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