Title 'Multiple Collinearity Example'.
Data list fixed records=1
/1 gpa 1-3 greq 5-7 grev 9-11 mat 13-14 ar 16-18.
begin data
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
end data.
compute new=greq+grev+mat+(.5*normal(1)).
execute.
Regression variables=gpa,greq,grev,mat,ar,new
/descriptives=mean,stddev,corr,n
/statistics=r,anova,cha,coeff,ci,collin,tol
/criteria=tolerance (0.00000001)
/dependent=gpa
/method=enter.
Regression variables=gpa,greq,grev,mat,ar
/descriptives=mean,stddev,corr,n
/statistics=r,anova,cha,coeff,ci,collin,tol,history
/dependent=gpa
/method=enter.
OUTPUT:
22 Dec 99 SPSS for Unix, Release 6.1 (AIX 3.2) Page 1
17:49:22 UCLA OAC IBM RS6000 AIX 3.2.5/4.
For AIX 3.2.5/4. UCLA OAC SPSS ID 90095
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Mean Std Dev Label
GPA 3.313 .600
GREQ 565.333 48.618
GREV 575.333 83.034
MAT 67.000 9.248
AR 3.567 .838
NEW 1207.569 118.205
N of Cases = 30
Correlation:
GPA GREQ GREV MAT AR NEW
GPA 1.000 .611 .581 .604 .621 .705
GREQ .611 1.000 .468 .267 .508 .759
GREV .581 .468 1.000 .426 .405 .927
MAT .604 .267 .426 1.000 .525 .486
AR .621 .508 .405 .525 1.000 .534
NEW .705 .759 .927 .486 .534 1.000
22 Dec 99 Multiple Collinearity Example Page 3
17:49:22 UCLA OAC IBM RS6000 AIX 3.2.5/4.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. GPA
Descriptive Statistics are printed on Page 2
Block Number 1. Method: Enter
* * * * * * * *** WARNING *** * * * * * * *
The following variables in the equation have low tolerances:
Variable Tolerance
NEW .00001
GREQ .00007
GREV .00002
* * * * * * *** END OF WARNING *** * * * * * *
Variable(s) Entered on Step Number 1.. NEW
2.. MAT
3.. AR
4.. GREQ
5.. GREV
Multiple R .81323 Analysis of Variance
R Square .66134 R Square Change .66134 DF Sum of Squares Mean Square
Adjusted R Square .59078 F Change 9.37336 Regression 5 6.90083 1.38017
Standard Error .38372 Signif F Change .0000 Residual 24 3.53384 .14724
F = 9.37336 Signif F = .0000
------------------------------------------ Variables in the Equation ------------------------------------------
Variable B SE B 95% Confdnce Intrvl B Beta Tolerance VIF T Sig T
GREQ .213276 .172125 -.141972 .568524 17.286077 7.250E-05 13792.328 1.239 .2273
GREV .212093 .173180 -.145333 .569519 29.359129 2.455E-05 40726.224 1.225 .2326
MAT .230845 .172926 -.126057 .587748 3.558834 .001985 503.661 1.335 .1944
AR .150697 .112061 -.080587 .381980 .210638 .575146 1.739 1.345 .1913
NEW -.210503 .173122 -.567810 .146804 -41.481229 1.212E-05 82477.926 -1.216 .2358
(Constant) -1.090440 1.081968 -3.323512 1.142633 -1.008 .3236
22 Dec 99 Multiple Collinearity Example Page 4
17:49:22 UCLA OAC IBM RS6000 AIX 3.2.5/4.
Collinearity Diagnostics
Number Eigenval Cond Variance Proportions
Index Constant GREQ GREV MAT AR NEW
1 5.94278 1.000 .00012 .00000 .00000 .00000 .00080 .00000
2 .03196 13.636 .01496 .00000 .00000 .00000 .71599 .00000
3 .01200 22.257 .04506 .00000 .00002 .00107 .01000 .00000
4 .01038 23.930 .06158 .00001 .00001 .00153 .07992 .00000
5 .00288 45.420 .63702 .00007 .00001 .00039 .19110 .00000
6 .00000 8796.670 .24127 .99991 .99997 .99701 .00218 1.00000
End Block Number 1 All requested variables entered.
