Original Program from program editor.
****************************************************; *** Multiple Regression Example ***; *** ***; ****************************************************; options ps=256 ls=99 nocenter nodate nonumber; title1 'Generic multiple regression introduction'; data one; infile cards missover; input Y X1 X2 X3; cards; run; 1 2 9 2 3 4 6 5 5 7 7 9 3 3 5 5 6 5 8 9 4 3 4 2 2 2 3 6 8 6 2 1 9 7 5 3 3 8 2 4 5 7 3 7 6 9 1 4 ; proc print data=one; title2 'Raw data listing'; run; title2 'All possible models with PROC REG'; proc reg data=one; model y = x1/ ss1 ss2; run; proc reg data=one; model y = x2 / ss1 ss2; run; proc reg data=one; model y = x3 / ss1 ss2; run; proc reg data=one; model y = x1 x2 / ss1 ss2; run; proc reg data=one; model y = x1 x3 / ss1 ss2; run; proc reg data=one; model y = x2 x3 / ss1 ss2; run; proc reg data=one; model y = x1 x2 x3 / ss1 ss2; run; proc mixed data=one; model y = x1 x2 x3 / solution HType=1 2 3; title2 'Multiple Regression with PROC MIXED'; run; proc glm data=one; model y = x1 x2 x3 / solution ss1 ss2 ss3 ss4; title2 'Multiple Regression with PROC GLM'; run;
Below is output from the SAS log (bold) and output from the SAS Output window.
1 ****************************************************; 2 *** Multiple Regression Example ***; 3 *** ***; 4 ****************************************************; 5 options ps=256 ls=99 nocenter nodate nonumber; 6 title1 'Generic multiple regression introduction'; 7 8 data one; infile cards missover; 9 input Y X1 X2 X3; 10 cards; NOTE: The data set WORK.ONE has 12 observations and 4 variables. NOTE: DATA statement used (Total process time): real time 0.03 seconds cpu time 0.03 seconds 10 ! run; 23 ; 24 proc print data=one; title2 'Raw data listing'; run; NOTE: There were 12 observations read from the data set WORK.ONE. NOTE: The PROCEDURE PRINT printed page 1. NOTE: PROCEDURE PRINT used (Total process time): real time 0.01 seconds cpu time 0.01 seconds Generic multiple regression introduction Raw data listing Obs Y X1 X2 X3 1 1 2 9 2 2 3 4 6 5 3 5 7 7 9 4 3 3 5 5 5 6 5 8 9 6 4 3 4 2 7 2 2 3 6 8 8 6 2 1 9 9 7 5 3 10 3 8 2 4 11 5 7 3 7 12 6 9 1 4 26 title2 'All possible models with PROC REG'; 27 proc reg data=one; model y = x1/ ss1 ss2; run; NOTE: 12 observations read. NOTE: 12 observations used in computations. NOTE: The PROCEDURE REG printed page 2. NOTE: PROCEDURE REG used (Total process time): real time 0.04 seconds cpu time 0.04 seconds Generic multiple regression introduction All possible models with PROC REG The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 23.97763 23.97763 6.16 0.0325 Error 10 38.93904 3.89390 Corrected Total 11 62.91667 Root MSE 1.97330 R-Square 0.3811 Dependent Mean 4.58333 Adj R-Sq 0.3192 Coeff Var 43.05377 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Type II SS Intercept 1 1.37613 1.41242 0.97 0.3529 252.08333 3.69640 X1 1 0.61089 0.24618 2.48 0.0325 23.97763 23.97763 28 proc reg data=one; model y = x2 / ss1 ss2; run; NOTE: 12 observations read. NOTE: 12 observations used in computations. NOTE: The PROCEDURE REG printed page 3. NOTE: PROCEDURE REG used (Total process time): real time 0.03 seconds cpu time 0.03 seconds Generic multiple regression introduction All possible models with PROC REG The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 4.11526 4.11526 0.70 0.4224 Error 10 58.80141 5.88014 Corrected Total 11 62.91667 Root MSE 2.42490 R-Square 0.0654 Dependent Mean 4.58333 Adj R-Sq -0.0281 Coeff Var 52.90691 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Type