How to Fit Data with Python: From Scatter Plot to Exponential Curve

Data fitting , also known as curve fitting, is a method of representing discrete data with a continuous mathematical function. In science and engineering, sampled or experimental data are often fitted to a curve to model the underlying relationship.

Given the data

x = [1, 2, 3, 4, 5, 6]
y = [300, 500, 800, 1300, 3000, 5000]

We first visualize the points using Matplotlib:

import matplotlib.pyplot as plt
%matplotlib inline
x = [1,2,3,4,5,6]
y = [300,500,800,1300,3000,5000]
plt.scatter(x, y)

To fit an exponential relationship we define a model function and use scipy.optimize.curve_fit to estimate its parameters:

# Define the function (x is the independent variable)
import numpy as np
def func(x, a, k):
    return a * np.e**(k * x)

# Perform the fitting
from scipy.optimize import curve_fit
(a, k), _ = curve_fit(func, x, y)

The fitting yields the coefficients:

a = 137.86824487839056, k = 0.6003825942342587

Thus the final fitted function is f(x) = 137.86824487839056 * e^(0.6003825942342587 * x). The fit quality is illustrated below:

Reference: Baidu Baike – Data Fitting