PYTHON

polynomial fit in python

import warnings
x = np.array([0.0, 1.0, 2.0, 3.0,  4.0,  5.0])
y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0])
z = np.polyfit(x, y, 3)
z
array([ 0.08703704, -0.81349206,  1.69312169, -0.03968254]) # may vary

polynomial fitting python

import matplotlib.pyplot as plt 
plt.style.use('seaborn-whitegrid') 
import numpy as np 
x = [1.00, 1.13, 1.27, 1.41, 1.55, 1.68, 1.82, 1.96, 2.10, 2.24, 2.37, 2.51, 2.65,
2.79, 2.93, 3.06, 3.20, 3.34, 3.48, 3.62, 3.75, 3.89, 4.03,
4.17, 4.31, 4.44, 4.58, 4.72, 4.86, 5.00]
y= [13.26, 14.15, 13.86, 14.81, 15.68, 15.64, 15.58, 15.67, 16.08, 16.36, 16.14,
16.68, 16.00, 15.66, 16.05, 16.22, 16.17, 16.03, 16.69, 15.83, 16.21, 16.13,
16.36, 16.42, 16.92, 16.65, 16.94, 17.47, 18.07, 17.52]
x = np.array(x)
y = np.array(y)

coeff_3 = np.polyfit(x, y, 3)
p3 = np.poly1d(coeff_3)
plt.plot(x,y,'ro', label = "Original Points")
plt.plot( x, p3(x), '-', label = "Degree 3 Model",color='b')
plt.legend()
plt.show()

y_residual = y - p3(x) # residual = actual - predicted(polynomial)
plt.plot(x,np.zeros(len(x)),color='b', label="Y=0 (shows accurate points)")
plt.scatter(x,y_residual,color='r',label="residuals")
plt.legend()
plt.show()