Abstract
Usual methods for fitting a straight line, Y =α + βX,to data fail if the “independent” variable Xis subject to error. The problem is further complicated if there is no strong reason for selecting one of the two variables as independent; neither of the two lines may be correct. This review article discusses the maximum likelihood estimators of α and β under functional and structural models. These models involve differing assumptions about the statistical distributions of the dependent and independent variables. In addition, least-squares procedures are also considered. All these methods lead to the same result, a quadratic equation which can be solved to give an estimate of β. This result requires knowledge of the ratio of the error variances, λ = φ 2/τ2, where φ2 is the variance of the Yresiduals and τ 2 is the variance of the X residuals. If φ 2 and τ2 are unknown, estimates of λ can be difficult to obtain. If replicate sampling was employed, estimates of the variances can be made, and then of λ.
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Contribution Number 1 of the series of review articles by the Mathematical Geologists of the United States.
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Jones, T.A. Fitting straight lines when both variables are subject to error.. Mathematical Geology 11, 1–25 (1979). https://doi.org/10.1007/BF01043243
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DOI: https://doi.org/10.1007/BF01043243