Menu
I have two lists of data, one with x values and the other with corresponding y values. How can I find the best fit? I've tried messing with scipy.optimize.leastsq but I just can't seem to get it right.
Any help is greatly appreciated
487
Normal Equation is the Closed-form solution for the Linear Regression algorithm which means that we can obtain the optimal parameters by just using a formula that includes a few matrix multiplications and inversions.
The disadvantages of this method are: It is not readily applicable to censored data. It is generally considered to have less desirable optimality properties than maximum likelihood. It can be quite sensitive to the choice of starting values.
This objective is known as Ridge Regression. It has a closed form solution of: w=(XX⊤+λI)−1Xy⊤, where X=[x1,…,xn] and y=[y1,…,yn].
I think it would be simpler to use numpy.polyfit, which performs Least squares polynomial fit. This is a simple snippet:
import numpy as np
x = np.array([0,1,2,3,4,5])
y = np.array([2.1, 2.9, 4.15, 4.98, 5.5, 6])
z = np.polyfit(x, y, 1)
p = np.poly1d(z)
#plotting
import matplotlib.pyplot as plt
xp = np.linspace(-1, 6, 100)
plt.plot(x, y, '.', xp, p(xp))
plt.show()
76
If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With