II SS Intercept 1 5.68743 1.49393 3.81 0.0034 252.08333 85.22336 X2 1 -0.24089 0.28795 -0.84 0.4224 4.11526 4.11526 29 proc reg data=one; model y = x3 / ss1 ss2; run; NOTE: 12 observations read. NOTE: 12 observations used in computations. NOTE: The PROCEDURE REG printed page 4. NOTE: PROCEDURE REG used (Total process time): real time 0.01 seconds cpu time 0.01 seconds Generic multiple regression introduction All possible models with PROC REG The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 0.23689 0.23689 0.04 0.8498 Error 10 62.67978 6.26798 Corrected Total 11 62.91667 Root MSE 2.50359 R-Square 0.0038 Dependent Mean 4.58333 Adj R-Sq -0.0959 Coeff Var 54.62385 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Type II SS Intercept 1 4.84809 1.54176 3.14 0.0104 252.08333 61.97728 X3 1 -0.05574 0.28671 -0.19 0.8498 0.23689 0.23689 30 proc reg data=one; model y = x1 x2 / ss1 ss2; run; NOTE: 12 observations read. NOTE: 12 observations used in computations. NOTE: The PROCEDURE REG printed page 5. NOTE: PROCEDURE REG used (Total process time): real time 0.03 seconds cpu time 0.03 seconds Generic multiple regression introduction All possible models with PROC REG The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 24.07446 12.03723 2.79 0.1141 Error 9 38.84220 4.31580 Corrected Total 11 62.91667 Root MSE 2.07745 R-Square 0.3826 Dependent Mean 4.58333 Adj R-Sq 0.2454 Coeff Var 45.32619 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Type II SS Intercept 1 1.07558 2.49743 0.43 0.6768 252.08333 0.80049 X1 1 0.63159 0.29369 2.15 0.0600 23.97763 19.95921 X2 1 0.04187 0.27955 0.15 0.8842 0.09684 0.09684 31 proc reg data=one; model y = x1 x3 / ss1 ss2; run; NOTE: 12 observations read. NOTE: 12 observations used in computations. NOTE: The PROCEDURE REG printed page 6. NOTE: PROCEDURE REG used (Total process time): real time 0.03 seconds cpu time 0.03 seconds Generic multiple regression introduction All possible models with PROC REG The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 25.37078 12.68539 3.04 0.0980 Error 9 37.54588 4.17176 Corrected Total 11 62.91667 Root MSE 2.04249 R-Square 0.4032 Dependent Mean 4.58333 Adj R-Sq 0.2706 Coeff Var 44.56341 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Type II SS Intercept 1 1.91576 1.73473 1.10 0.2981 252.08333 5.08794 X1 1 0.63161 0.25732 2.45 0.0365 23.97763 25.13390 X3 1 -0.13650 0.23621 -0.58 0.5775 1.39316 1.39316 32 proc reg data=one; model y = x2 x3 / ss1 ss2; run; NOTE: 12 observations read. NOTE: 12 observations used in computations. NOTE: The PROCEDURE REG printed page 7. NOTE: PROCEDURE REG used (Total process time): real time 0.03 seconds cpu time 0.03 seconds Generic multiple regression introduction All possible models with PROC REG The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 4.13721 2.06860 0.32 0.7363 Error 9 58.77946 6.53105 Corrected Total 11 62.91667 Root MSE 2.55559 R-Square 0.0658 Dependent Mean 4.58333 Adj R-Sq -0.1419 Coeff Var 55.75837 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Type II SS Intercept 1 5.62891 1.87021 3.01 0.0147 252.08333 59.16272 X2 1 -0.24662 0.31913 -0.77 0.4595 4.11526 3.90032 X3 1 0.01784 0.30776 0.06 0.9550 0.02195 0.02195 33 proc reg data=one; model y = x1 x2 x3 / ss1 ss2; run; NOTE: 12 observations read. NOTE: 12 observations used in computations. 