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## Main Question or Discussion Point

Hello! I have some data points obtained from a measurement and one of them is defined as the reference point. I need to compute the difference between that reference point and all the others (including itself) and plot the difference as a function of another variable (which doesn't have an error associated to it) and make a linear fit to the data (I know from theory that I need a linear fit). For concreteness, say that I have 3 data points with values ##10\pm1##, ##20\pm2##, ##30\pm3## (the ratio between errors and actual values is not constant in my case, I just picked these numbers for simplicity) and that the middle one, 20, is the reference. The differences are thus: 10, 0 and -10. I am not sure what errors to put on these differences. If I treat the measured reference value as a constant, I would end up with: ##10 \pm 1##, ##0 \pm 2##, ##-10 \pm 3##. Doing a linear, chi-square fit now it's straightforward, but I am not sure if defining the errors like this is correct. Mainly I am not sure about the error on the reference point. That point is DEFINED as the reference point, so it shouldn't have an error associated to it, right? I could also do a propagation of errors (using the error on the 20 as the one to be propagated) and get: ##10 \pm \sqrt 5##, ##0 \pm 2\sqrt 2##, ##-10 \pm \sqrt 13##, but again, I have an error on the reference point and I am not sure if that is right. Lastly I could try one of the 2 methods mentioned above, but just completely drop the error on the reference point. But in that case a simple chi-square fit would give me infinities (as I would divide by an error of zero), so I am not sure if that is correct either. Can someone advise me on what is the right way to do this?

For completeness, the data I have is the transition frequency between 2 energy levels in an atom. I measure this frequency for different isotopes of that atom, and one of these isotopes is defined as the reference one (this is called an isotope shift measurement).

For completeness, the data I have is the transition frequency between 2 energy levels in an atom. I measure this frequency for different isotopes of that atom, and one of these isotopes is defined as the reference one (this is called an isotope shift measurement).