Machine Learning Series – Part 3: Polynomial Regression Explained Simply

Welcome back to my Machine Learning Series! 👋 In the last two posts, we explored Linear Regression and Multiple Linear Regression—both of which are great for drawing straight-line predictions. But what if your data doesn’t follow a straight line? That’s where Polynomial Regression steps in.

What is Polynomial Regression?

Polynomial Regression is a form of regression where the relationship between the independent variable (X) and the dependent variable (Y) is modeled as an nth-degree polynomial.

In simpler terms:

If Linear Regression draws a straight line, Polynomial Regression draws a curve to fit your data better.

Why Use Polynomial Regression?

Real-world data often has non-linear relationships.

Example:

Let’s say you’re trying to predict the growth of a plant over time. The growth might start slow, accelerate in the middle, and then level off. That’s not a straight line—it’s a curve. Polynomial regression is a perfect choice here.

Polynomial Regression Equation

Y = b0 + b1*X + b2*X² + b3*X³ + ... + bn*Xⁿ

Where:

• is the predicted value

• is the input variable

• are the model coefficients

• is the degree of the polynomial (e.g., 2 for a quadratic curve)

Python Example Using scikit-learn

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]).reshape(-1, 1)

y = np.array([1, 4, 9, 16, 25, 36]) # Perfect square relationship (non-linear)

# Convert to Polynomial Features

poly = PolynomialFeatures(degree=2)

X_poly = poly.fit_transform(X)

# Train Model

model = LinearRegression()

model.fit(X_poly, y)

# Predict and Plot

X_test = np.linspace(1, 6, 100).reshape(-1, 1)

X_test_poly = poly.transform(X_test)

y_pred = model.predict(X_test_poly)

plt.scatter(X, y, color='blue', label='Actual')

plt.plot(X_test, y_pred, color='red', label='Polynomial Fit')

plt.title('Polynomial Regression')

plt.xlabel('X')

plt.ylabel('Y')

plt.legend()

plt.show()

When to Use Polynomial Regression?

✅ When your data forms a curve, not a straight line ✅ When linear regression underperforms on your dataset ✅ When you need more flexibility in fitting complex patterns

Caution: Don’t Overfit!

Polynomial regression is powerful, but be careful with very high degrees (like 5, 10, or more). It might fit the training data perfectly but fail to generalize to new data. Always test your model with unseen data.

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