I performed nonlinear curve fitting on my data using Origin pro.
I think there is no problem with the fitting in the shape of the graph itself, but two values confuse me. Chi-square and R-square.
Both are understood as values that mean the variation between the actual data and the fitted data.
The R-square is calculated very close to 1, as I intended, but the Chi-square is too large. These results are believed to be conflicting.
Strictly speaking, the origin provides a reduced chi-square, but when I directly obtained the chi-square, it still showed a large value (~9794).
Some say that R-square does not apply to nonlinear regression.
Also, some say that it is difficult to believe the chi-square when the sample size (I understood sample size as data value.) is too large.
What should I believe?
It is a significant negative curvilinear croorrelation between your two variables. It is really beautiful. Regards.
It's helpful to look at the software documentation. Here it explains what they mean by reduced chi-square:
The reduced chi-square is obtained by dividing the residual sum of squares (RSS) by the degrees of freedom (DOF).
By itself, it's not a particularly useful measure. (Except relative to other models on the same data). The reason it's so large in your case is that your dependent variable is so large in magnitude.
https://www.originlab.com/doc/Quick-Help/measure-fitresult
Technically, r-squared isn't defined for non-linear models. Your software is calculating something. Probably 1 - (RSS - TSS), which is reasonable.
If one more thing can be added (to the other responses) then this could be about the chi-square value. Technically and usually, a chi-square value, or a statistics value, is associated with a p-value. And, the p-value (probability) is the one which is utilized for making valuable judgements. See for example the second half here for p-value related conclusions:
https://www.graphpad.com/support/faq/some-nonlinear-regression-programs-report-the-chi-square-of-a-fit-what-does-this-mean-why-doesnt-prism-report-the-chi-square-value/
Briefly, people like small p-values because this implies small type one error.
Use reduced chi²!
See an example here:
https://www.lerenisplezant.be/teksten/FittingKVdm-Manual.pdf
(chapter About “goodness of fit” and “confidence intervals”)
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