estimated regression equation is ˆ y = 45.06 + 1.94 x 1 An estimate of y when x 1 = 45 is ˆ y = 45.06 + 1.94(45) = 132.36 b. The estimated regression equation is ˆ y = 85.22 + 4.32 x 2 An estimate of y when x 2 = 15 is ˆ y = 85.22 + 4.32(15) = 150.02 c. The estimated regression equation is ˆ y = -18.37 + 2.01 x 1 + 4.74 x 2 An estimate of y when x 1 = 45 and x 2 = 15 is ˆ y = -18.37 + 2.01(45) + 4.74(15) = 143.18 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. b 3 = 7.6 is an estimate of the change in y corresponding to a 1 unit change in x 3 when x 1 , x 2 , and x 4 are held constant. b 4 = 2.7 is an estimate of the change in y corresponding to a 1 unit change in x 4 when x 1 , x 2 , and x 3 are held constant. 4. a. ˆ y = 25 + 10(15) + 8(10) = 255; sales estimate: \$255,000 b. Sales can be expected to increase by \$10 for every dollar increase in inventory investment when advertising expenditure is held constant. Sales can be expected to increase by \$8 for every dollar increase in advertising expenditure when inventory investment is held constant.
Multiple Regression 15 - 3 5. a. The Minitab output is shown below: The regression equation is Revenue = 88.6 + 1.60 TVAdv Predictor Coef SE Coef T P Constant 88.638 1.582 56.02 0.000 TVAdv 1.6039 0.4778 3.36 0.015 S = 1.215 R-Sq = 65.3% R-Sq(adj) = 59.5% Analysis of Variance Source DF SS MS F P Regression 1 16.640 16.640 11.27 0.015 Residual Error 6 8.860 1.477 Total 7 25.500 b. The Minitab output is shown below: The regression equation is Revenue = 83.2 + 2.29 TVAdv + 1.30 NewsAdv Predictor Coef SE Coef T P Constant 83.230 1.574 52.88 0.000 TVAdv 2.2902 0.3041 7.53 0.001 NewsAdv 1.3010 0.3207 4.06 0.010 S = 0.6426 R-Sq = 91.9% R-Sq(adj) = 88.7% Analysis of Variance Source DF SS MS F P Regression 2 23.435 11.718 28.38 0.002 Residual Error 5 2.065 0.413 Total 7 25.500 Source DF Seq SS TVAdv 1 16.640 NewsAdv 1 6.795

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