THE RUNS TESTS - AN ALTERNATIVE (OR ADDITIONAL) NONPARAMETRIC TEST OF AUTOCORRELATION OF RESIDUALS WITH THE DIVORCE DATA SET

>USE "D:\mydocs\ys209\divorce.syd"

SYSTAT Rectangular file D:\mydocs\ys209\divorce.syd,
created Wed Apr 19, 2000 at 00:25:57, contains variables:

 YEAR         DIVPOP       DIVMF        UNEMP        FLFPRT       MARUMF
 TREND

First do the regression and save the residuals (repeat).

>mglh
>select year <= 1970
>model divmf=constant+unemp+flfprt+marumf
>save divres01/data
>estimate

Data for the following results were selected according to:
      year <= 1970

Dep Var: DIVMF   N: 51   Multiple R: 0.866237   Squared multiple R: 0.750366
Adjusted squared multiple R: 0.734432   Standard error of estimate: 1.206846

Effect         Coefficient    Std Error     Std Coef Tolerance     t   P(2 Tail)
CONSTANT         -9.243243     2.117510     0.000000   .       -4.36515  0.00007
UNEMP             0.047519     0.035985     0.125499  0.588047  1.32052  0.19306
FLFPRT            0.239771     0.029453     0.672784  0.777664  8.14082  0.00000
MARUMF            0.137210     0.019332     0.606853  0.726515  7.09745  0.00000

                             Analysis of Variance

Source             Sum-of-Squares   df  Mean-Square     F-ratio       P
Regression            205.764749     3    68.588250   47.091854    0.000000
Residual               68.454466    47     1.456478

*** WARNING ***
Case           26 is an outlier        (Studentized Residual =     3.239025)
Case           27 has large leverage   (Leverage =     0.347000)
Case           27 is an outlier        (Studentized Residual =     3.955823)

Durbin-Watson D Statistic     0.429
First Order Autocorrelation   0.711

Residuals have been saved.
-------------------------------------------------------------------------------

Plot of Residuals against Predicted Values

Second, use the file of residuals, go to the npar (nonparametric statistics) module, and do the runs test.  A significant result indicates that the residuals are correlated

>use divres01

SYSTAT Rectangular file d:\mydocs\ys209\divres01.SYD,
created Wed Apr 26, 2000 at 13:29:59, contains variables:

 ESTIMATE     RESIDUAL     LEVERAGE     COOK         STUDENT      SEPRED
 YEAR         DIVPOP       DIVMF        UNEMP        FLFPRT       MARUMF
 TREND

>npar
>runs residual
 

Wald-Wolfowitz runs test using cutpoint =        0.000
                                                                   Probability
 Variable    Cases LE Cut  Cases GT Cut   Runs         Z              (2-tail)
 RESIDUAL          32            19         8     -5.103269          0.000000

Thus one concludes that the residuals in this case are correlated.