[SAS Program]
data rawres;
input gpa greq grev mat ar;
title 'Using Raw Residuals';
cards;
3.2 625 540 65 2.7
4.1 575 680 75 4.5
3.0 520 480 65 2.5
2.6 545 520 55 3.1
3.7 520 490 75 3.6
4.0 655 535 65 4.3
4.3 630 720 75 4.6
2.7 500 500 75 3.0
3.6 605 575 65 4.7
4.1 555 690 75 3.4
2.7 505 545 55 3.7
2.9 540 515 55 2.6
2.5 520 520 55 3.1
3.0 585 710 65 2.7
3.3 600 610 85 5.0
3.2 625 540 65 2.7
4.1 575 680 75 4.5
3.0 520 480 65 2.5
2.6 545 520 55 3.1
3.7 520 490 75 3.6
4.0 655 535 65 4.3
4.3 630 720 75 4.6
2.7 500 500 75 3.0
3.6 605 575 65 4.7
4.1 555 690 75 3.4
2.7 505 545 55 3.7
2.9 540 515 55 2.6
2.5 520 520 55 3.1
3.0 585 710 65 2.7
3.3 600 610 85 5.0
;
proc reg;
model greq = grev / stb;
output out=resid1 residual=rgreq;
proc reg data=resid1;
model gpa = grev / stb;
output out=resid2 residual=resgpa;
proc reg simple corr data=resid2;
model gpa = rgreq / stb;
model resgpa = rgreq / stb;
model gpa = grev greq / stb;
run;
[SAS Output]
Using Raw Residuals 08:45 Wednesday, February 3, 1999 1
Model: MODEL1
Dependent Variable: GREQ
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 15017.37802 15017.37802 7.855 0.0091
Error 28 53529.28864 1911.76031
C Total 29 68546.66667
Root MSE 43.72368 R-square 0.2191
Dep Mean 565.33333 Adj R-sq 0.1912
C.V. 7.73414
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 407.659543 56.82088827 7.174 0.0001
GREV 1 0.274056 0.09778216 2.803 0.0091
Standardized
Variable DF Estimate
INTERCEP 1 0.00000000
GREV 1 0.46806254
Model: MODEL1 Dependent Variable: GPA
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 3.52782 3.52782 14.302 0.0008
Error 28 6.90685 0.24667
C Total 29 10.43467
Root MSE 0.49666 R-square 0.3381
Dep Mean 3.31333 Adj R-sq 0.3144
C.V. 14.98980
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 0.896672 0.64543448 1.389 0.1757
GREV 1 0.004200 0.00111072 3.782 0.0008
Standardized
Variable DF Estimate
INTERCEP 1 0.00000000
GREV 1 0.58145214
Descriptive Statistics
Variables Sum Mean Uncorrected SS
RGREQ 0 0 53529.288644
GPA 99.4 3.3133333333 339.78
RESGPA -3.55271E-15 -1.18424E-16 6.9068458256
GREV 17260 575.33333333 10130200
GREQ 16960 565.33333333 9656600
Variables Variance Std Deviation
RGREQ 1845.8375394 42.963211466
GPA 0.359816092 0.5998467237
RESGPA 0.2381670974 0.4880236648
GREV 6894.7126437 83.034406385
GREQ 2363.6781609 48.617673339
Correlation
CORR RGREQ GPA RESGPA GREV GREQ
RGREQ 1.0000 0.3836 0.4715 0.0000 0.8837
GPA 0.3836 1.0000 0.8136 0.5815 0.6111
RESGPA 0.4715 0.8136 1.0000 0.0000 0.4167
GREV 0.0000 0.5815 0.0000 1.0000 0.4681
GREQ 0.8837 0.6111 0.4167 0.4681 1.0000
Model: MODEL1 Dependent Variable: GPA
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 1.53551 1.53551 4.831 0.0364
Error 28 8.89916 0.31783
C Total 29 10.43467
Root MSE 0.56376 R-square 0.1472
Dep Mean 3.31333 Adj R-sq 0.1167
C.V. 17.01494
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 3.313333 0.10292832 32.191 0.0001
RGREQ 1 0.005356 0.00243669 2.198 0.0364
Standardized Variable
Variable DF Estimate Label
INTERCEP 1 0.00000000 Intercept
RGREQ 1 0.38360683 Residual
Model: MODEL2 Dependent Variable: RESGPA Residual
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 1.53551 1.53551 8.004 0.0085
Error 28 5.37134 0.19183
C Total 29 6.90685
Root MSE 0.43799 R-square 0.2223
Dep Mean -0.00000 Adj R-sq 0.1945
C.V. -3.698481E17
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 -1.18424E-16 0.07996533 -0.000 1.0000
RGREQ 1 0.005356 0.00189307 2.829 0.0085
Standardized Variable
Variable DF Estimate Label
INTERCEP 1 0.00000000 Intercept
RGREQ 1 0.47150439 Residual
Model: MODEL3 Dependent Variable: GPA
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 2 5.06333 2.53166 12.726 0.0001
Error 27 5.37134 0.19894
C Total 29 10.43467
Root MSE 0.44603 R-square 0.4852
Dep Mean 3.31333 Adj R-sq 0.4471
C.V. 13.46153
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 -1.286698 0.97652072 -1.318 0.1987
GREV 1 0.002733 0.00112876 2.421 0.0225
GREQ 1 0.005356 0.00192781 2.778 0.0098
Standardized Variable
Variable DF Estimate Label
INTERCEP 1 0.00000000 Intercept
GREV 1 0.37826900
GREQ 1 0.43409398