Polynomial Regression

Polynomial Regression

The model fits a polynomial equation to the data:

Y = β₀ + β₁X + β₂X² + β₃X³ + ... + βₙXⁿ + ε

• β₀, β₁, ..., βₙ are the polynomial coefficients.
• Xⁿ represents the independent variable raised to the nth power.
• Can capture curves and nonlinear trends in data.
• Higher degree polynomials can lead to overfitting.

Polynomial Regression Example in Python

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures

# Sample data
X = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9]).reshape(-1, 1)
y = np.array([1, 4, 9, 16, 25, 36, 49, 64, 81])  # y = x^2

# Transform features to polynomial features degree=2
poly = PolynomialFeatures(degree=2)
X_poly = poly.fit_transform(X)

# Create and train model
model = LinearRegression()
model.fit(X_poly, y)

# Predictions
y_pred = model.predict(X_poly)

# Plot
plt.scatter(X, y, color='blue')
plt.plot(X, y_pred, color='red')
plt.title('Polynomial Regression (Degree=2)')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()