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In 1969, Derek York published a highly general solution to the common problem of how to fit a straight line to points measured with error in both x and y. Unfortunately York's solution is almost unknown outside the geophysical literature, and new studies wrestle with the problem each year. We introduce York's solution and demonstrate it using an example from biogeochemistry: the isotopic mixing line. By Monte Carlo simulation, we show that York’s solution is superior to all popular fit methods.
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Articles | Volume 14, issue 1
Biogeosciences, 14, 17–29, 2017
https://doi.org/10.5194/bg-14-17-2017
Biogeosciences, 14, 17–29, 2017
https://doi.org/10.5194/bg-14-17-2017

Research article 03 Jan 2017

Research article | 03 Jan 2017

The long-solved problem of the best-fit straight line: application to isotopic mixing lines

Richard Wehr and Scott R. Saleska

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Cited articles

Bowling, D. R., Ballantyne, A. P., Miller, J. B., Burns, S. P., Conway, T. J., Menzer, O., Stephens, B. B., and Vaughn, B. H.: Ecological processes dominate the 13C land disequilibrium in a Rocky Mountain subalpine forest, Global Biogeochem. Cy., 28, 352–370, https://doi.org/10.1002/2013GB004686, 2014.
Feigelson, E. D. and Babu, G. J.: Linear regression in astronomy. II, Astrophys. J., 397, 55–67, 1992.
Hirsch, R. M. and Gilroy, E. J.: Methods of fitting a straight line to data: Examples in water resources, Water Resour. Bull., 20, 705–711, 1984.
Kayler, Z. E., Ganio, L., Hauck, M., Pypker, T. G., Sulzman, E. W., Mix, A. C., and Bond, B. J.: Bias and uncertainty of δ13CO2 isotopic mixing models, Oecologia, 163, 227–234, https://doi.org/10.1007/s00442-009-1531-6, 2010.
Keeling, C. D.: The concentration and isotopic abundances of atmospheric carbon dioxide in rural areas, Geochim. Cosmochim. Ac., 13, 322–334, 1958.
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The requested paper has a corresponding corrigendum published. Please read the corrigendum first before downloading the article.

Short summary
In 1969, Derek York published a highly general solution to the common problem of how to fit a straight line to points measured with error in both x and y. Unfortunately York's solution is almost unknown outside the geophysical literature, and new studies wrestle with the problem each year. We introduce York's solution and demonstrate it using an example from biogeochemistry: the isotopic mixing line. By Monte Carlo simulation, we show that York’s solution is superior to all popular fit methods.
Citation
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Final-revised paper
Preprint