Fitting equations to data with the perfect correlation relationship

Abstract

We present a simple method for estimating a single relationship between multiple variables, which are all treated symmetrically i.e. there is no distinction between dependent and independent variables. This is of interest when estimating a law from observations in the natural sciences, although workers in the social sciences may also find this of interest when fitting relationships to data. All variables are assumed to have error but no information about the error is assumed. Unlike other symmetric methods, the weights or coefficients can be obtained easily – indeed, these can be expressed in terms of least squares coefficients. The approach has the important properties of providing a functional relationship which is scale invariant and unique