Correlation and Regression

Abstract

Functional forms of association between hydrologic variables may be useful in a wide range of water-resources related studies to derive mathematical relationships for estimating and/or predicting unobserved values of a given variable of interest, related to a physical or hydrological phenomenon, on the basis of explanatory random or nonrandom elements. In this chapter, techniques for assessing the degree of association between pairs of random variables, which are generally termed correlation analysis, are discussed, with an emphasis on the linear functional form of relationship. Estimation of the statistic that summarizes the degree of linear association, namely, the Pearson correlation coefficient, as well as interval estimation and hypothesis testing related thereto is also addressed. In addition, this chapter deals with the modeling of the linear relationship between variables through regression analysis. Such an approach involves methods for parameter estimation of a linear equation, which describes the behavior of the hydrologic variable of interest as a response to the joint variation of a set of explanatory variables. Assumptions on model construction and additional inference procedures on the regression coefficients and the regression equation itself are presented, along with worked out examples focusing on hydrologic applications. Finally, there is a brief discussion on the limitations and possible misuses of regression analysis, in order to provide hydrologists and engineers with the tools for the correct use of the technique.