Re: st: about residuals and coefficients

[Yuval Arbel <yuval.arbel@gmail.com>]

David,

I don't see any difference between the theorem described by Valerio
Filoso and by William Greene (accept for the fact that Greene
generalizes the theorem to matrix notation).

Maybe what is bothering you is the fact that Greene (or other textbook
writers) does not show a practical application to this theorem.But
this is done very nicely by Valerio Filoso in the Stata article, which
provides a formal proof, exemplifies that the theorem works - and
talks about -reganat- command

On Thu, Sep 5, 2013 at 4:10 AM, David Hoaglin <dchoaglin@gmail.com> wrote:
> Yuval,
>
> I am grateful for Greene's textbook.  Unfortunately, however, it is
> not difficult to find textbooks (in various fields) that interpret an
> estimated coefficient in a multiple regression as the change in Y when
> that predictor variable is increased by one unit and the other
> predictors are held constant.  The authors of those books apparently
> do not realize that, as the quotation from Greene shows, such an
> interpretation does not reflect the way multiple regression works.
>
> David Hoaglin
>
> On Thu, Sep 5, 2013 at 2:55 AM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>> I also checked in Greene's textbook - which is considered to be (at
>> least by economists) the most extensive econometric textbook - which
>> covers almost everything. On page 73 he specifically mentions the
>> Frisch-Waugh (1933)-Lovell (1963) Theorem as Theorem 3.2.
>>
>> "In the linear least squares regression of vector y on two sets of
>> variables, X1 and X2, the subvector b2 is the set of coefficients
>> obtained when the residuals from a regression of y on X1 alone are
>> regressed on the set of residuals obtained when each column of X2 is
>> regressed on X1"
>>
>> P.S. It is possible that someone does not get the credit he or she
>> deserves, but this is a matter for history researchers. A very famous
>> example is the L'Hopital Rule, named after the wrong person. The story
>> says that L'Hopital bought the right to be named as the original
>> discoverer of the rule
>>
>> Reference: William H. Greene: Econometric Analysis, Seventh Edition
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/faqs/resources/statalist-faq/
> *   http://www.ats.ucla.edu/stat/stata/



-- 
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
e-mail1: yuval.arbel@carmel.ac.il
e-mail2: yuval.arbel@gmail.com
You can access my latest paper on SSRN at:  http://ssrn.com/abstract=2263398
You can access previous papers on SSRN at: http://ssrn.com/author=1313670
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/