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. <[email protected]>
Doctoral Student, Graduate School of Law and Politics,
The University of Tokyo
On Wed, 09 Jun 2004 12:25:31 -0500
Richard Williams <[email protected]> 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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