In the context of a linear regression model where the independent variable ($X$) was log-transformed, like:
$Y = \alpha + \beta·ln(X)$
Is there a straightforward way to transform a regression coefficient ($\beta$) that was estimated using log-transformed independent variable $X$?
I know that in this model, an increase of 1% in $X$ would mean an increase of $\beta·ln(X)$ in the value of $Y$.
Is there a way to transform $\beta$ so I could say that an increase of 1% in $X$ means an increase of $\beta'·X $ in variable $Y$?