# How many possible subsets in all possible regressions

Suppose that there are three candidate predictors, x1 , x2, and x3, for a final regression model. Suppose further that the intercept term, β0 is always included in all the model equations. How many models must be estimated and examined if one applies all possible regressions approach?

Thanks!

How many ways can we make a model with $$0$$ of the predictors? With $$1$$? With $$2$$? With all $$3$$?
• Not quite. You have listed out all of the possibilities, but some of them you have listed out more than once. (I see x1 up there three times). When I ask how many models use one predictor, I am referring to the models with x1 only or x2 only or x3 only. Once you have figured out how many models there are for the cases of $0$, $1$, $2$, $3$ then you add up the possibilities to get the total – WaveX Jun 4 '19 at 11:14