Finding the root and the estimation error of a fitted function

Question

I'm kind of new to Python and I want to find the root of an linear fit function inclusive errors.

I fitted the function with

import numpy as np
import scipy.optimize as op

def lin_fit(x, a, b):
    return a * x + b

...

popt, pconv = op.curve_fit(lin_fit, U, sqrt_I)
x = np.linspace(np.min(U), np.max(U), 100)
y = lin_fit(x, *popt)

Then I found the root with

def root(x):
    return lin_fit(x, *popt)

return op.fsolve(root, 0)

That was no problem, but I don't now, how to find the error of these roots.

Can anyone help?

Answer 1

The error is contained in pconv, where the diagonal contains the variance for each one estimated coefficients, which in this case are a and b.

From the MathWorld the correlation coefficient r which measures the overall quality of the fit can be computed as:

sxy = pconv[0,1]*x.shape[0]
sxx = pconv[0,0]
syy = pconv[1,1]
r = (sxy**2/(sxx*syy))**0.5