I used scipy.optimize.curve_fit to fit a line through my data. The data are rheograms (shear stress versus shear rate). I have multiple data sets and I need to compare them statistically. I am also open to R as an alternative if Python is not efficient at this sort of thing. I would appreciate some guidance as I am unfamiliar as to what type of statistical test is appropriate here.

Also, how can I obtain a non-linear fit with its corresponding p-value or coefficient of correlation?