# st: R: interpretting log transformed co-efficients

 From "Carlo Lazzaro" To Subject st: R: interpretting log transformed co-efficients Date Sun, 8 Feb 2009 20:04:06 +0100

```Ashwin wrote:

<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?>

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.

Hence, a coefficient = 0.2 in your log-linear model means that the length of
stay for females increases by [(0.2*100)%]=20% for each additional unit of
X.

HTH and Kind Regards,
Carlo

-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Ashwin
Ananthakrishnan
Inviato: domenica 8 febbraio 2009 17.35
A: statalist@hsphsun2.harvard.edu
Oggetto: st: interpretting log transformed co-efficients

Hi,

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?

Thanks.

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