# [R] two methods for regression, two different results

From: John Sorkin <jsorkin_at_grecc.umaryland.edu>
Date: Wed 06 Apr 2005 - 12:54:40 EST

Please forgive a straight stats question, and the informal notation.

let us say we wish to perform a liner regression: y=b0 + b1*x + b2*z

There are two ways this can be done, the usual way, as a single regression,
fit1<-lm(y~x+z)
or by doing two regressions. In the first regression we could have y as the dependent variable and x as the independent variable fit2<-lm(y~x).
The second regrssion would be a regression in which the residuals from the first regression would be the depdendent variable, and the independent variable would be z.
fit2<-lm(fit2\$residuals~z)

I would think the two methods would give the same p value and the same beta coefficient for z. The don't. Can someone help my understand why the two methods do not give the same results. Additionally, could someone tell me when one method might be better than the other, i.e. what question does the first method anwser, and what question does the second method answer. I have searched a number of textbooks and have not found this question addressed.

Thanks,
John

John Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
Baltimore VA Medical Center GRECC and
University of Maryland School of Medicine Claude Pepper OAIC

University of Maryland School of Medicine Division of Gerontology
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