A Property of Geometric Mean Regression

This article gives an overview of four classical regressions: regression of Y on X, regression of X on Y, orthogonal regression, and geometric mean regression. It also compares two general parametric families that unify all four regressions: Deming's parametric family and Roos' parametric family. It is shown that Roos regression can be done by minimizing the sum of squared α-distance, and as a special case, geometric mean regression can be obtained by minimizing the sum of squared adjusted distances between the sample points and an imaginary line.