SAT 3/06/99 3:09:02 PM
SYSTAT VERSION 7.0.1
COPYRIGHT (C) 1997, SPSS INC.
Welcome to SYSTAT!
>USE 'C:\SYSTAT7\S209\GRAD.SYD'
SYSTAT Rectangular file C:\SYSTAT7\S209\GRAD.SYD,
created Wed Feb 17, 1999 at 08:32:46, contains variables:
ID STATE$
GRAD INC
PWHI PBLA
PHIS EDEXP
URB
>corr
The HADI robust outlier detection and
covariance matrix estimation is part of
SYSTAT's CORR module
>print=long
>idvar=state$
>save gradhad
>cova grad inc pbla phis edexp urb/hadi
These 6 outliers are identified:
Case Distance
------------ ------------
AZ
5.02053
CA
5.67307
AK
5.70352
TX
6.72038
DC
7.06904
NM
13.90230
Means of variables of non-outlying cases
GRAD INC
PBLA PHIS
EDEXP
74.558 12071.178
9.549 2.644
3340.200
URB
62.596
HADI estimated covariance matrix
GRAD INC
PBLA PHIS
EDEXP
GRAD
56.921
INC
2555.267 2640730.604
PBLA
-49.626 -3045.791
91.413
PHIS
-4.847 2027.335
-2.655 7.217
EDEXP
1123.927 900395.850 -1949.574
807.632 571965.618
URB
-45.306 24011.094
40.903 27.858
6608.983
URB
URB
499.580
Number of observations: 51
Matrix has been saved.
>mglh
>USE 'C:\SYSTAT7\S209\GRADHAD.SYD'
SYSTAT Covariance file C:\SYSTAT7\S209\GRADHAD.SYD,
created Sat Mar 06, 1999 at 15:11:32, contains variables:
GRAD INC
PBLA PHIS
EDEXP URB
>model grad=inc+pbla+phis+edexp+urb/n=51
>estimate
Since the model is estimated from a variance-covariance
matrix the number od cases
has to be specified, and the model does
not include a constant; the output includes
the detailed collinearity diagnostics
(discussed later) as a by-product because we
had specified PRINT=LONG earlier
Eigenvalues of unit scaled X'X
1 2
3 4
5
2.598 1.178
0.643 0.409
0.172
Condition indices
1 2
3 4
5
1.000 1.485
2.010 2.520
3.891
Variance proportions
1 2
3 4
5
INC
0.034 0.000
0.039 0.014
0.913
PBLA
0.005 0.464
0.026 0.393
0.112
PHIS
0.052 0.004
0.828 0.098
0.018
EDEXP
0.042 0.022
0.091 0.397
0.448
URB
0.035 0.074
0.004 0.340
0.546
Dep Var: GRAD N: 51 Multiple R: 0.816
Squared multiple R: 0.667
Adjusted squared multiple R: 0.630 Standard error of estimate:
4.404
Effect Coefficient
Std Error Std Coef Tolerance
t P(2 Tail)
INC
0.002 0.001
0.518 0.277 3.165
0.003
PBLA
-0.465 0.078
-0.590 0.756 -5.956
0.000
PHIS
-1.047 0.286
-0.373 0.715 -3.663
0.001
EDEXP
-0.001 0.001
-0.078 0.433 -0.597
0.553
URB
-0.099 0.045
-0.295 0.414 -2.203
0.033
Effect Coefficient
Lower < 95%> Upper
INC
0.002 0.001
0.004
PBLA
-0.465 -0.623
-0.308
PHIS
-1.047 -1.623
-0.471
EDEXP
-0.001 -0.003
0.002
URB
-0.099 -0.190
-0.009
Correlation matrix of regression coefficients
INC PBLA
PHIS EDEXP
URB
INC
1.000
PBLA
0.255 1.000
PHIS
-0.046 0.118
1.000
EDEXP
-0.613 0.106
-0.130 1.000
URB
-0.594 -0.430
-0.283 0.145
1.000
Analysis of Variance
Source
Sum-of-Squares df Mean-Square
F-ratio P
Regression
1745.384 5 349.077
17.994 0.000
Residual
872.968 45 19.399
An alternative to estimating the regression model
from the Hadi covariance matrix saved in the CORR module (as shown above)
is to estimate the model from the original data after excluding the 6 cases
flagged as outliers by the Hadi procedure. The results are the same.