Curve fitting for Polynomial, Logarithmic, and Power

curve_fitting_like_excel.py

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

df = pd.DataFrame({
    'y': [0.996559203, 0.99161362, 0.9925214090000001, 0.986498352,
                0.9826329420000001, 0.977550635, 0.9542758440000001, 0.941359915,
                0.933388103, 0.929990698, 0.920058004, 0.90789857, 0.909764261,
                0.8944469829999999, 0.912682288, 0.913135466, 0.913485262,
                0.911788038, 0.912034259, 0.910293632, 0.9170476590000001,
                0.907575858, 0.9098013140000001, 0.90602062, 0.8972021179999999,
                0.9008619929999999, 0.891679112, 0.909098825, 0.8898716590000001,
                0.90187596, 0.8846790999999999, 0.902215421, 0.900445068,
                0.894368245, 0.891844857, 0.893816449, 0.885442787, 0.887642119,
                0.877802234, 0.8745246609999999, 0.8620522279999999, 0.825483603],
    'X': [
        3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
        19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 31, 33, 35, 38,
        41, 45, 49, 55, 61, 70, 82, 98, 122, 163, 244, 487]},
                  columns=['X', 'y'])

x = np.linspace(df['X'].min(), df['X'].max(), 1000)
for i in range(1, 5):
    poly = np.polyfit(df['X'], df['y'], i)
    curve = np.polyval(poly, x)
    if i == 1:
        plt.scatter(df['X'], df['y'], label='Correlations')
    plt.plot(x, curve, label='Deg: {}'.format(i))

# logarithmic curve fit y = A + B log x
popt, pcov = curve_fit(lambda t,a,b: a+b*np.log(t),  df['X'],  df['y'])
logy = popt[0] + popt[1]*np.log(df['X'])
plt.plot(df['X'], logy, label='log-fit')

# power curve fit y = A x^-B
# note that df['X'] is passed in as t and we're solving for a and b variables
popt, pcov = curve_fit(lambda t,a,b: a*t**-b,  df['X'],  df['y'])
powery = popt[0]*df['X']**-popt[1]
plt.plot(df['X'], powery, label='power-fit')

plt.legend()
plt.show()