# Re: R: st: R: linear regression question

 From dr kardos laszlo To statalist@hsphsun2.harvard.edu Subject Re: R: st: R: linear regression question Date Tue, 17 Mar 2009 11:52:54 +0100

```dear carlo,

```
that is not exactly what i was suggesting. the way i see this, thoroughly checking that the base is natural is not enough. 100*beta% is practically always different from 100*(exp(beta)-1)%. one can use the former and go the extra step judging each time whether the deviance from the real thing is tolerable. i know i wouldn't. there is simply no gain in simplicity or anything.
```
best regards,
laszlo

Carlo Lazzaro wrote:
```
```Dear Laszlo,
thanks for your remark. The potential misleading arises because the use of
natural log is the reference in econometrics textbook. However, as you
suggested, a thorough check of this requirement should be made, in order to
```
avoid bewildering results.
```Kind Regards,
Carlo

-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di dr kardos laszlo
Inviato: martedi` 17 marzo 2009 8.34
A: statalist@hsphsun2.harvard.edu
Oggetto: Re: st: R: linear regression question

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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