RE: re: st: Simple regression and Multiple regression?

[DE SOUZA Eric <eric.de_souza@coleurope.eu>]

What you need to do is to partial off the effect of the other regressors on the regressor whose coefficient you are interested in.
http://www.econ.washington.edu/user/startz/581_2007/Class%20Notes/Proof%20of%20Frisch-Waugh-Lovell.pdf

Read the first paragraph of the linked text. Then skip to after equation 1.4 where the formula for beta_2_hat is given. From there it is clear that it suffices to remove the effects of X1 on X2.


Eric de Souza
College of Europe
BE-8000 Brugge (Bruges)
Belgium

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of gjhxmu@sina.com
Sent: 14 March 2010 19:03
To: statalist
Subject: Re: re: st: Simple regression and Multiple regression?

Dear Kit and Alan,
Thank you very much for your help!
I helps a lot.
By the way,"Frisch-Waugh-Lovell theorem says that the coefficient of turn should be the same in multiple regression or in a regression  of price on turn, with the effects of other regressors partialled-off from both." In Woodbridge's book,  the effect of other regressors is only partialled-off from the concerned regressor, not from the dependent variable. 
It is also OK, right?
What I  tried in stata told me it was OK.

Thank you very much again!
Best regards,
Rose

----- Original Message -----
From: Kit Baum <baum@bc.edu>
To: statalist@hsphsun2.harvard.edu
Subject: re: st: Simple regression and Multiple regression?
Date: 2010-3-15 00:18:14

<>
Alan said

To add to Kit's point, I believe that the coefficients could be identical but it would require that all of the independent measures are uncorrelated.

Quite so. Iff the regressors are mutually orthogonal, then simple regression and multiple regression coefficients are identical. But when they are not, you must partial-off the other regressors to get a simple regression of Y on X to equal the multiple regression coefficient of Y on X, Z, R, P, Q etc. That is the essence of the FWL theorem.

Kit Baum | Boston College Economics & DIW Berlin | http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming | http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata | http://www.stata-press.com/books/imeus.html


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