I am trying to fit an experimental dataset. The data is highly nonlinear and so I am using different mathematical expressions to fit the data. How do I "quantitatively" compare the quality of fit that I obtain using different expressions? I do not want to pick one and undermine other expressions based on my visual-only appeal as it is subjective.

I guess "coefficient of determination" which varies from 0 to 1 is mostly applicable to linear data only.

Also the tests mentioned in https://en.wikipedia.org/wiki/Goodness_of_fit seems to be mostly applicable to probability distribution data.

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