What is stepwise regression, and when is it desirable to make use of this multiple regression technique?

Stepwise regression is a multiple regression estimation technique whereby independent variables are added to the regression equation one at a time. The first x variable to enter the regression is the one that explains the greatest amount of variation in y. The second variable to enter is the one that explains the greatest amount of the remaining variation. The use of stepwise regression can reduce the possibility for multicollinearity since it is unlikely that two highly correlated x variables will be included in a multiple regression that is estimated using the stepwise technique. This technique is useful when there are a great many independent variables.