[SAS Program]
data collin;
input gpa greq grev mat ar;
new = greq + grev + mat + 0.5*NORMAL(0);
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 simple corr;
model gpa = greq grev mat ar new / stb tol vif collin;
model gpa = greq grev mat ar / stb tol vif collin;
run;
[SAS Output]
Descriptive Statistics
Variables Sum Mean Uncorrected SS
INTERCEP 30 1 30
GREQ 16960 565.33333333 9656600
GREV 17260 575.33333333 10130200
MAT 2010 67 137150
AR 107 3.5666666667 402.02
NEW 36229.833459 1207.6611153 44160067.073
GPA 99.4 3.3133333333 339.78
Variables Variance Std Deviation
INTERCEP 0 0
GREQ 2363.6781609 48.617673339
GREV 6894.7126437 83.034406385
MAT 85.517241379 9.2475532645
AR 0.7029885057 0.8384440982
NEW 14024.344525 118.42442537
GPA 0.359816092 0.5998467237
Correlation
CORR GREQ GREV MAT AR NEW GPA
GREQ 1.0000 0.4681 0.2669 0.5078 0.7599 0.6111
GREV 0.4681 1.0000 0.4257 0.4053 0.9267 0.5815
MAT 0.2669 0.4257 1.0000 0.5248 0.4865 0.6042
AR 0.5078 0.4053 0.5248 1.0000 0.5337 0.6207
NEW 0.7599 0.9267 0.4865 0.5337 1.0000 0.7068
GPA 0.6111 0.5815 0.6042 0.6207 0.7068 1.0000
Model: MODEL1
Dependent Variable: GPA
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 5 7.13991 1.42798 10.402 0.0001
Error 24 3.29476 0.13728
C Total 29 10.43467
Root MSE 0.37052 R-square 0.6842
Dep Mean 3.31333 Adj R-sq 0.6185
C.V. 11.18256
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 -1.521684 0.91706284 -1.659 0.1101
GREQ 1 -0.282456 0.15705028 -1.799 0.0847
GREV 1 -0.284595 0.15685960 -1.814 0.0821
MAT 1 -0.267259 0.15823661 -1.689 0.1042
AR 1 0.161932 0.10851707 1.492 0.1487
NEW 1 0.286159 0.15687834 1.824 0.0806
Standardized Variance
Variable DF Estimate Tolerance Inflation
INTERCEP 1 0.00000000 . 0.00000000
GREQ 1 -22.89312894 0.00008120 12315.476998
GREV 1 -39.39537035 0.00002790 35836.358732
MAT 1 -4.12020754 0.00221079 452.32763126
AR 1 0.22634232 0.57183426 1.74875845
NEW 1 56.49474628 0.00001372 72911.163277
Collinearity Diagnostics
Condition Var Prop Var Prop Var Prop Var Prop Var Prop
Number Eigenvalue Index INTERCEP GREQ GREV MAT AR
1 5.94278 1.00000 0.0002 0.0000 0.0000 0.0000 0.0008
2 0.03196 13.63684 0.0194 0.0000 0.0000 0.0000 0.7120
3 0.01200 22.25403 0.0586 0.0000 0.0000 0.0012 0.0099
4 0.01038 23.93038 0.0799 0.0000 0.0000 0.0017 0.0795
5 0.00289 45.38066 0.8249 0.0001 0.0000 0.0004 0.1898
6 8.70175E-8 8264.000 0.0171 0.9999 1.0000 0.9967 0.0081
Var Prop
Number NEW
1 0.0000
2 0.0000
3 0.0000
4 0.0000
5 0.0000
6 1.0000
Model: MODEL2
Dependent Variable: GPA
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 4 6.68313 1.67078 11.134 0.0001
Error 25 3.75153 0.15006
C Total 29 10.43467
Root MSE 0.38738 R-square 0.6405
Dep Mean 3.31333 Adj R-sq 0.5829
C.V. 11.69147
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 -1.738107 0.95073990 -1.828 0.0795
GREQ 1 0.003998 0.00183065 2.184 0.0385
GREV 1 0.001524 0.00105016 1.451 0.1593
MAT 1 0.020896 0.00954884 2.188 0.0382
AR 1 0.144234 0.11300126 1.276 0.2135
Standardized Variance
Variable DF Estimate Tolerance Inflation
INTERCEP 1 0.00000000 . 0.00000000
GREQ 1 0.32406205 0.65323552 1.53084143
GREV 1 0.21091228 0.68051841 1.46946795
MAT 1 0.32214467 0.66361422 1.50689959
AR 1 0.20160444 0.57644244 1.73477859
Collinearity Diagnostics
Condition Var Prop Var Prop Var Prop Var Prop Var Prop
Number Eigenvalue Index INTERCEP GREQ GREV MAT AR
1 4.94514 1.00000 0.0002 0.0002 0.0005 0.0005 0.0012
2 0.03083 12.66549 0.0277 0.0067 0.0199 0.0007 0.7146
3 0.01093 21.26687 0.0405 0.0000 0.7623 0.3269 0.0041
4 0.01038 21.83079 0.0778 0.1042 0.1570 0.5445 0.0814
5 0.00272 42.65270 0.8538 0.8889 0.0603 0.1274 0.1987