# Re: st: How -ovtest- works?

 From UENOHARA Hideaki 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.

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)
>
> . 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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```