# Re: st: R: linear regression question

 From dr kardos laszlo To statalist@hsphsun2.harvard.edu Subject Re: st: R: linear regression question Date Tue, 17 Mar 2009 08:33:31 +0100

```unless i got something wrong,
```
the relative change in y associated with a unit change in x in such models works out as antilog(beta) on the appropriate base. in this case, because galina explicitly mentioned natural log, and using carlo's example, it is exp(.2) = 1.2214, a 22.14% increase. try with base-10 and you will get something completely different.
```
```
the approximation 100*beta% works better and better as beta approaches zero (and as the log-transformation base approaches 1, but that's not typical in practice). in the stata journal article referred to below, beta=.0741516 and exp(beta)=1.07697, arguably close to 1.07415. in other cases, the difference might be to an extent you do not want to ignore.
```
laszlo

Galina Hayes wrote:
```
```Thanks very much everyone, very helpful.
Galina
----- Original Message -----
From: "Maarten buis" <maartenbuis@yahoo.co.uk>
To: statalist@hsphsun2.harvard.edu
Sent: Sunday, March 15, 2009 11:48:52 AM GMT -05:00 US/Canada Eastern
Subject: Re: st: R: linear regression question

--- On Sun, 15/3/09, Carlo Lazzaro wrote:
```
```your thread seems to refer to a log-linear model, where
only the dependent variable (i.e., Y) is log-transformed.

In a log-linear model, a unit-change in the independent
```
variable X (i.e., DeltaX=1)is associated with a 100*Beta% change in Y.
```
```
This is one possible way of interpreting such a model. An alternative way is discussed in: Roger Newson (2003) "Stata
```Tip 1: The eform() option with regress" The Stata Journal,
```
3(4): 445. http://www.stata-journal.com/article.html?article=st0054
```
Both interpretations are correct, they are just different
ways of looking at the same model.

Hope this helps,
Maarten

-----------------------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

```
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