34 NOTE: The PROCEDURE REG printed page 8. NOTE: PROCEDURE REG used (Total process time): real time 0.03 seconds cpu time 0.01 seconds Generic multiple regression introduction All possible models with PROC REG The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 26.18995 8.72998 1.90 0.2078 Error 8 36.72672 4.59084 Corrected Total 11 62.91667 Root MSE 2.14262 R-Square 0.4163 Dependent Mean 4.58333 Adj R-Sq 0.1974 Coeff Var 46.74817 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Type II SS Intercept 1 1.14454 2.57778 0.44 0.6688 252.08333 0.90503 X1 1 0.70578 0.32202 2.19 0.0598 23.97763 22.05274 X2 1 0.13483 0.31918 0.42 0.6838 0.09684 0.81916 X3 1 -0.18621 0.27431 -0.68 0.5164 2.11548 2.11548 35 proc mixed data=one; model y = x1 x2 x3 / solution HType=1 2 3; 36 title2 'Multiple Regression with PROC MIXED'; 37 run; NOTE: The PROCEDURE MIXED printed page 9. NOTE: PROCEDURE MIXED used (Total process time): real time 0.01 seconds cpu time 0.01 seconds Generic multiple regression introduction Multiple Regression with PROC MIXED The Mixed Procedure Model Information Data Set WORK.ONE Dependent Variable Y Covariance Structure Diagonal Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Residual Dimensions Covariance Parameters 1 Columns in X 4 Columns in Z 0 Subjects 1 Max Obs Per Subject 12 Observations Used 12 Observations Not Used 0 Total Observations 12 Covariance Parameter Estimates Cov Parm Estimate Residual 4.5908 Fit Statistics -2 Res Log Likelihood 49.7 AIC (smaller is better) 51.7 AICC (smaller is better) 52.3 BIC (smaller is better) 51.7 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 1.1445 2.5778 8 0.44 0.6688 X1 0.7058 0.3220 8 2.19 0.0598 X2 0.1348 0.3192 8 0.42 0.6838 X3 -0.1862 0.2743 8 -0.68 0.5164 Type 1 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F X1 1 8 5.22 0.0516 X2 1 8 0.02 0.8881 X3 1 8 0.46 0.5164 Type 2 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F X1 1 8 4.80 0.0598 X2 1 8 0.18 0.6838 X3 1 8 0.46 0.5164 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F X1 1 8 4.80 0.0598 X2 1 8 0.18 0.6838 X3 1 8 0.46 0.5164 38 proc glm data=one; model y = x1 x2 x3 / solution ss1 ss2 ss3 ss4; 39 title2 'Multiple Regression with PROC GLM'; 40 run; 41 NOTE: The PROCEDURE GLM printed pages 10-11. NOTE: PROCEDURE GLM used (Total process time): real time 0.01 seconds cpu time 0.01 seconds NOTE: SAS Institute Inc., SAS Campus Drive, Cary, NC USA 27513-2414 NOTE: The SAS System used: real time 1.42 seconds cpu time 0.43 seconds Generic multiple regression introduction Multiple Regression with PROC GLM The GLM Procedure Number of observations 12 Dependent Variable: Y Sum of Source DF Squares Mean Square F Value Pr > F Model 3 26.18994658 8.72998219 1.90 0.2078 Error 8 36.72672008 4.59084001 Corrected Total 11 62.91666667 R-Square Coeff Var Root MSE Y Mean 0.416264 46.74817 2.142625 4.583333 Source DF Type I SS Mean Square F Value Pr > F X1 1 23.97762646 23.97762646 5.22 0.0516 X2 1 0.09683730 0.09683730 0.02 0.8881 X3 1 2.11548283 2.11548283 0.46 0.5164 Source DF Type II SS Mean Square F Value Pr > F X1 1 22.05273729 22.05273729 4.80 0.0598 X2 1 0.81916182 0.81916182 0.18 0.6838 X3 1 2.11548283 2.11548283 0.46 0.5164 Source DF Type III SS Mean Square F Value Pr > F X1 1 22.05273729 22.05273729 4.80 0.0598 X2 1 0.81916182 0.81916182 0.18 0.6838 X3 1 2.11548283 2.11548283 0.46 0.5164 Source DF Type IV SS Mean Square F Value Pr > F X1 1 22.05273729 22.05273729 4.80 0.0598 X2 1 0.81916182 0.81916182 0.18 0.6838 X3 1 2.11548283 2.11548283 0.46 0.5164 Standard Parameter Estimate Error t Value Pr > |t| Intercept 1.144541173 2.57777758 0.44 0.6688 X1 0.705779391 0.32202071 2.19 0.0598 X2 0.134827053 0.31918191 0.42 0.6838 X3 -0.186211994 0.27431463 -0.68 0.5164