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From |
"Lynn Lee" <lynn09v@gmail.com> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: coefficient interpretation in OLS |

Date |
Sat, 18 Aug 2012 10:37:34 -0700 |

Dear David, I appreciate your suggestion about IMS Bulletin regarding this interpretation issue. The two points are much more informative and detailed than what I learned from textbook. Best Regards, Lynn Lee -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of David Hoaglin Sent: Friday, August 17, 2012 7:09 AM To: statalist@hsphsun2.harvard.edu Subject: Re: st: coefficient interpretation in OLS Dear Lynn, In interpreting the coefficients in a multiple regression, two facts are important. 1. The definition of each coefficient includes the set of other predictors in the model. 2. The coefficient of a predictor, say X1, tells how Y changes in response to change in X1 after adjusting for the contributions of the other predictors in the model (in the data at hand). A coefficient is a slope, so it gives change in Y per unit increase in X1, not necessarily the change in Y when X1 is increased by 1 unit (unless the values of X1 are only 0 and 1). Some textbooks, unfortunately, interpret the coefficient of X1 as telling how Y changes with an increase of 1 unit in X1 when the other predictors are held fixed, but that is simply not how OLS works; that interpretation is oversimplified and often incorrect. Terry Speed's column in the current issue of the IMS Bulletin discusses both of these points. David Hoaglin On Fri, Aug 17, 2012 at 6:25 PM, Lynn Lee <lynn09v@gmail.com> wrote: > Dear all, > > When I run simple OLS regression or pooled OLS regression, I find if I add > more variables to the model, the coefficient on specific explanatory > variable can vary in magnitude. For example, > Y1=beta+beta1*X1+beta2*X2+beta3*X3+error term; > Y2=alpha+alpha1*X1+ alpha2*X2+ alpha3*X3+ alpha4*X4+error term. > The absolute value of estimates of beta1 or alpha1 can increase or sometimes > decrease. I am not confident to explain this theoretically. Is it related > to potential endogeneity issue? > > Best Regards, > Lynn Lee * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: coefficient interpretation in OLS***From:*"Lynn Lee" <lynn09v@gmail.com>

**Re: st: coefficient interpretation in OLS***From:*David Hoaglin <dchoaglin@gmail.com>

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