Application of the multiple regression approach in evaluating parameters affecting water yields of river basins

Abstract

The efficacy of the use of the multiple correlation and regression approach in evaluating parameters affecting water yields of river basins is examined. Results of several analyses of annual and monthly streamflow of the Delaware River Basin in Kansas are presented to provide a background for an examination of the method. Hydrologic data, in general, and factors affecting water yield, in particular, may not fit the premises upon which the multiple regression method of analysis is based: (1) There are no errors in the independent variables; errors occur only in the dependent variable. (2) The variance of the dependent variable (streamflow) does not change with changing levels of the independent variables (precipitation, for example). (3) The observed values of the dependent variable are uncorrelated random events. Hydrologic data may not fit the further assumption implicit in tests of significance of multiple correlation and regression coefficients, that is, that the dependent variable (streamflow) is normally distributed about the regression line for fixed levels of the independent variables under consideration. It is concluded that (1) although the multiple regression approach will result in a line of best fit and best estimating equation for hydrologie data, it is not safe to place too much reliance on values estimated by such equations, particularly at levels far removed from the mean, despite very high correlation coefficients and (2) some of the more modern statistical procedures may be better tools than the multiple regression approach for evaluating effects of watershed parameters on water yield.