Fitting straight lines when both variables are subject to error.

Usual methods for fitting a straight line, Y = + X,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 and 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 . This result requires knowledge of the ratio of the error variances, = ²/², where ² is the variance of the Yresiduals and ² is the variance of the X residuals. If ² and ² are unknown, estimates of can be difficult to obtain. If replicate sampling was employed, estimates of the variances can be made, and then of .Contribution Number 1 of the series of review articles by the Mathematical Geologists of the United States.