Definition and Uses of the Linear Regression Model

A simple three‐element model is proposed as an interpretation of the regression equation for the relationship between annual rainfall and annual runoff from watersheds. The model employs two parameters that are related to the constants used in the regression equation. The parameters of the model can be evaluated by the usual least squares equations if the runoff data do not include zero or near zero values. For arid or semiarid watersheds where runoff may be zero for some years, a special procedure is proposed for evaluating the parameters. The procedure seeks the minimum of an objective function defined as the sum of squared deviations between observed data and prediction lines defined by the regression model.