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
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
 
410-605-7119 
- NOTE NEW EMAIL ADDRESS:
jsorkin@grecc.umaryland.edu

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