A proposal for a neutral regression

In cases of modest correlation, parameters calculated from a Standard least squares linear regression can vary; depending on the selection of dependen t and independent variates. A neutral regression that addresses this proble m is proposed. The eigenvector corresponding to the smallest eigenvalue of the cross-correlation matrix of the two variates is used as a set of regres sion coefficients. Error bars are calculated for the eigenvalues and eigenv ectors by means of a perturbation expansion of the cross-correlation matrix and are then verified by Monte Carlo simulation: A procedure is suggested for extension of the technique to the multivariate case. Examples of a line ar fit for low-correlation and a quadratic fit for high-correlation cases a re given. Conclusions are presented regarding the strengths and weaknesses of both the least squares and the neutral regression.