EXST7034 – Regression Techniques Fall 2004 Geaghan Multiple Regression SAS examples Page 1 05-MultRegIntroHandout.doc 1 ************************************************************************; 2 *** EXST7034 Multiple Regression Example ***; 3 *** Problem from Neter, Kutner, Nachtsheim & Wasserman 1996, #6.18 ***; 4 ************************************************************************; 5 6 OPTIONS LS=132 PS=80 NOCENTER NODATE NONUMBER; 7 8 DATA ONE; INFILE CARDS MISSOVER; 9 TITLE1 'EXST7034 - NKNW 6.18 : Mathematician salaries'; 10 LABEL X1 = 'Index of publication quality'; 11 LABEL X2 = 'Number of years experience'; 12 LABEL X3 = 'Grant support success'; 13 LABEL Y = 'Thousands of dollars'; 14 INPUT Y X1 X2 X3; 15 CARDS; NOTE: The data set WORK.ONE has 24 observations and 4 variables. NOTE: DATA statement used: real time 0.06 seconds cpu time 0.06 seconds 15 ! RUN; 40 ; 41 PROC REG DATA=ONE; TITLE2 'Multiple Regression Example'; 42 MODEL Y = X1 X2 X3 / XPX I SS1 SS2 COVB; RUN; NOTE: 24 observations read. NOTE: 24 observations used in computations. NOTE: The PROCEDURE REG printed pages 1-2. NOTE: PROCEDURE REG used: real time 0.14 seconds cpu time 0.13 seconds EXST7034 - NKNW 6.18 : Mathematician salaries Multiple Regression Example The REG Procedure Model: MODEL1 Model Crossproducts X'X X'Y Y'Y Variable Label Intercept X1 X2 X3 Y Intercept Intercept 24 128.6 599 143.7 948 X1 Index of publication quality 128.6 727.44 3365.3 782.49 5188.17 X2 Number of years experience 599 3365.3 17847 3671.9 24873.7 X3 Grant support success 143.7 782.49 3671.9 899.49 5767.77 Y Thousands of dollars 948 5188.17 24873.7 5767.77 38135.26EXST7034 – Regression Techniques Fall 2004 Geaghan Multiple Regression SAS examples Page 2 05-MultRegIntroHandout.doc EXST7034 - NKNW 6.18 : Mathematician salaries Multiple Regression Example The REG Procedure Model: MODEL1 Dependent Variable: Y Thousands of dollars X'X Inverse, Parameter Estimates, and SSE Variable Label Intercept X1 X2 X3 Y Intercept Intercept 1.3044630488 -0.101873528 0.0004420084 -0.121579266 17.846930636 X1 Index of publication quality -0.101873528 0.035355881 -0.001674335 -0.007647007 1.1031303951 X2 Number of years experience 0.0004420084 -0.001674335 0.0004482371 -0.000443861 0.3215196814 X3 Grant support success -0.121579266 -0.007647007 -0.000443861 0.0289991653 1.2889408958 Y Thousands of dollars 17.846930636 1.1031303951 0.3215196814 1.2889408958 61.443003635 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 627.81700 209.27233 68.12 <.0001 Error 20 61.44300 3.07215 Corrected Total 23 689.26000 Root MSE 1.75276 R-Square 0.9109 Dependent Mean 39.50000 Adj R-Sq 0.8975 Coeff Var 4.43735 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Type I SS Type II SS Intercept Intercept 1 17.84693 2.00188 8.92 <.0001 37446 244.17168 X1 Index of publication quality 1 1.10313 0.32957 3.35 0.0032 306.73233 34.41851 X2 Number of years experience 1 0.32152 0.03711 8.66 <.0001 263.79445 230.62548 X3 Grant support success 1 1.28894 0.29848 4.32 0.0003 57.29022 57.29022 Covariance of Estimates Variable Label Intercept X1 X2 X3 Intercept Intercept 4.0075063923 -0.312970778 0.0013579161 -0.373509763 X1 Index of publication quality -0.312970778 0.1086185761 -0.005143808 -0.023492755 X2 Number of years experience 0.0013579161 -0.005143808 0.0013770518 -0.001363607 X3 Grant support success -0.373509763 -0.023492755 -0.001363607 0.0890897911EXST7034 – Regression Techniques Fall 2004 Geaghan Multiple Regression SAS examples Page 3 05-MultRegIntroHandout.doc 43 PROC REG DATA=ONE; TITLE2 'Sub-models'; 44 MODEL Y = X1; 45 MODEL Y = X2; 46 MODEL Y = X3; 47 MODEL Y = X1 X2; 48 MODEL Y = X1 X3; 49 MODEL Y = X2 X3; 50 MODEL Y = X1 X2 X3; 51 run; NOTE: 24 observations read. NOTE: 24 observations used in computations. EXST7034 - NKNW 6.18 : Mathematician salaries Sub-models The REG Procedure Model: MODEL1 Dependent Variable: Y Thousands of dollars Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 306.73233 306.73233 17.64 0.0004 Error 22