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

Abstract

One of the principal problems in hydrology regression problems in hydrology will show is to define the effects of changes in land use that they do not conform to a multivariate on the regi'men of streams. Because of the normal distribution. Such variables as water many factors affecting streamflow, the in-year, degree of urbanization, percentage of ability even to recognize some of them, and basin in row crops, and miles of terracing are the lack of precision in describing them quanti-not randomly distributed. For statistical retitively, streamflow must be expressed by a lations which include at least one variable statistical relation. Multiple regression is a of this type the correlation coefficient may not useful tool for this purpose provided that the give a valid measure of the relation between required assumptions can be met. variables. Sharp, Gibbs, Owen, and Harris [1960]The distinctions between regression and recognized the weakness of the correlation correlation must be recognized in order to coefficient as an indicator of the quality of the successfully apply and interpret either of the estimating equation. Most texts on applied methods. These distinctions are very marked, statistics emphasize the correlation rather than although they may seem of little importance the regression model, and as a consequence because of the similarity of the computation hydrologists tend to evaluate results of reprocedures. In the case of linear correlation gression a•mlyses as if they were correlation the assumptions are made that the data are analyses. A recognition of the regression problem drawn from a bivariate or a multivariate normal is necessary before the appropriate interpretation distribution and that the observed values are of a specific analysis can be made.

A critique of current methods in hydrologic systems investigation

“…Not only is it possible to obtain almost equally good prediction equations on the basis of sets of different parameters, but judg ment must be exercised to avoid using phys ically irrelevant parameters or parameters which possess strong interdependence. Unfortunately wholly reliable, nonsubjective procedures to eliminate these personal factors do not exist at the present time [Sharp et al, 1960].…”

An improved statistical model for evaluating parameters affecting water yields of river basins

“…continued for a statistical model more applicable than the multiple regression approach for evaluating the many parameters affecting the water yielded as stream flow by river basins. The application of the multiple regression method to this problem was explored by Sharp, Gibbs, Owen, and Harris [1960], who concluded that assumptions inherent in the method are violated by hydrologic data, that common tests of significance generally applied to the results derived from such methods are questionable, and that confidence may be falsely placed in estimates obtained from estimating equations resulting from regression analyses. It was further indicated that the applicability of some of the more modern statistical techniques to the problems confronting the project should be investigated.…”

An application of principal component analysis and analysis in the study of water yield

“…Matalas and Reiher [1967] concluded that factor analysis is still largely undeveloped technically, and there are serious doubts as to its usefulness. However, the limitations of the normal multiple regression approach to water yield studies were pointed out in detail by Sharp et al [1960]. Snyder [1962] concluded that, for hydrologic studies, multivariate analysis offers the more satisfactory solution to the problem of estimating independent effects when the independent variables are correlated.…”