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, c1for
(y1, x)etc. and calculate
aas the mean of
a1, a2, ..., an, the same for
- B) Determine
a, b, cin 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.