Re: [Gretl-users] Heteroskedasticity / correction
On Fri, 10 Jan 2014, Ana Amaro ISG wrote:
When you multiply all the terms of the model by 1 / sqrt(x) the
const of the original model turns out to be
const / sqrt(x)
So this term of the corrected model is now a parameter (const)
times a variable (1/ sqrt(x)) meaning that a 'const' alone
disapeared in the new model.
Is this clear?
Yes. But the model in question still has two regressors: the
adjusted "x" and the adjusted "const" (which, I agree, is no longer
a true constant).
So now if you want to test the weighted regression for any remaining
heteroskedasticity the question is, should the auxiliary regression
for White's test include a true constant (in addition to the term
(1/sqrt(x))?
I suppose the answer has to be Yes (to give the null hypothesis a
fighting chance). And that is what gretl will now do, after
modification in response to your first posting. Here's an
illustrative script:
<hansl>
open data4-1
# unweighted regression and test
ols price const sqft
modtest --white
# generate weighted data
series w = sqrt(sqft)
series wy = price/w
series w0 = const/w
series wx = sqft/w
# weighted regression and test
ols wy w0 wx
modtest --white
</hansl>
If you run this with current CVS/snapshot you'll see that the second
White's test auxiliary regression includes "const" as well as w0
(plus wx and the squares of w0 and wx).
Allin Cottrell