The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data

1974/05/01 by Albert E. Beaton, John W. Tukey · 32 citations
Chemistry · Mathematics · #Advanced Statistical Methods and Models #Algorithm #Applied mathematics #Arithmetic #Computer science #Curve fitting #Decimal #Linear regression #Mathematical analysis #Mathematics #Nonlinear regression #Polynomial #Polynomial regression #Regression #Regression analysis #Series (stratigraphy) #Spectroscopy and Chemometric Analyses #Statistical and numerical algorithms #Statistics #Variable (mathematics)

paper · doi:10.1080/00401706.1974.10489171

openalex publication_date 1974/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The prototype of fitting polynomials to equally-spaced data—in which the equalspacing is theoretically precise and the data is accurate to many decimal places—arises in the analysis of band spectra. A hard look at such examples forces us to reexamine our thinking on such diverse issues as: How to formulate such problems, the use of robust/resistant techniques in polynomial regression, which coordinates to use and why, the basic properties of linear least squares, choices in stopping a fit, and improved ways to describe our answers. Our results and attitudes apply rather directly to other situations where we are fitting a sum of functions of a single variable. When two or more different variables, subject to error, blunder, or omission, underlie the carriers to be considered, regression/fitting problems are likely to need not only the considerations presented here, but others as well. To a varying extent, the same will be true of nonlinear fitting/regression problems.

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