# RE: st: RE: why is F statistic still missing even though there is no singleton dummy problem?

 From "Jian Zhang" To "Schaffer, Mark E" , statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu Subject RE: st: RE: why is F statistic still missing even though there is no singleton dummy problem? Date Fri, 18 Aug 2006 13:09:59 -0700 (PDT)

```Thanks, Mark and Maarten!  Your answers are really helpful!

Best regards,
Jian Zhang

> Jian Zhang,
>
> In fact, it is a singleton dummy problem.  The key variables are var5
> and var6.  You can drop var3 and
>
> reg var1 var5 var6, nocons robust
>
> gives you the same problem.
>
> The way this arises is as follows.  var5 and var6 are collinear, with
> the exception of observation 5:
> Maarten
>      +-------------+
>      | var5   var6 |
>      |-------------|
>   1. |    0      0 |
>   2. |    0      0 |
>   3. |   -4      4 |
>   4. |    0      0 |
>   5. |   14     -7 |
>      |-------------|
>   6. |    0      0 |
>   7. |    0      0 |
>   8. |    0      0 |
>   9. | -123    123 |
>  10. |    0      0 |
>      |-------------|
>  11. |    0      0 |
>  12. |    0      0 |
>  13. |    0      0 |
>      +-------------+
>
> After your regression (or the regression dropping var3), the residual
> for observation 5 is essentially zero:
>
> . reg var1 var5 var6, nocons robust
>
> <snip>
>
> . predict double e, resid
>
> . list e in 5
>
>      +-----------+
>      |         e |
>      |-----------|
>   5. | 1.927e-13 |
>      +-----------+
>
> Recall that the robust var-cov matrix comes from the inverse of X'e*e'X,
> where e is the residual and X is the matrix of regressors.  Thus each of
> the observations of var5 and var6 is getting weighted by the residual
> for that observation.  But after weighting by e, var5 and var6 collinear
> because the residual for observation 5 is zero, and observation 5 was
> the only thing that stopped them from being collinear.  The result is a
> var-cov matrix that is not full rank.
>
> To see that this is the same thing as the singleton dummy problem,
> create a new variable var567 which is a linear transformation of var5
> and var6:
>
> . gen var567=(var5+var6)/7
>
> . list var5 var6 var567
>
>      +----------------------+
>      | var5   var6   var567 |
>      |----------------------|
>   1. |    0      0        0 |
>   2. |    0      0        0 |
>   3. |   -4      4        0 |
>   4. |    0      0        0 |
>   5. |   14     -7        1 |
>      |----------------------|
>   6. |    0      0        0 |
>   7. |    0      0        0 |
>   8. |    0      0        0 |
>   9. | -123    123        0 |
>  10. |    0      0        0 |
>      |----------------------|
>  11. |    0      0        0 |
>  12. |    0      0        0 |
>  13. |    0      0        0 |
>      +----------------------+
>
> This new variable is a singleton dummy.  But since it's a linear
> transformation of var5 and var6, you can replace either var5 or var6 and
> you get the same regression, e.g.,
>
> . qui regress var1 var5 var6, nocons robust
>
> . di _b[var6]
> .84687073
>
> . di e(mss)
> 91.557676
>
> . qui regress var1 var5 var56, nocons robust
>
> . di _b[var56]
> .84687073
>
> . di e(mss)
> 91.557676
>
> --Mark
>
>
> Prof. Mark E. Schaffer
> Director
> Centre for Economic Reform and Transformation
> Department of Economics
> School of Management & Languages
> Heriot-Watt University
> Edinburgh EH14 4AS  UK
> 44-131-451-3494 direct
> 44-131-451-3296 fax
> http://www.sml.hw.ac.uk/cert
>
>
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jian Zhang
> > Sent: Friday, August 18, 2006 12:51 AM
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: why is F statistic still missing even though
> > there is no singleton dummy problem?
> >
> > Dear Statalisters,
> >
> > I am running a ols regression on a small data set.  The
> > reported F statistic is still mssing although the data set
> > doesn' have so-called singleton dummies.  Is there anyone
> > knowing what is going on?  Here are the data set and the
> > regression results.  Many thanks!
> >
> >
> > . list var1 var3 var5 var6
> >
> > +---------------------------+
> >       var1   var3   var5   var6
> > ---------------------------
> > 1.     1    789      0      0
> > 2.     3     45      0      0
> > 3.     5   2358     -4      4
> > 4.     4     65      0      0
> > 5.     5     12     14     -7
> > ---------------------------
> > 6.   453     12      0      0
> > 7.     6      4      0      0
> > 8.    45      2      0      0
> > 9.     8      3   -123    123
> > 10.   897      5      0      0
> > ---------------------------
> > 11.    43     87      0      0
> > 12.    43     56      0      0
> > 13.     4     25      0      0
> > +---------------------------+
> >
> >
> >  reg var1 var3 var5 var6,	robust nocons
> >
> > Linear regression			Number of obs	=      13
> > 			F(  2,    10)	=       .
> > 			Prob > F	=       .
> > 			R-squared	=  0.0002
> > 			Root MSE	=  318.67
> >
> >
> > 	Robust
> > var1       Coef.	Std. Err.      t	P>t	[95%
> > Conf.	Interval]
> >
> > var3    .0046225	.0031     1.49	0.167	-.0022847
.0115297
> > var5    .7696625	.0060938   126.30	0.000
> > .7560848	.7832403
> > var6    .8329636	.007418   112.29	0.000
> > .8164353	.8494919
> >
> >
> >
> >
> >
> >
> >
> > Best regards,
> > Jian Zhang
> > *
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> >
> >
>
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```