The first thing we need to do is develop a way of getting the combinations of regressors we want to test. Since this is a combinatorial problem, the number of combinations is exponential with the number of available options. In our case, with the 19 available variables, the number of possible models is the sum of the number of models we can create with one regressor plus the number of models we can create with two regressors, and so on, until we sum the number of models we can create with all 19 regressors. This is what the sum is:
Of course, computing so many models, although easy for a computer, may take a while, ...
