I'm using a log linear regression to model a log transformed continuous positive variable, eg a quantity $Y$ that cannot be negative.


$$ log(Y) = \beta_0Const + \beta X$$

The coefficients of my predictors, after exponentiation should indicate proportional changes in the quantity $Y$ isn't it?

How do I call this effect in scientific publication? I read that for poisson regression it is used the term "Incidence Rate Ratio". But I guess this is correct only in the case $Y$ is a count variable, which is not my case.



If the $X$ values are also on the same log scale, the regression coefficients are what economists call "elasticities". That's the fractional change in $Y$ per fractional change in $X$. If $X$ is not log transformed, this Wikipedia page uses the term "semi-elasticity" for the fractional change in $Y$ per unit change in $X$. (First I've heard of that term.)

If I were putting together a table of results, I might nevertheless just call your regression coefficients "slopes" or "coefficients" and specify the units (fractional change in $Y$ per unit change or per fractional change in $X$) in a table footnote. A name more directly related to what $Y$ and $X$ represent might be more useful to your readers rather than a generic (and potentially unfamiliar) term like "semi-elasticity."


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.