文档介绍：Principles and Applications of
Non-Linear Least Squares: An
Introduction for Physical
Scientists using Excel’s Solver
Les Kirkup, Department of Applied Physics, Faculty of Science, University of
Technology, Sydney, New South Wales 2007, Australia.
email: Les.******@
Version date: October 2003
Preamble
Least squares is an extremely powerful technique for fitting equations to data and is
carried out in laboratories every day. Routines for calculating parameter estimates
using linear least squares are mon, and many inexpensive pocket calculators
are able to do this. As we move away from fitting the familiar equation, y = a + bx to
data, we usually need to puter based programs such as spreadsheets, or
specialised statistical packages to do the ‘number crunching’. In situations where an
equation plex, we may need to use non-linear least squares to fit the equation to
experimental or observational data.
Non-linear least squares is treated in this document with a focus on how Excel’s
Solver utility may be employed to perform this task. Though I had originally intended
to concentrate more or less exclusively on using Solver to carry out non-linear least
squares (due to the general availability of Excel and the fact that I’d already written a
text discussing data analysis using Excel!), several other related topics emerged
including model identification, Monte Carlo simulations and uncertainty propagation.
I have included something about those topics in this document. In addition, I have
tried to include helpful worked examples to illustrate the techniques discussed.
I hope the document serves its purpose (I had senior undergraduates and graduates in
the physical sciences in mind when I wrote it) and I would appreciate ments
as to what might have been included (or discarded).
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CONTENTS
Section 1: Introduction 5
Reasons for fitting equations to data 7
Section 2: Linear Least square