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date: 2026-03-06

Polynomial Regression

Polynomial Regression is a machine learning technique used when the relationship between the independent variable and dependent variable is non-linear.
Instead of fitting a straight line like Linear Regression, Polynomial Regression fits a curved line to better capture complex patterns in the data.

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📌 Concept

Linear Regression equation:

y = b0 + b1x

Polynomial Regression equation:

y = b0 + b1x + b2x² + b3x³ + ... + bnxⁿ

Here the model learns polynomial relationships between the variables.

Although it is called Polynomial Regression, it is actually Linear Regression applied on transformed polynomial features.

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📊 Example

For a dataset like:

X	y
1	1
2	4
3	9
4	16

The relationship follows:

y = x²

Polynomial Regression with degree = 2 can perfectly model this pattern.

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⚙️ Steps to Implement

1. Import required libraries
2. Create dataset
3. Convert features into polynomial features
4. Train Linear Regression model
5. Make predictions
6. Evaluate model using R² score
7. Visualize results

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🧠 Libraries Used

• numpy
• pandas
• matplotlib
• scikit-learn

Install dependencies:

pip install numpy pandas matplotlib scikit-learn

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💻 Implementation

import numpy as np
import matplotlib.pyplot as plt

from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score

# Dataset
X = np.array([1,2,3,4,5,6,7,8,9,10]).reshape(-1,1)
y = np.array([1,4,9,16,25,36,49,64,81,100])

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

# Train model
model = LinearRegression()
model.fit(X_poly, y)

# Prediction
y_pred = model.predict(X_poly)

# R2 Score
print("R2 Score:", r2_score(y, y_pred))

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📈 Visualization

plt.scatter(X, y, color='blue')
plt.plot(X, y_pred, color='red')

plt.title("Polynomial Regression")
plt.xlabel("X")
plt.ylabel("y")

plt.show()

Blue points represent actual data
Red line represents the polynomial regression curve

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📊 Model Evaluation

R² Score measures how well the model explains the variance in the data.

R² = 1 → Perfect prediction
R² ≈ 0 → Model performs poorly

In this example, the score is 1.0 because the dataset perfectly follows a quadratic relationship.

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⚠️ Overfitting

Choosing a very high polynomial degree can cause overfitting.

Example:

Degree	Result
1	Underfitting
2	Good Fit
10	Overfitting

Always choose an appropriate polynomial degree.

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🚀 Applications

Polynomial Regression is used in:

• Population growth prediction
• Stock trend analysis
• Temperature forecasting
• Sales trend prediction
• Scientific curve fitting

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📚 Machine Learning Series

This project is part of my Machine Learning learning series where I practice one algorithm daily and share the implementation on GitHub.

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🔗 Author

Suraj Singh
Learning Machine Learning and building projects in public.