I have these points I want to fit:
x y err
24.0 0.0386341 4.29118e-5
24.33 0.03952 2.10541e-5
24.66 0.0398329 1.76137e-5
25.0 0.0399503 1.75643e-5
25.33 0.0399654 1.63191e-5
25.66 0.0398724 1.72015e-5
26.0 0.0397342 2.06237e-5
I’m using LsqFit.jl to do this. The problem is that I’m not sure how to use the errors. I think I have to give a weight vector to the curve_fit function, but I get crazy results when I try this. For example, fitting this data without weights, only using the y column, with the model
(x, p) -> p[2] .+ p[3] .* (x .- p[1]) .^ 2 + p[4] .* (x .- p[1]) .^ 3 + p[5] .* (x .- p[1]) .^ 4
yields these parameters:
25.111393704165895
0.039954617396037284
-0.00027948006042561755
0.0003111490269699087
-0.00035643137150145855
with these errors (which are provided by LsqFit’s stderror function)
0.0869412489407782
2.055454237390897e-5
0.00016140094273954191
0.00019062903506274383
0.00010671690424624444
I then tried to build a weight vector. My idea was to give the maximum weight to the point with the least error, and viceversa. So, I took the inverse squared of the err column above, and I normalized the result by dividing each number by the maximum of the vector. I got:
0.14462239237947602
0.6007810802559573
0.8584025972308643
0.8632298289063326
1.0
0.9000334378603128
0.6261211360104819
Using this vector as weights in curve_fit, yielded these model parameters:
25.120191638543336
0.03995798049346908
-0.00030331529662780605
0.0002925450095476317
-0.0003231972927598868
which are close enough, but the associated errors for these parameters are nonsensical:
3146.8126470564166
0.7860552955285658
6.117611017553491
6.862314788647446
4.823917655489848
Clearly, I’m using weights in the wrong way. What should I do?