How to calculate coefficient of determination (R2) and root mean square error (RMSE) for non linear curve fitting in python. Following code does until curve fitting. Then how to calculate R2 and RMSE?

import numpy as np

import matplotlib.pyplot as plt

from scipy.optimize import curve_fit

def func(x, a, b, c):

return a * np.exp(-b * x) + c

x = np.linspace(0,4,50)

y = func(x, 2.5, 1.3, 0.5)

yn = y + 0.2*np.random.normal(size=len(x))

popt, pcov = curve_fit(func, x, yn)

plt.figure()

plt.plot(x, yn, 'ko', label="Original Noised Data")

plt.plot(x, func(x, *popt), 'r-', label="Fitted Curve")

plt.legend()

plt.show()

解决方案

You could do it like this:

print "Mean Squared Error: ", np.mean((y-func(x, *popt))**2)

ss_res = np.dot((yn - func(x, *popt)),(yn - func(x, *popt)))

ymean = np.mean(yn)

ss_tot = np.dot((yn-ymean),(yn-ymean))

print "Mean R :", 1-ss_res/ss_tot

This is taking the definitions directly, as for example in the wikipedia:

http://en.wikipedia.org/wiki/Coefficient_of_determination#Definitions