The Convergence of Efroymson's Stepwise Regression Algorithm

The stepwise regression algorithm that is widely used is due to Efroymson. He stated that the F-to-remove value had to be not greater than the F-to-enter value, but did not show that the algorithm could not cycle. Until now nobody appears to have shown this. To prove that the algorithm does converge, an objective function is introduced. It is shown that this objective function decreases or can occasionally remain constant at each step in the algorithm, and hence the algorithm cannot cycle provided that Efroymson's condition is satisfied.