# Re: st: st)why log linear model is better?

 From Richard Goldstein To statalist@hsphsun2.harvard.edu Subject Re: st: st)why log linear model is better? Date Thu, 31 Aug 2006 08:14:30 -0400

```If you really want to use things like R-squared when the dependent
variables differ, look at Patrick Royston's -brsq- command, originally
in STB-14

Rich

woong-tae chung wrote:

```
WT ----- Original Message ----- From: "Nick Cox" <n.j.cox@durham.ac.uk>
To: <statalist@hsphsun2.harvard.edu>
Sent: Tuesday, August 29, 2006 6:10 AM
Subject: RE: st: st)why log linear model is better?

The same applies, even more strongly, to interpretation of standard errors, which are no longer on the same scale.
In addition, look at diagnostic plots
such as residual vs fitted, in each case.
Nick n.j.cox@durham.ac.uk
David Greenberg

YOu have to be careful in comparing R-square for a regression in which
the dependent variable has been transformed with one in which it has not
been transformed. The dependent variables are not measured on the same
scale, and this can throw off the comparison. IF it does turn out that
the equation with transformed variables provides a better fit, the
explanation will not be a statistical one, but a substantive one. The
equation with transformed variables better describes the processes at
work. Only someone with a knowledge of those processes could offer an
explanation as to why that is.
```Woong.Chung@colorado.edu

```
I need a help to find out reasonable explanation for my model specification.After running simple linear regression using OLS, ROBUST standard errors(due to
heteroskadasticty) and SUR, it turned out that log linear
```regression:
```
log(y)=a1+a2log(x1)+a3log(x2)+a4log(x3)+...e
seems to be fit so well in any cases rather than level or other transformationregressions:
y=a1+a2x1+a3x2+a4x3+.....+e

in terms of lower standard errors and higher R squares.

I am looking some explanations why this happens and also want to know how tell
whether the log linear regression method is my best specification

Mostly y x2 x3 are ratio and x1 is level( but x1 is not a denominator of other
ratios)
Within my knowledge, the log transformation would be helpful for multiplicativedata set. I don't know it would be applied to my case
```
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