Multiple Neutral Regression

Abstract

We present a multiple regression fitting method which, unlike least-squares regression, treats each variable in the same way. It can be used when seeking an empirical relationship between a number of variables for which data is available. It does not suffer from being scale-dependent - a disadvantage of orthogonal regression (total least squares). Thus changing the units of measurement will still lead to an equivalent model - this is clearly important if a model is to be meaningful. By formulating the estimation procedure as a fractional programming problem, we show that the optimal solution will be both global and unique.For the case of two variables the method has appeared under different names in different disciplines throughout the twentieth century- as the reduced major axis or line of organic correlation in biology, as Stromberg's impartial line in astronomy, and as diagonal regression in economics (in which field two Nobel laureates have published work on the method). We gather together the most important results already established.