# Interpretation of incrementing both variables in an interaction term

I run a regression with an interaction term similar to the form below: $$Y = B_0 + B_1 X_1 + B_2 X_2 + B_3 X_1X_2$$ where $Y$, $X_1$, and $X_2$ are continuous variables. In terms of the interpretation, the effect of a $1$ unit increase in $X_1$ is: $$B_1+B_3X_2$$ Similarly, the effect of a $1$ unit increase in $X_2$ is: $$B_2+B_3X_1$$ But can I conclude about the impact of $X_1$ and $X_2$ from the same regression? Or am I mistakenly using the same result twice?

Is there any way to examine the incremental effects of both: $X_1$ on $X_2$, and $X_2$ on $X_1$?

If both $X_1$ and $X_2$ increase by $1$-unit simultaneously, $Y$ will increase by $B_1 + B_2 + B_3 + B_3X_{1i} + B_3 X_{2i}$, where $X_{1i}$ and $X_{2i}$ are the values of $X_1$ and $X_2$ from which you started. The fitted $B$s are automatically scaled to the units of your variables, so the result is just simplifying a mathematical expression.