I have an experimental data with relative uncertainties. And I would applied a fourth degree polynomial considering a specified model with logarithms. The issue im facing is how can I get an uncertainty on the fit considering the experimental data. I have no idea how can I do this. Any suggestion would be appreciated.
Thank you.
import numpy as np
import matplotlib.pyplot as plt
x = [121.78, 244.69, 344.278, 411.1165, 778.904, 867.38, 964.079, 1112.076, 1212.948, 1299.142, 1408.013]
y = [2.98E-03, 2.18E-03, 1.64E-03, 1.79E-03, 8.09E-04, 7.54E-04, 6.80E-04, 6.11E-04, 5.83E-04, 5.49E-04, 5.01E-04]
error_abs = [4.72E-05, 3.64E-05, 2.63E-05, 3.38E-05, 1.38E-05, 1.50E-05, 1.15E-05, 1.06E-05, 1.66E-05, 1.51E-05, 8.41E-06] # y_err
# x and y in logarithms
t1 = np.log(x)
t2 = np.log(y)
l = np.linspace(np.min(t1),np.max(t1),1000)
p,cov = np.polyfit(t1,t2,4, cov=True)
fit = np.polyval(p,l)
plt.errorbar(x, y, yerr=error_abs, lw=0.5, capsize=2, capthick=0.5, linestyle='none', marker='s',markersize=3, label='efficiency', color='orange')
plt.plot(np.exp(l),np.exp(fit), label ='Fit')
plt.show()
print(np.sqrt(np.diag(cov)))
question from:
https://stackoverflow.com/questions/65944349/how-can-i-calculate-the-uncertainty-of-a-fourth-degree-polynomial-fit 
