[SAS Program]
data rsq;
input gpa greq grev mat ar;
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 gpa = greq grev mat ar / selection=backward;
run;
[SAS Output]
The SAS System 08:37 Friday, January 29, 1999 1
Backward Elimination Procedure for Dependent Variable GPA
Step 0 All Variables Entered R-square = 0.64047409 C(p) = 5.00000000
DF Sum of Squares Mean Square F Prob>F
Regression 4 6.68313369 1.67078342 11.13 0.0001
Error 25 3.75153298 0.15006132
Total 29 10.43466667
Parameter Standard Type II
Variable Estimate Error Sum of Squares F Prob>F
INTERCEP -1.73810660 0.95073990 0.50153141 3.34 0.0795
GREQ 0.00399829 0.00183065 0.71582146 4.77 0.0385
GREV 0.00152365 0.00105016 0.31588005 2.11 0.1593
MAT 0.02089606 0.00954884 0.71861483 4.79 0.0382
AR 0.14423354 0.11300126 0.24447515 1.63 0.2135
Bounds on condition number: 1.734779, 24.96795
--------------------------------------------------------------------------------
Step 1 Variable AR Removed R-square = 0.61704497 C(p) = 4.62916834
DF Sum of Squares Mean Square F Prob>F
Regression 3 6.43865853 2.14621951 13.96 0.0001
Error 26 3.99600813 0.15369262
Total 29 10.43466667
Parameter Standard Type II
Variable Estimate Error Sum of Squares F Prob>F
INTERCEP -2.14876987 0.90540557 0.86565831 5.63 0.0253
GREQ 0.00492553 0.00170055 1.28937279 8.39 0.0076
GREV 0.00161220 0.00106047 0.35521639 2.31 0.1405
MAT 0.02611914 0.00873135 1.37533265 8.95 0.0060
Bounds on condition number: 1.463054, 11.94897
--------------------------------------------------------------------------------
Step 2 Variable GREV Removed R-square = 0.58300302 C(p) = 4.99630990
DF Sum of Squares Mean Square F Prob>F
Regression 2 6.08344215 3.04172107 18.87 0.0001
Error 27 4.35122452 0.16115646
Total 29 10.43466667
Parameter Standard Type II
Variable Estimate Error Sum of Squares F Prob>F
INTERCEP -2.12937702 0.92703773 0.85027230 5.28 0.0296
GREQ 0.00597632 0.00159103 2.27382925 14.11 0.0008
MAT 0.03080742 0.00836462 2.18608048 13.56 0.0010
Bounds on condition number: 1.076704, 4.306815
--------------------------------------------------------------------------------
All variables left in the model are significant at the 0.1000 level.
Summary of Backward Elimination Procedure for Dependent Variable GPA
Variable Number Partial Model
Step Removed In R**2 R**2 C(p) F Prob>F
1 AR 3 0.0234 0.6170 4.6292 1.6292 0.2135
2 GREV 2 0.0340 0.5830 4.9963 2.3112 0.1405