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Re: st: How -ovtest- works?


From   UENOHARA Hideaki <uhideaki@td6.so-net.ne.jp>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: How -ovtest- works?
Date   Fri, 11 Jun 2004 20:40:32 +0900

Many thanks to Richard and Andreas.

I understand how -ovtest- is working. I should have read the manual
carefully.
But I have still one question.

Why does Stata normalize the y-hat variable before powers are taken?
(Reference N-R p.381)
And why does it change the outcome, that is, the F statistic?
I don't think a normalization of regressors change F statistic.

Any comment would be helpful.

UENOHARA Hideaki, LL.M. <uhideaki@td6.so-net.ne.jp>
 Doctoral Student, Graduate School of Law and Politics,
 The University of Tokyo


On Wed, 09 Jun 2004 12:25:31 -0500
Richard Williams <Richard.A.Williams.5@ND.edu> wrote:

> At 07:04 PM 6/9/2004 +0200, Andreas Kuhn wrote:
> 
> >- ovtest - also includes the fourth power of yhat as a regressor. thus, 
> >including yhat^4 in your regression should give the same result as ovtest.
> 
> That is part of the problem, but not all.  As the reference manual N-R 
> points out, p. 381, the y-hat variable is normalized to have mean 0 and 
> variance one before powers are taken.  So, try this:
> 
> . sysuse auto
> 
> . quietly reg price mpg weight foreign
> 
> . predict y
> (option xb assumed; fitted values)
> 
> . quietly sum y
> 
> . replace y = (y - r(mean))/r(sd)
> (74 real changes made)
> 
> . gen y2 = y^2
> 
> . gen y3 = y^3
> 
> . gen y4 = y^4
> 
> . quietly reg price mpg weight foreign y2 y3 y4
> 
> . test y2 y3 y4
> 
>   ( 1)  y2 = 0
>   ( 2)  y3 = 0
>   ( 3)  y4 = 0
> 
>         F(  3,    67) =   15.31
>              Prob > F =    0.0000
> 
> .
> 
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