Notes on an approximation method for fitting parabolic equations to experimental data

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 ofX. 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 versusX, and so cannot be fitted satisfactorily by the approximation method.This study was done in cooperation with the Systems Division, Naval Research Laboratory, under Contract N5-ori-166, Task Order I, between the Office of Naval Research and The Johns Hopkins University. This is Report No. 166-I-156, Project Designation No. NR-507-470, under that contract. The author is indebted to Dr. Hermann von Schelling, of the Naval Medical Research Laboratory, U. S. Naval Submarine Base, New London, Connecticut, for technical advice. Miss Judith T. Parker and Mr. William T. Pollock assisted capably in the tedious computations required for this note.