The best on the basis of the following criteria is chosen from the different regression equations: the lowest value of the standard regression error or the highest value of the coefficient of determination.

Follow the stepwise selection of regressors , e.g forward selection or backward elimination algorithm, the procedures are well explained in the book : Applied Regression Analysis by Draper and Smith, these algorithms can be easily implemented on a computer.

Apply forward selection or backward elimination techniques and choose less AIC model (Akike Information Criteria) to get best multiple regression model

I am sorry but most of these answers are way out of date. Please see the three references attached. Best, David Booth