Fitting of a Straight Line by Total Least Squares

摘要

The fitting of a line or curve to a set of data points is a routine procedure in metrology. There are two variables: the 'explanatory' variable, plotted along the x-axis, and the 'response' variable, plotted along the y-axis. The fitting is usually accomplished using ordinary least-squares (OLS), in which the basic assumption is that the y-values have errors but that the x-values all have zero error. There are many cases where this assumption is dubious and where the x-values should also be regarded as having errors. The resulting fitting procedure is called total least-squares (TLS). This paper describes elementary TLS as applied to straight-line fitting, and compares its results with those of OLS.