# Curve fitting - multiple indepedent fits or a single combined fit?

Assume, I have a list of actual, noisy, independent scalar measurements

• [y1, y2, ..., yn] (think: y1 = [0%, 12%, 52%, 79%, 99%]) for a scalar series
• x (think: x = [0 min, 2 min, 4 min, 6 min, 10 min]).

under the same conditions.

I know the underlying function y= f(x, a, b, c) and want to determine the coefficients a, b, c with curve fitting (least-square). What is the theoretically correct approach?

• A) Determine a1, b1, c1 for (y1, x) etc. and calculate a as the mean of a1, a2, ..., an, the same for b and c?
• B) Determine a, b, c in a curve fit for all pairs [(y1, x), (y2, x), ..., (yn, x)] simultaneously?

I was sure that A) is the correct approach but in retrospect and having spent some time on SciPy's curve fitting, I am not so sure that this was not a practical limitation because the commercially available software used only allowed A). However, in B), one would lose the connection within each independent observation, y1, y2, ..., yn.

I would be surprised if there were no duplicate questions but I cannot find them, so any comment is welcome.

• No, the coefficients should not be different for the measurements y1, ..., yn. These y-series data are just repetitions of the same experiment under the same condition. Your answer reinforces my understanding that the software forced a specific stats model on my mind. – Mr. T Dec 21 '20 at 18:57