The question is raised as to the reliability of regression relations in which stream flow, the dependent variable, is related to characteristics of the drainage basin. The values of such a dependent variable are often interrelated and thus fail to satisfy one of the basic assumptions of regression theory. The consequences of such conditions are first examined on hydrologic grounds. A statistical demonstration is then presented for a simple regression model in which the dependent variable is intercorrelated. Exact relations are given for the reliability of the regression constant, a, the slope of the regression line, b, and the predicted value of the dependent variable, ŷ. Although interstation correlation does not affect the expected values of a, b, and ŷ, it does affect their variance. Hence, in order that valid inferences may be made from a regression analysis, the interstation correlation must be taken into consideration when it is present. The results are general and apply to many hydrologic relations, as well as to any other phenomena with similar conditions of interrelation in the dependent variable.
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Matalas et al. (1961) studied this question.