Multiple neutral data fitting

A method is proposed for estimating the relationship between a number of variables; this differs from regression where the emphasis is on predicting one of the variables. Regression assumes that only one of the variables has error or natural variability, whereas our technique does not make this assumption; instead, it treats all variables in the same way and produces models which are units invariant – this is important for ensuring physically meaningful relationships. It is thus superior to orthogonal regression in that it does not suffer from being scale-dependent. We show that the solution to the estimation problem is a unique and global optimum. For two variables the method has appeared under different names in various disciplines, with two Nobel laureates having published work on it.