计算python中非线性曲线拟合的确定系数(R2)和均方根误差(RMSE) [英] calculate coefficient of determination (R2) and root mean square error (RMSE) for non linear curve fitting in python

问题描述

如何为Python中的非线性曲线拟合计算确定系数(R2)和均方根误差(RMSE).下面的代码会一直进行直到曲线拟合.那么如何计算R2和RMSE?

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()

推荐答案

您可以这样做:

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

这直接采用了定义，例如在Wikipedia中: http://en.wikipedia.org/wiki/Coefficient_of_determination#Definitions

This is taking the definitions directly, as for example in the wikipedia: http://en.wikipedia.org/wiki/Coefficient_of_determination#Definitions

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