When errors in both coordinates make a difference in the fitting of straight lines by least squares

The least squares method for straight line fittings is commonly used in many areas of experimental research. The problems of assessing the incidence of the \+i\x\-i\ errors on the fitting parameters and their uncertainties in straight line fittings are addressed. The case in which the \+i\x\-i\ and...

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Bibliographic Details
Published in:Measurement science & technology 1998-12, Vol.9 (12), p.2007-2011
Main Authors: Bruzzone, H, Moreno, C
Format: Article
Language:English
Subjects:
Exact sciences and technology
Interpolation
curve fitting
Mathematical methods in physics
Measurement and error theory
Metrology
Metrology, measurements and laboratory procedures
Numerical approximation and analysis
Physics
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Summary:The least squares method for straight line fittings is commonly used in many areas of experimental research. The problems of assessing the incidence of the \+i\x\-i\ errors on the fitting parameters and their uncertainties in straight line fittings are addressed. The case in which the \+i\x\-i\ and \+i\y\-i\ errors are proportional to each other is studied in detail. Limits for the maximum expected variation of the fitting values due to the inclusion of the \+i\x\-i\ errors are given in terms of the standard fitting results, namely those obtained disregarding the \+i\x\-i\ errors. Closed expressions for the parameters' values and their uncertainties are also given in terms of the standard fitting results. The main inaccuracies of the standard fitting are investigated analytically. (Original abstract - amended)
ISSN:0957-0233
1361-6501
DOI:10.1088/0957-0233/9/12/012