Validation strategies for multiple regression analysis: Using the coefficient of determination

Multiple regression equations designed to explain or predict should be validated. This tutorial shows how recalculation of the coefficient of determination on hold-out sample data or new sample data can be used to improve regression equations and to test them for validity. The Herzberg equation is used as a criterion for acceptable shrinkage when the coefficient of determination is calculated on new data. Nevertheless, validation is an art rather than a science because elimination of unstable variables as well as different types of data splitting, use of new sample data, and adjustments for external differences when test samples are used from different time periods can lead to different decisions on whether the equations have been validated. Various strategies can be used to find effective validation techniques.