[R] Can I do regression by steps?

John Sorkin jsorkin at grecc.umaryland.edu
Wed Jul 9 00:11:20 CEST 2008

Be very careful!
When regression is performed by steps, you often will not get the same results as you would get from a single multivariable regression. The explanation for this is not simple, but a simplified explanation is that when you do your first regression,
all the total variance that can be accounted for is sucked up by x1 leaving little varinace to be accounted for by your second regression,
residuals=f(x2). In contrast when you perform a multivariable regression,
y=f(x1,x2) the total variance is proportioned between x1 and x2.

John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)

>>> rlearner309 <unixunix99 at gmail.com> 7/8/2008 8:53 AM >>>

I saw this type of models in some of my company projects.  

To simplify:
Y is regressed on X1 and X2.  But the regression is done by two steps: 
First Y is regressed on X1 with intercept, and the residuals from the first
step are used to regress on X2, without the constant.  The reason to do so
is some observations have X1 data but do not have X2, so I guess the person
wants to use as much information as he can to get the coef. for X1, and then
use part of the residuals (that have X2 data) to catch what is left to be
explained by X2.

But my concern is, should we consider the correlation between X1 and X2?  If
residuals from the first step are used, then X1 effect has been removed. 
Then what does it really mean by regressing residuals on X2, which has some
X1 effect correlated with?? should X2 be adjusted by X1, too (regress X2 on
X1 and use the residuals)?  

What if both X1 and X2 are dummy variables?  Dummy variables can have a
meaningful correlation, too, right?

Thanks a lot!
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