given a linear regression model such as
$ y= \beta_0 + \beta_1X_1 + \beta_2X_2 + \beta_3D + \beta_4D*X_1 + \beta_5D*X_2 $
where $D$ is a dummy variable, what are the proper interpretations of the coefficients $\beta_1$ and $\beta_4$ ?
My understanding is that the partial base effect of a one unit change in $X_1$ will lead to a change in $y$ by $\beta_1$ units for both groups. (when $D=1 $ or $ D=0$)
and that there is an additional effect on $y$ of $\beta_4$ units only when $D=1$ given a one unit change in $X_1$
a classmate told me that $\beta_1$ only describes changes when $D=0$