On the Standard Errors in the Fitting of Polynomials to Unequally Spaced Observations

Abstract

From the observed values of the independent variable two parameters are derived which specify the departure from uniform spacing. Expressions are obtained for the standard errors of the coefficients and fitted values in terms of these parameters, and numerical tables for the estimation of the errors are given. It is shown that the errors calculated in this way lie within a few per cent. of the exact least squares values for polynomials of the first and second degree, but when the polynomial is of the third degree the deviations may be much greater.