MultipleRegressionExamples

# MultipleRegressionExamples - Example What is the...

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90 80 70 60 50 300 250 200 150 100 50 HT WT Scatterplot of WT vs HT Example – What is the relationship between height and weight for UF students? Data on UF students’ heights and weights collected by STA3024 students. N=1309 Questions about some data – are these heights correct? HT WT F 50.0 111 F 51.0 115 F 51.0 95 F 52.0 113 F 53.0 118 F 53.0 120 F 53.0 120 F 53.0 130 F 54.0 117 F 54.0 130 F 55.0 121 F 55.0 128 F 56.0 120 F 56.0 122 F 56.0 128 F 57.0 103 F 57.0 116 F 57.0 140 M 57.0 165 F 58.0 104 F 58.0 130 F 58.0 90 F 58.0 92 F 58.0 95 F 59.0 104 F 59.0 110 F 59.0 115 F 59.0 125 F 59.0 96 F 59.0 97 F 59.5 145 M 80 160 M 83 227 M 83 227 M 84 255 M 89 296 M 72 60 M 73 105 F 64 270

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100 50 0 -50 -100 99.99 99 90 50 10 1 0.01 Residual Percent 240 200 160 120 80 150 100 50 0 -50 Fitted Value Residual 125 100 75 50 25 0 -25 -50 120 90 60 30 0 Residual Frequency 1 2 0 9 8 7 6 5 4 3 150 100 50 0 -50 Observation Order Normal Probability Plot Versus Fits Histogram Versus Order Residual Plots for WT Regression Analysis: WT versus HT The regression equation is WT = - 279 + 6.41 HT Predictor Coef SE Coef T P Constant -279.01 11.19 -24.92 0.000 HT 6.4088 0.1649 38.86 0.000 S = 24.2205 R-Sq = 54.2% R-Sq(adj) = 54.2% Analysis of Variance Source DF SS MS F P Regression 1 885986 885986 1510.29 0.000 Residual Error 1276 748543 587 Total 1277 1634529 Predicted Values for New Observations New Obs HT Fit SE Fit 95% CI 95% PI 1 65 137.562 0.816 (135.961, 139.163) (90.019, 185.106) 2 60 105.518 1.448 (102.678, 108.359) (57.917, 153.120) 3 76 208.059 1.519 (205.080, 211.038) (160.449, 255.669) 80 75 70 65 60 300 250 200 150 100 HT WT S 24.2205 R-Sq 54.2% R-Sq(adj) 54.2% Fitted Line Plot WT = - 279.0 + 6.409 HT
Regression Analysis: WT_F versus HT_F The regression equation is WT_F = - 125 + 3.96 HT_F Predictor Coef SE Coef T P Constant -125.21 17.53 -7.14 0.000 HT_F 3.9614 0.2700 14.67 0.000 S = 19.1292 R-Sq = 24.9% R-Sq(adj) = 24.8% Analysis of Variance Source DF SS MS F P Regression 1 78781 78781 215.29 0.000 Residual Error 650 237852 366 Total 651 316633 Regression Analysis: WT_M versus HT_M The regression equation is WT_M = - 184 + 5.14 HT_M Predictor Coef SE Coef T P Constant -184.21 25.73 -7.16 0.000 HT_M 5.1421 0.3633 14.16 0.000 S = 26.5446 R-Sq = 24.3% R-Sq(adj) = 24.2% Analysis of Variance Source DF SS MS F P Regression 1 141187 141187 200.37 0.000 Residual Error 624 439681 705 Total 625 580868 Regression Analysis: WT versus HT, GENDER_M_1 The regression equation is WT = - 165 + 4.57 HT + 21.0 GENDER_M_1 Predictor Coef SE Coef T P Constant -164.68 14.76 -11.16 0.000 HT 4.5699 0.2271 20.12 0.000 GENDER_M_1 20.963 1.866 11.23 0.000 S = 23.1134 R-Sq = 58.3% R-Sq(adj) = 58.3% Analysis of Variance Source DF SS MS F P Regression 2 953389 476695 892.31 0.000 Residual Error 1275 681140 534 Total 1277 1634529

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Example: Predicting College GPA – data from book Regression Analysis: CGPA versus Height, Gender, etc The regression equation is CGPA = 0.53 + 0.0194 Height + 0.047 Gender - 0.00163 Haircut - 0.042 Job
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## This note was uploaded on 12/15/2011 for the course STA 3024 taught by Professor Ta during the Spring '08 term at University of Florida.

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MultipleRegressionExamples - Example What is the...

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