Orthogonal regression methods in chemical modeling

In many fields of Chemistry, ordinary or traditional Least Squares fitting method (LS) is preferentially used to fit data, especially in QSAR/QSPR and in many scientific and chemistry-related fields. Nevertheless, least-squares univariate linear regression analysis has some drawbacks which are usually overlooked. Sometimes, one alternative is to use least squares Orthogonal Regression (OR) fitting, a method that, if it is appropriate, avoids both the unsymmetrical treatment of the data and the effects of regression towards the mean. The classical least squares method only minimizes the squared distance parallel to the y-axis between the experimental points and the fitting line (the so called 'vertical errors'), while ignores the distance parallel to the x-axis, as it is assumed that x values are error free. Instead, the OR method minimizes the sum of quadratic orthogonal distances, constituting a good alternative for obtaining symmetric data treatments when necessary. Four different OR variants are revisited here. Its performance in statistics and economics are considered superior in most cases to LS.