Two-variable linear regression: Modeling with orthogonal least-squares analysis

In many fields of chemistry, the ordinary least-squares method is preferentially used to fit data. Nevertheless, univariate linear regression by least-squares analysis, as devised by Gauss and Legendre, has some drawbacks that are usually overlooked in experimental science courses and even in many chemical research papers. Orthogonal least-squares fitting is a good method to avoid the unsymmetrical treatment of the data and also to avoid effects of regression toward the mean. These result because the classical least-squares method only minimizes the squared distance parallel to the y axis between the experimental points and the fitting line, whereas the distance parallel to the x axis is not considered because it is understood or assumed to be error free. The orthogonal least-squares regression is an alternative for obtaining symmetric treatments because it minimizes the sum of quadratic orthogonal distances from the points to the fitted line. The method is also related to the firstprincipal component computation, as it is shown here.