Is there a way to plot chi-square error ($\chi^2$) vs. some other variable?

I'm trying to replicate plots from the following paper, Figure 1-C, more specifically:

Figure 1-C from Fernandez-Seara Algorithm

As additional information, the formula being subject to study is this one:

$m*\exp{(-R2*TE)}*zo*sinc((\gamma/2)*Gb*TE*z)$ and after plug-in the values, we have $1.64*\exp{(-97*TE)}*sinc(3.1352*Gb*TE)$.

GB can be fixed to different values within the range of 0 until 64. While TE goes from 0 to $60*10^-3$ or something.

I can't find a way to apply chi-square error to this function and plot it against the different values GB can have. Can anybody here help me or suggest an article for reading that could be applied to my case?

I already know this isn't a distribution curve (Y-axis goes beyond 1), but I don't know what would be the proper strategy to reproduce this plot correctly.

Does anybody have a clue?

  • $\begingroup$ If you were curve fitting a data set to that equation, you could repeatedly perform the fit while holding Gb constant at different values for each fit. This would allow you to plot chi-squared from each fit vs. the value of Gbfrom each fit. $\endgroup$ – James Phillips May 2 '18 at 12:56
  • $\begingroup$ Yes. But I think I prepared the inputs from chi-squared poorly and that's why I could not replicate the plot in the beginning. How would you do it? I know my "Observed" values would be the ones acquired by the formula... how can I get my "Expected" ones? I tried using average value but that didn't helped me a lot. $\endgroup$ – Aquiles Páez May 9 '18 at 4:15
  • $\begingroup$ Apparently I would have to pay money in order to read the paper you referenced, and so have no further advice. $\endgroup$ – James Phillips May 9 '18 at 11:27
  • $\begingroup$ @JamesPhillips actually the whole paper is available in that link. But that's ok. My concern still is what should the observed value be and in which order should chi-squared be because the largest my TE vector is, X^2 sum will be bigger as well. $\endgroup$ – Aquiles Páez May 9 '18 at 18:03

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