# Re: st: Weighted Least Squares

 From "Tam Phan" To statalist@hsphsun2.harvard.edu Subject Re: st: Weighted Least Squares Date Tue, 15 Apr 2008 13:14:26 -0400

```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 "adjust"
> > 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?
> > > >
> > > >
> > > > 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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> > >
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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:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>
*
*   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/
```