[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=stepwise;
run;
[SAS Output]
The SAS System 08:41 Friday, January 29, 1999 1
Stepwise Procedure for Dependent Variable GPA
Step 1 Variable AR Entered R-square = 0.38529398 C(p) = 16.74420939
DF Sum of Squares Mean Square F Prob>F
Regression 1 4.02041421 4.02041421 17.55 0.0003
Error 28 6.41425245 0.22908044
Total 29 10.43466667
Parameter Standard Type II
Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 1.72944408 0.38804679 4.55022494 19.86 0.0001
AR 0.44408110 0.10600367 4.02041421 17.55 0.0003
Bounds on condition number: 1, 1
--------------------------------------------------------------------------------
Step 2 Variable GREV Entered R-square = 0.51549156 C(p) = 9.69078781
DF Sum of Squares Mean Square F Prob>F
Regression 2 5.37898260 2.68949130 14.36 0.0001
Error 27 5.05568407 0.18724756
Total 29 10.43466667
Parameter Standard Type II
Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 0.49717794 0.57651557 0.13925724 0.74 0.3961
GREV 0.00285138 0.00105858 1.35856839 7.26 0.0120
AR 0.32962504 0.10483495 1.85116176 9.89 0.0040
Bounds on condition number: 1.196581, 4.786325
--------------------------------------------------------------------------------
Step 3 Variable MAT Entered R-square = 0.57187378 C(p) = 7.77019304
DF Sum of Squares Mean Square F Prob>F
Regression 3 5.96731222 1.98910407 11.58 0.0001
Error 26 4.46735444 0.17182132
Total 29 10.43466667
Parameter Standard Type II
Variable Estimate Error Sum of Squares F Prob>F
INTERCEP -0.14410465 0.65199045 0.00839364 0.05 0.8268
GREV 0.00231735 0.00105430 0.83009542 4.83 0.0371
MAT 0.01881259 0.01016662 0.58832962 3.42 0.0756
AR 0.24217230 0.11098884 0.81802648 4.76 0.0383
Bounds on condition number: 1.491861, 12.74089
--------------------------------------------------------------------------------
Step 4 Variable GREQ 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 5 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
--------------------------------------------------------------------------------
All variables left in the model are significant at the 0.1500 level.
No other variable met the 0.1500 significance level for entry into the model.
Summary of Stepwise Procedure for Dependent Variable GPA
Variable Number Partial Model
Step Entered Removed In R**2 R**2 C(p) F Prob>F
1 AR 1 0.3853 0.3853 16.7442 17.5502 0.0003
2 GREV 2 0.1302 0.5155 9.6908 7.2555 0.0120
3 MAT 3 0.0564 0.5719 7.7702 3.4241 0.0756
4 GREQ 4 0.0686 0.6405 5.0000 4.7702 0.0385
5 AR 3 0.0234 0.6170 4.6292 1.6292 0.2135