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ADVANCED COLLINEARITY DIAGNOSTICS FOR BODY FAT EXAMPLE
>USE 'C:\SYSTAT7\S209\BODYFAT.SYD'
SYSTAT Rectangular file C:\SYSTAT7\S209\BODYFAT.SYD,
created Tue Mar 09, 1999 at 13:03:38, contains variables:
X1 X2 X3 Y
>let bodfat=y
>let triceps=x1
>let thigh=x2
>let midarm=x3
>mglh
>print=long
>FORMAT 12,6
>model bodfat = constant + triceps + thigh + midarm
>estimate
Eigenvalues of unit scaled X'X
1 2 3 4
3.967957 0.020523 0.011512 0.000009
Condition indices
1 2 3 4
1.000000 13.904816 18.565705 677.372065
Condition indices are sqrt (largest eigenvalue/each successive eigenvalue);
EX: sqrt (3.967957/0.020523) = 13.904816; largest condition index (here 677.4) is the
"condition number" of X; a high condition number means that X is "ill-conditioned".
Variance proportions
1 2 3 4
CONSTANT 0.000002 0.000372 0.000599 0.999027
TRICEPS 0.000003 0.001319 0.000219 0.998459
THIGH 0.000001 0.000033 0.000326 0.999641
MIDARM 0.000010 0.001389 0.006934 0.991668
Dep Var: BODFAT N: 20 Multiple R: 0.895186 Squared multiple R: 0.801359
Adjusted squared multiple R: 0.764113 Standard error of estimate: 2.479981
Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail)
CONSTANT 117.084695 99.782403 0.0 . 1.17340 0.25781
TRICEPS 4.334092 3.015511 4.263705 0.001411 1.43727 0.16991
THIGH -2.856848 2.582015 -2.928701 0.001772 -1.10644 0.28489
MIDARM -2.186060 1.595499 -1.561417 0.009560 -1.37014 0.18956
Effect Coefficient Lower < 95%> Upper
CONSTANT 117.084695 -94.444551 328.613941
TRICEPS 4.334092 -2.058507 10.726691
THIGH -2.856848 -8.330476 2.616780
MIDARM -2.186060 -5.568367 1.196247
Correlation matrix of regression coefficients
CONSTANT TRICEPS THIGH MIDARM
CONSTANT 1.000000
TRICEPS 0.997684 1.000000
THIGH -0.999001 -0.999107 1.000000
MIDARM -0.996656 -0.995174 0.993935 1.000000
Analysis of Variance
Source Sum-of-Squares df Mean-Square F-ratio P
Regression 396.984612 3 132.328204 21.515712 0.000007
Residual 98.404888 16 6.150306
-------------------------------------------------------------------------------
Durbin-Watson D Statistic 2.243
First Order Autocorrelation -0.168
Calculate VIF as VIF = 1/TOL
>calc 1/0.001411
708.717222
>calc 1/0.001772
564.334086
>calc 1/0.00956
104.602510
Last modified 11 April 1999