Polynomial Regression with Visualization

This project demonstrates how to perform polynomial regression using multiple approaches in Python. The goal is to fit a curve to generated data that follows a noisy polynomial pattern.

What This Project Does

• Generates synthetic data points with a polynomial relationship and added randomness.
• Creates polynomial features up to a chosen degree.
• Trains polynomial regression models using:
  • Normal Equation (analytical method)
  • Gradient Descent (iterative method with optional standardization)
  • Scikit-learn Pipeline (using built-in tools for efficiency)
  • Scikit-learn Manual setup (explicit feature transformation and model fitting)

What You’ll See in the Graphs

Each approach produces a plot:

• The scatter points show the noisy data.
• The curve shows how well the model has learned to fit the data.

All models use degree 3 polynomial features to capture the pattern in the data.

Libraries Used

• numpy for data operations
• matplotlib for plotting
• scikit-learn for machine learning tools

Why This Matters

This project provides a hands-on comparison between manual and built-in methods for polynomial regression. It helps understand both the math-driven and library-driven sides of machine learning in a visual way.

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How to Clone and Run This Project Locally

Open your terminal or command prompt and run the following commands:

# Clone the repository (replace the URL with the actual repo URL if hosted on GitHub)
git clone https://github.com/CodeLoopdroid/Polynomial-Regression-Comparisons.git
cd Polynomial-Regression-Comparisons

# (Optional) Create and activate a virtual environment
python -m venv venv
# On Windows:
venv\Scripts\activate
# On Mac/Linux:
source venv/bin/activate

# Install required packages
pip install numpy matplotlib scikit-learn

# Run the project script
python polynomial_regression.py