How to interpret dummy variables and interactions terms on dummy variables in a regression? Suppose I have a linear regression form of
$$
\log(Y) = \beta_0 + \beta_1X_2 + \beta_2X_3 + \beta_3X_1Z + \beta_4X_2Z + \epsilon
$$
where $X_1, X_2, X_3$ are binary and $X_1$ is omitted as a reference variable. Suppose $Z$ is also binary 0-1. I am wondering how  we would be interpret $\beta_1$ and $\beta_2$?

You can interpret $\beta_1$ as the percent change in Y when the treatment effect $X_2$ is applied, when you're holding other variables constant, in this case that is Z.
You can scale this interpretation to other $\beta_s$ as well.
Hope this helps.
