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Suppose I have a mathematical model $y=mx$ and I have data for $x$ and $y$ and I want to fit the mathematical model on the data and determine the value of slope. I also have uncertainties of $x$ and $y$. The uncertainty in the slope of the fit can be calculated from the data and the fit. But I can also quantify the uncertainty in the slope by transferring $x$ and $y$ uncertainties for individual points to uncertainty $m$ for individual values.

My questions is: Whats the difference?

My guess is that the total uncertainty in $m$ is the combination of both of these uncertainties. Because the equation to calculate the uncertainty of slope does not include the uncertainty of $x$ and $y$.

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  • $\begingroup$ If you're using a proper fitter, then the uncertainty in the positions of the data points was accounted for in the uncertainty in the slope that the fitter returns. Do you know if your fitter is doing that? $\endgroup$ – probably_someone Sep 13 '18 at 13:21
  • $\begingroup$ The fitter that we use in he undergrad lab is called EzFit. It only uses the data points, not the uncertainty associated of the data points. Also the uncertainty in slope is calculated by a separate, external Matlab code. So I think both uncertainties are independently calculated. $\endgroup$ – Shaz Sep 14 '18 at 13:04
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There are generally many ways to compute the uncertainty on a derived quantity from a set of measured values (each with their own uncertainties). For example, one might use the method of maximum likelihood. Or one might perform a $\chi^2$ analysis.

Different uncertainty analyses will yield qualitatively similar but quantitatively different uncertainties. So long as you accurately report the specific uncertainty method you used and the result, you're doing correct science.

Cowan's Statistical Data Analysis book is a nice reference.

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