Orthogonal regression: a teaching perspective

A well-known approach to linear least squares regression is that which involves minimizing the sum of squared orthogonal projections of data points onto the best fit line. This form of regression is known as orthogonal regression, and the linear model that it yields is known as the major axis. A similar method, reduced major axis regression, is predicated on minimizing the total sum of triangular areas formed between data points and the best fit line. Either of these methods is appropriately applied when both x and y are measured, a typical case in the natural sciences. In comparison to classical linear regression, equation derivation for the slope of the major axis and reduced major axis lines is a nontrivial process. For this reason, derivations are presented herein drawing from previous literature with as few steps as possible to enable an easily accessible understanding. Application to eruption data for Old Faithful geyser, Yellowstone National Park, Wyoming and Montana, USA enables a teaching opportunity for choice of model.