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weighted total least squares straight line fit

version 1.0.0.0 (3.01 KB) by Mathias Anton
Calculates the parameters (and their uncertainties) to data with uncertainties in both coordinates

5.3K Downloads

Updated 13 Nov 2007

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The problem of fitting a straight line to data with uncertainties in both coordinates is solved using a weighted total least-squares algorithm. The parameters are transformed from the usual slope/y-axis intersection pair to slope angle and distance to the origin. The advantages of this are that a) global convergence is assured b) a solution is found even for a vertical line. The complete uncertainty matrix (i.e. variances AND covariance of the fitting parameters) is determined. For non-vertical straight lines the usual parameters (slope/y-axis intersect.) are also given, together with their uncertainty matrix. The algorithm is especially useful for precision measurements, where the knowledge of the complete uncertainty matrix is a must. The algorithm was published in Measurement Science and Technology 18 (2007) pp3438-3442 by M.Krystek and M.Anton, Physikalisch-Technische Bundesanstalt Braunschweig, Germany. An attached script named pearson_york_tetdata.m contains a standard statistical test data set for the problem (see e.g. Lybanon,M in Am.J.Phys.52(1)1984 pp22-26)

Cite As

Mathias Anton (2022). weighted total least squares straight line fit (https://www.mathworks.com/matlabcentral/fileexchange/17466-weighted-total-least-squares-straight-line-fit), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2007a
Compatible with any release
Platform Compatibility
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