# st: re: interpretting log transformed co-efficients

 From Christopher Baum To statalist@hsphsun2.harvard.edu Subject st: re: interpretting log transformed co-efficients Date Sun, 8 Feb 2009 13:54:27 -0500

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Ashwin said
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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 variable? 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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You are now calculating what economists would call a semi-elasticity of LOS wrt gender. Roughly, d log LOS / d Gender. So 0.2 is ~20%.
```You might for comparison run the original model of LOS and then do

mfx compute, eydx

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which calculates the same thing at a point in the model space (the point of means). In a model with a log-transformed variable, the eydx (or semi-elasticity) is constant throughout the model space.
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Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html

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