I think rent control advocates would tell you that the point of rent control is not necessarily to control aggregate rents but to provide stability in the lives of renters. When you vacate a private rent-controlled unit in SF, my understanding is that its rent resets to market value. So in that sense it probably works — the question is whether it has unintended consequences. Seems to me that this data suggests that it might have some, but they also might not be catastrophically bad. Really hard to say for sure though.
As for the formula itself, I believe they are all factors multiplied together and by the appropriate coefficients. As Noah Smith pointed out on Twitter, the formula is quite possibly too closely fitted to actually be right, but it is still a suggestion of a relationship between these three variables and the price outcome in SF. But you should ask Fischer, he’s the math dude and he’s been very gracious in responding to comments on his original post.