22 Dec 99 Multiple Collinearity Example Page 5
17:49:22 UCLA OAC IBM RS6000 AIX 3.2.5/4.
Preceding task required .27 seconds CPU time; .50 seconds elapsed.
46 0 Regression variables=gpa,greq,grev,mat,ar
47 0 /descriptives=mean,stddev,corr,n
48 0 /statistics=r,anova,cha,coeff,ci,collin,tol,history
49 0 /dependent=gpa
50 0 /method=enter.
51 0
1908 bytes of memory required for REGRESSION procedure.
0 more bytes may be needed for Residuals plots.
22 Dec 99 Multiple Collinearity Example Page 6
17:49:22 UCLA OAC IBM RS6000 AIX 3.2.5/4.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Mean Std Dev Label
GPA 3.313 .600
GREQ 565.333 48.618
GREV 575.333 83.034
MAT 67.000 9.248
AR 3.567 .838
N of Cases = 30
Correlation:
GPA GREQ GREV MAT AR
GPA 1.000 .611 .581 .604 .621
GREQ .611 1.000 .468 .267 .508
GREV .581 .468 1.000 .426 .405
MAT .604 .267 .426 1.000 .525
AR .621 .508 .405 .525 1.000
22 Dec 99 Multiple Collinearity Example Page 7
17:49:22 UCLA OAC IBM RS6000 AIX 3.2.5/4.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. GPA
Descriptive Statistics are printed on Page 6
Block Number 1. Method: Enter
Variable(s) Entered on Step Number 1.. AR
2.. GREV
3.. MAT
4.. GREQ
Multiple R .80030 Analysis of Variance
R Square .64047 R Square Change .64047 DF Sum of Squares Mean Square
Adjusted R Square .58295 F Change 11.13400 Regression 4 6.68313 1.67078
Standard Error .38738 Signif F Change .0000 Residual 25 3.75153 .15006
F = 11.13400 Signif F = .0000
------------------------------------------ Variables in the Equation ------------------------------------------
Variable B SE B 95% Confdnce Intrvl B Beta Tolerance VIF T Sig T
GREQ .003998 .001831 2.27987E-04 .007769 .324062 .653236 1.531 2.184 .0385
GREV .001524 .001050 -6.39208E-04 .003687 .210912 .680518 1.469 1.451 .1593
MAT .020896 .009549 .001230 .040562 .322145 .663614 1.507 2.188 .0382
AR .144234 .113001 -.088497 .376964 .201604 .576442 1.735 1.276 .2135
(Constant) -1.738107 .950740 -3.696192 .219979 -1.828 .0795
Collinearity Diagnostics
Number Eigenval Cond Variance Proportions
Index Constant GREQ GREV MAT AR
1 4.94514 1.000 .00022 .00019 .00054 .00049 .00117
2 .03083 12.665 .02767 .00671 .01992 .00074 .71464
3 .01093 21.267 .04052 .00000 .76228 .32693 .00412
4 .01038 21.831 .07780 .10418 .15699 .54448 .08140
5 .00272 42.653 .85379 .88892 .06027 .12736 .19868
End Block Number 1 All requested variables entered.
22 Dec 99 Multiple Collinearity Example Page 8
17:49:22 UCLA OAC IBM RS6000 AIX 3.2.5/4.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. GPA
Summary table
-------------
Step MultR Rsq AdjRsq F(Eqn) SigF RsqCh FCh SigCh Variable BetaIn Correl
1 In: AR .6207 .6207
2 In: GREV .3947 .5815
3 In: MAT .2900 .6042
4 .8003 .6405 .5829 11.134 .000 .6405 11.134 .000 In: GREQ .3241 .6111
22 Dec 99 Multiple Collinearity Example Page 9
17:49:22 UCLA OAC IBM RS6000 AIX 3.2.5/4.
Preceding task required .00 seconds CPU time; .02 seconds elapsed.
52 0
51 command lines read.
0 errors detected.
0 warnings issued.
0 seconds CPU time.
1 seconds elapsed time.
End of job.