Notes on an Approximation Method for Fitting Parabolic Equations to Experimental Data

Abstract

When a numerical transformation of raw data is used only to simplify the arithmetic of curve fitting, the transformation may lead to undesirable and even highly distorted results. This principle is illustrated with an approximation method of fitting parabolic equations to experimental data, as described recently in texts by Johnson and Lewis. Although the approximation method will never yield as good fits as the exact, least-squares method, satisfactory results are in general achieved whenever the transformed scores yield a linear plot as a function of X. The principal difficulty with the method is that some data which fall along a parabola may not yield a linear plot of the transformed scores versus X, and so cannot be fitted satisfactorily by the approximation method.