# Re: st: Weighted Least Squares

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: Weighted Least Squares Date Tue, 15 Apr 2008 18:50:12 +0100 (BST)

```I think I understand your problem now, but I am afraid that I don't
have much of an answer, other than that it reminds me of the ecological
fallacy, see (Robinson 1950). Maybe others on this list have something
more productive to offer.

-- Maarten

Robinson, W.S. (1950). "Ecological Correlations and the Behavior of
Individuals". American Sociological Review 15: 351–357.

--- Tam Phan <tamdphan@gmail.com> wrote:

> Hi Maarten,
>
> So, there several zones within a pricing area.  Suppose there is 1
> pricing area, and in this area, there are 2 zones.  The explanatory
> variables have been define at the zone levels.  Say Zone 1 has
> exlanatory variables X12, X13 that corresponds to a dependent
> variable
> Q1.  Say Zone 2, it has explanatory variable X22, X24 (note there is
> no X23 that correspond with X13 for zone 2), and its dependent
> variable is Q2.
>
> In this context, I would like to do one regression equation, mainly
>
> Q1+Q2 = alpha + [  (Q1/(Q1+Q2))*X12 + (Q2/(Q1+Q2))*X22 ]b + [
> (Q2/(Q1+Q3)X24)]v+ e
>
> Note that X12 and X22 are the same explanatory variables, its just
> that numerically they have different values in each zones, hence,
> they
> are weighted by the corresponding dependent variables (this can be
> the
> quanity sold for a particular item in both demand zone).
>
> Tam
>
> On 4/15/08, Maarten buis <maartenbuis@yahoo.co.uk> wrote:
> > Sorry, but I still do not understand your question. It may help if
> you
> > tell a bit more about your project, for instance:
> >
> > what are your levels?
> >
> > what is the purpose of your analysis?
> >
> > -- Maarten
> >
> > --- Tam Phan <tamdphan@gmail.com> wrote:
> >
> > > Maarten, X1 = % and X2= %, however, X1 +X2 does not necessary
> have to
> > > add up to 100% (as a matter of fact they dont).
> > >
> > > The % are calculated based on the zone, they are not calcualted
> > > across
> > > zone (say zone 1 and zone 2).
> > >
> > > Basically the explanatory variables are at a zone level, however,
> the
> > > regression is taking place at a higher level.  In order to
> > > the zone explanatory varaibles, these are weighted to the higher
> > > level.
> > >
> > > Tam
> > >
> > > On 4/15/08, Maarten buis <maartenbuis@yahoo.co.uk> wrote:
> > > > I read your question as follows:
> > > > - you have two (or more) variables: x1 = % in zone1, and x2 = %
> in
> > > >  zone 2, which must add up to 100%
> > > > - x1 and x2 are explanatory variables
> > > > - you want these variables to have only one effect instead two
> (or
> > > >  more) because you see them as one variable.
> > > >
> > > > Is that correct?
> > > >
> > > > -- Maarten
> > > >
> > > >
> > > > --- Tam Phan <tamdphan@gmail.com> wrote:
> > > >
> > > > > Hello Stata Users:
> > > > >
> > > > > I have a quick question on weighted Least squares:  Below is
> the
> > > > > following econometric equation:
> > > > >
> > > > > Q1+Q2 = alpha + [  (Q1/(Q1+Q2))*X1 + (Q2/(Q1+Q2))*X2 ]b + e
> > > > >
> > > > > Where X1 and X2 are the same explanatory variables, however
> with
> > > > > different numerical values.  For example, X1 would be the %
> in
> > > one
> > > > > zone, and X2 is the percent in another zone.
> > > > >
> > > > > Is there anything wrong w/ this logic?
> > > > >
> > > > > How about this econometric model:
> > > > >
> > > > > y1=alpha1+beta1(P)+e
> > > > > y2= alpha2 +beta2(P)+v
> > > > >
> > > > > To obtain the aggregate effect one would sum:
> > > > >
> > > > > y1+y2=(alpha1+alpha2) +(beta1+beta2)P+(e+v)
> > > > >
> > > > > Is there anything wrong with the above logic?
> > > > >
> > > > > Tam
> > > > >
> > > > > Tam
> > > > > *
> > > > > *   For searches and help try:
> > > > > *   http://www.stata.com/support/faqs/res/findit.html
> > > > > *   http://www.stata.com/support/statalist/faq
> > > > > *   http://www.ats.ucla.edu/stat/stata/
> > > > >
> > > >
> > > >
> > > > -----------------------------------------
> > > > Maarten L. Buis
> > > > Department of Social Research Methodology
> > > > Vrije Universiteit Amsterdam
> > > > Boelelaan 1081
> > > > 1081 HV Amsterdam
> > > > The Netherlands
> > > >
> > > > visiting address:
> > > > Buitenveldertselaan 3 (Metropolitan), room Z434
> > > >
> > > > +31 20 5986715
> > > >
> > > > http://home.fsw.vu.nl/m.buis/
> > > > -----------------------------------------
> > > >
> > > >
> > > >
> ___________________________________________________________
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> > >
> >
> >
> > -----------------------------------------
> > Maarten L. Buis
> > Department of Social Research Methodology
> > Vrije Universiteit Amsterdam
> > Boelelaan 1081
> > 1081 HV Amsterdam
> > The Netherlands
> >
> > visiting address:
> > Buitenveldertselaan 3 (Metropolitan), room Z434
> >
> > +31 20 5986715
> >
> > http://home.fsw.vu.nl/m.buis/
> > -----------------------------------------
> >
> >
> >      ___________________________________________________________
> > Yahoo! For Good helps you make a difference
> >
> > http://uk.promotions.yahoo.com/forgood/
> > *
> > *   For searches and help try:
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> >
> *
> *   For searches and help try:
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>

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

___________________________________________________________
Yahoo! For Good helps you make a difference

http://uk.promotions.yahoo.com/forgood/
*
*   For searches and help try:
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```