Abstract

CAMPOS-ARANDA, Daniel Francisco. An Hydrological Application of Weighted Multiple Linear Regression. Tecnol. cienc. agua [online]. 2016, vol.7, n.4, pp.161-173. ISSN 2007-2422.

Multiple linear regression has two basic hydrological applications: (1) to extend short records based on long series that are close and (2) to derive empirical equations to estimate flood design (QTr) at sites of interest where records are not available. Since both applications are made in a regional context, multicollinearity is always present in the first case, and the lack of homoscedasticity in the second. In order to correct the non-uniformity with the variances of the dependent variable (Yi) a weighting function (wi) in the least squares fit is used, which leads to the weighted least squares (WLS) technique. In this work two methods to estimate the optimal w. are discussed in detail; the first one takes into account the theory of residuals and the mean error of setting ordinary least squares and the second one is based on data that are close neighbors, seeking for changes on the variances of Yi. Both methods are applied to empirical equations that estimate the average annual maximum flow (Qaa) of Hydrological Region No. 10 (Sinaloa). Based on the results it is concluded that it is advisable to always apply the method of WLS, to obtain empirical equations that estimate the Qaa or the QTr, due to the improvement of adjustment of the performance indicators evaluated in the real domain.

Keywords : Homoscedasticity; ordinary least squares; weighted least squares; mean absolute deviation; mean standard error; means standard relative error; average annual flood; Hydrological Region No. 10.