Is it completely valid, to have an equation with a certain amount of variables, where two of the variables multiply each other?
For example, I want to have an equation $Y = B_0 + B_1X_1 + B_2X_2 +B_3X_3X_4$ where $X_3$ is a binary variable of {0,1}. My idea is that $X_4$ is a variable which I only want to include in the equation, if some predetermined factor is true.
So if $Y$ is calculating the amount of light coming into my room, $X_4$ would be the amount of light coming from a window, and $X_3$ would be $1$ if the blinds are open and $0$ if the blinds are closed, so that it doesn't include that part. Would this be sound logic? Or is there a more practical way of doing this? Thanks!
It's ok to do mathematically, just keep in mind that it means completely ignoring $X_4$ when "the blinds are closed".