Hydrologic regression with weighted least squares

Abstract

Ordinary least squares (OLS) regression and weighted least squares (WLS) regression are compared by simulating a model of the form Q 50 =α A β1 , where Q 50 is the 50‐year peak discharge, A is drainage area, and α and β 1 are regional parameters estimated from a regression of observed 50‐year peaks at gaging stations. Results indicate that OLS has a larger expected standard error of prediction than WLS when the following weighting function is used: for i = 1, 2,…, N , where ĉ 0 and ĉ 1 are constants estimated from sample data, n i , is the record length of station i , N is the number of stations, and ŵ i , is the weight given to data for station i .