Abstract

Much of scientific inference involves fitting numerical data with a curve, or functional relation. The received view is that the fittest curve is the curve which best balances the conflicting demands of simplicity and accuracy, where simplicity is measured by the number ofparameters in the curve. The problem with this view is that there is no commonly accepted justification for desiring simplicity.This paper presents a measure of the stability of equations. It is argued that the fittest curve is the curve which best balances stability and accuracy. The received view is defended with a proof that simplicity corresponds to stability, for linear regression equations.