How to interpret a regression coefficient of an independent variable expressed as a percentage? I fitted a continuous dependent variable against two explanatory variables. However, one of the explanatory variables is expressed as a percentage. Consider the regression model: $y = 0.05 + 0.032x_1 + 0.024x_2,$ where $x_2$ is expressed as a percentage. How can one interpret $\hat{\beta}_2=0.024$?

This is easy to get wrong. A $1$ percentage point ($1\%p$) increase in $X_2$ is associated with a $0.024$ unit increase in $Y$. That is, if two observations have equal values of $X_1$ while their $X_2$ values differ by $1\%p$, the estimated expected difference in their $Y$ values is $0.024$.
Note the subtle difference between percent and percentage points: values $50\%$ and $51\%$ differ by $1\%p$, yet at the same time the latter is $2\%$ larger than the former $(\frac{51\%-50\%}{50\%}=0.02=2\%)$. Here is a related thread.
