Re: [R] Can I do regression by steps?

From: John Sorkin <>
Date: Tue, 08 Jul 2008 18:11:20 -0400

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, y=f(x1)
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

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 <> 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!

View this message in context: 
Sent from the R help mailing list archive at

______________________________________________ mailing list 
PLEASE do read the posting guide 
and provide commented, minimal, self-contained, reproducible code.

Confidentiality Statement:
This email message, including any attachments, is for th...{{dropped:6}}

______________________________________________ mailing list
PLEASE do read the posting guide
and provide commented, minimal, self-contained, reproducible code.
Received on Tue 08 Jul 2008 - 22:21:54 GMT

Archive maintained by Robert King, hosted by the discipline of statistics at the University of Newcastle, Australia.
Archive generated by hypermail 2.2.0, at Wed 09 Jul 2008 - 03:31:34 GMT.

Mailing list information is available at Please read the posting guide before posting to the list.

list of date sections of archive