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Add the "effective variance" method to deal with both uncertainties on y as well as x following Jay Orear:
https://aapt.scitation.org/doi/abs/10.1119/1.12972
This is also what's used in gnuplot 5. It may be somewhat worse than a total least squares approach, but it's easy to implement. See gnuplots implementation here:
https://sourceforge.net/p/gnuplot/gnuplot-main/ci/master/tree/src/fit.c#l529
Additional explanation:
https://ned.ipac.caltech.edu/level5/Sept01/Orear/Orear21.html
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