Why fitting models to data reveals relationships in SciPy

Introduction

Fitting models to data helps us find patterns and connections between things. It shows how one thing changes when another changes.

You want to predict future sales based on past sales data.

You want to understand how temperature affects ice cream sales.

You want to see if study time affects test scores.

You want to find the trend in stock prices over time.

Syntax

SciPy

from scipy.optimize import curve_fit

# Define a model function
def model(x, a, b):
    return a * x + b

# Fit the model to data
params, covariance = curve_fit(model, xdata, ydata)

You first define a function that describes the relationship you expect.

Then you use curve_fit to find the best parameters that match your data.

Examples

This fits a straight line to data points that follow y = 2x.

SciPy

from scipy.optimize import curve_fit

def linear(x, m, c):
    return m * x + c

xdata = [1, 2, 3, 4, 5]
ydata = [2, 4, 6, 8, 10]

params, _ = curve_fit(linear, xdata, ydata)
print(params)

This fits a curve y = ax² + bx + c to the data points.

SciPy

from scipy.optimize import curve_fit
import numpy as np

def quadratic(x, a, b, c):
    return a * x**2 + b * x + c

xdata = np.array([0, 1, 2, 3, 4])
ydata = np.array([1, 3, 7, 13, 21])

params, _ = curve_fit(quadratic, xdata, ydata)
print(params)

Sample Program

This program fits a straight line to the data points and prints the equation. It also shows a plot with the data and the fitted line.

SciPy

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

def linear_model(x, m, c):
    return m * x + c

# Sample data
xdata = np.array([0, 1, 2, 3, 4, 5])
ydata = np.array([1, 3, 5, 7, 9, 11])

# Fit the model
params, covariance = curve_fit(linear_model, xdata, ydata)
m, c = params

print(f"Fitted line: y = {m:.2f}x + {c:.2f}")

# Plot data and fitted line
plt.scatter(xdata, ydata, label='Data points')
plt.plot(xdata, linear_model(xdata, m, c), color='red', label='Fitted line')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()

Important Notes

Fitting finds the best parameters that make the model close to the data.

Good fits help us understand how variables relate to each other.

Always check if the model makes sense for your data.

Summary

Fitting models helps find patterns in data.

It shows how one thing changes with another.

Using curve_fit in scipy is a simple way to do this.