# What's the name for the effect size of a log linear regression model?

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

eg:

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

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.

Thanks

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."