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METHODS OF FITTING A STRAIGHT LINE TO DATA: EXAMPLES IN WATER RESOURCES 1
Author(s) -
Hirsch Robert M.,
Gilroy Edward J.
Publication year - 1984
Publication title -
jawra journal of the american water resources association
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.957
H-Index - 105
eISSN - 1752-1688
pISSN - 1093-474X
DOI - 10.1111/j.1752-1688.1984.tb04753.x
Subject(s) - ordinary least squares , statistics , set (abstract data type) , line (geometry) , least squares function approximation , calibration , moment (physics) , variance (accounting) , mathematics , data set , computer science , physics , geometry , accounting , classical mechanics , estimator , business , programming language
Three methods of fitting straight lines to data are described and their purposes are discussed and contrasted in terms of their applicability in various water resources contexts. The three methods are ordinary least squares (OLS), least normal squares (LNS), and the line of organic correlation (OC). In all three methods the parameters are based on moment statistics of the data. When estimation of an individual value is the objective, OLS is the most appropriate. When estimation of many values is the objective and one wants the set of estimates to have the appropriate variance, then OC is most appropriate. When one wishes to describe the relationship between two variables and measurement error is unimportant, then OC is most appropriate. Whee the error is important in descriptive problems or in calibration problems, then structural analysis techniques may be most appropriate. Finally, if the problem is one of describing some geographic trajectory, then LNS is most appropriate.