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SBE10 CP15

# SBE10 CP15 - Chapter 15 Multiple Regression Chapter 15...

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Chapter 15 Multiple Regression Chapter 15 Multiple Regression Case Problem 1: Consumer Research, Inc. Descriptive statistics for these data are shown below: N MEAN MEDIAN TRMEAN STDEV SEMEAN INCOME 50 43.48 42.00 43.41 14.55 2.06 SIZE 50 3.420 3.000 3.341 1.739 0.246 AMOUNT 50 3964 4090 3973 933 132 MIN MAX Q1 Q3 INCOME 21.00 67.00 30.00 55.00 SIZE 1.000 7.000 2.000 5.000 AMOUNT 1864 5678 3109 4747 The following scatter diagrams suggest a linear relationship. 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000 10 20 30 40 50 60 70 Income Amount Charged CP - 48

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Chapter 15 Multiple Regression 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000 0 1 2 3 4 5 6 7 8 Size Amount Minitab was used to obtain the following regression analysis output: The regression equation is AMOUNT = 2204 + 40.5 INCOME Predictor Coef SE Coef T p Constant 2204.0 329.0 6.70 0.000 INCOME 40.480 7.184 5.63 0.000 S = 731.7 R-sq = 39.8% R-sq(adj) = 38.6% Analysis of Variance SOURCE DF SS MS F p Regression 1 16999744 16999744 31.75 0.000 Residual Error 48 25699404 535404 Total 49 42699148 Unusual Observations Obs. INCOME AMOUNT Fit Stdev.Fit Residual St.Resid 3 32.0 5100 3499 132 1601 2.22R 5 31.0 1864 3459 137 -1595 -2.22R R denotes an observation with a large standardized residual The regression equation is AMOUNT = 2582 + 404 SIZE Predictor Coef SE Coef T p Constant 2581.9 195.3 13.22 0.000 SIZE 404.13 51.00 7.92 0.000 S = 620.8 R-sq = 56.7% R-sq(adj) = 55.8% CP - 49
Chapter 15 Multiple Regression Analysis of Variance SOURCE DF SS MS F p Regression 1 24200718 24200718 62.80 0.000 Residual Error 48 18498432 385384 Total 49 42699152 Unusual Observations Obs SIZE AMOUNT Fit SE Fit Residual St Resid 5 2.00 1864.0 3390.2 113.8 -1526.2 -2.50R R denotes an observation with a large standardized residual The regression equation is AMOUNT = 1305 + 33.1 INCOME + 356 SIZE Predictor Coef SE Coef T p Constant 1304.9 197.7 6.60 0.000 INCOME 33.133 3.968 8.35 0.000 SIZE 356.30 33.20 10.73 0.000 S = 398.1 R-sq = 82.6% R-sq(adj) = 81.8% Analysis of Variance SOURCE DF SS MS F p Regression 2 35250756 17625378 111.22 0.000 Residual Error 47 7448393 158476 Total 49 42699148 SOURCE DF SEQ SS INCOME 1 16999744 SIZE 1 18251010 Unusual Observations Obs INCOME AMOUNT Fit SE Fit Residual St Resid 3 32.0 5100.0 3790.3 76.9 1309.7 3.35R 5 31.0 1864.0 3044.6 83.9 -1180.6 -3.03R 11 25.0 4208.0 3202.1 91.6 1005.9 2.60R R denotes an observation with a large standardized residual CP - 50

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Chapter 15 Multiple Regression The standardized residual plot for the model involving both independent variables is shown below: Fitted Value Standardized Residual 6000 5500 5000 4500 4000 3500 3000 2500 4 3 2 1 0 -1 -2 -3 Although the multiple regression model explains a high percentage of the variability in the dependent variable, the output identifies three observations as having a large standardized residual; thus, these 3 observations should be treated as possible outliers. Case Problem 2: Predicting Student Proficiency Test Scores A variety of models can be developed for these data. The Minitab output for one possible model is shown below: The regression equation is %Passed = 64.6 - 0.272 %onADC - 0.202 %FreeLch +0.000542 Income Predictor Coef SE Coef T P Constant 64.620 1.879 34.39 0.000 %onADC -0.27183 0.04628 -5.87 0.000 %FreeLch -0.20228 0.03624 -5.58 0.000 Income 0.00054168 0.00006049 8.95 0.000 S = 4.979 R-Sq = 68.0% R-Sq(adj) = 67.8% Analysis of Variance Source DF SS MS F P Regression 3 31764 10588 427.15 0.000 Residual Error 604 14972 25 Total 607 46736 Source DF Seq SS %onADC 1 26638 %FreeLch 1 3139 Income 1 1988 CP - 51
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SBE10 CP15 - Chapter 15 Multiple Regression Chapter 15...

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