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st: RE: interpretting log transformed co-efficients

From   "Newson, Roger B" <>
To   <>
Subject   st: RE: interpretting log transformed co-efficients
Date   Mon, 9 Feb 2009 11:33:48 -0000

If you are regressing a log-transformed outcome on one or more
X-variates using -regerss-, then you should probably use the -eform-
option. This implies that the coefficients displayed are geometric
means, or geometric mean ratios, or geometric mean per-unit ratios
(assuming an exponential relationship between the original untransformed
Y-variable and the X-variable. For instance, if the X-variable is female
gender, and the untransformed Y-variable is length of stay, then the
coefficient for female gender is the geometric mean ratio between length
of stay in females and length of stay in otherwise equivalent males.

This principle is explained in a Stata Tip in the Stata Journal (Newson,
2003). If you want the exponentiated intercept (equal in your case to
the geometric mean length of stay im males), then it is a good idea to
use the -noconst- option, and to define a second X-variate containing
values all equal to 1, whose coefficient is the exponentiated intercept.

I hope this helps.

Best wishes



Newson R. Stata tip 1: The eform() option of regress. The Stata Journal
2003; 3(4): 445.
Download from

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Web page:
Departmental Web page:

Opinions expressed are those of the author, not of the institution.

-----Original Message-----
[] On Behalf Of Ashwin
Sent: 08 February 2009 16:35
Subject: st: interpretting log transformed co-efficients


I'm having some trouble interpretting the linear regression
co-efficients for log transformed variables. 

I have outcomes (such as length of stay or costs) that are not normally
distributed, so I'm including the log transformed (now normal) variables
as the outcome measures in linear regression models. 

But I'm not really sure how to interpret the resulting co-efficients. Do
they represent a % change in outcome for a defined change in a predictor

Just for example, suppose I'm modelling length of stay against gender
(male 0 female 1). 

Without log transformation, if I get a linear regression co-efficient of
0.6, I can say that females have a 0.6 days longer stay. 

But if I use log (length of stay) as the outcome and get a co-efficient
0.2 for the same linear regression model, how do I interpret this? 


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