🧠 Linear Regression from Scratch — Python & NumPy

This project demonstrates a complete implementation of Linear Regression from scratch using only Python and NumPy.
It covers fundamental concepts of Machine Learning, including cost function computation, gradient derivation, and gradient descent optimization.

---

📘 Project Overview

Linear Regression is one of the simplest yet most powerful algorithms in Machine Learning.
In this project, we:

• Implement the Cost Function:
  J(w,b) = (1 / 2m) * Σ (f_wb(xᶦ) - yᶦ)²
• Compute Gradients for parameters w and b: ∂J/∂w = (1/m) * Σ (f_wb(xᶦ) - yᶦ)xᶦ
  ∂J/∂b = (1/m) * Σ (f_wb(xᶦ) - yᶦ)
• Use Gradient Descent to update parameters iteratively: w := w - α ∂J/∂w
  b := b - α ∂J/∂b

---

🧩 Features

• Compute cost and gradients manually
• Implement gradient descent loop
• Visualize training data and fitted line
• Compare predicted vs actual values
• Modular code structure with comments

---

🧮 Example Results

Parameter	Value
Initial w	0
Initial b	0
Final w	~2.0
Final b	~0.0
Final Cost	≈ 0.0

---

🚀 Technologies Used

• Python 3
• NumPy
• Matplotlib
• Jupyter Notebook

---

🧠 Learning Outcomes

• Understand linear regression fundamentals
• Derive and compute the gradient from scratch
• Implement optimization using gradient descent
• Strengthen Python and NumPy vectorization skills

---

📂 Repository Structure

linear-regression-from-scratch/
│
├── Linear_Regression_From_Scratch.ipynb   # Main Jupyter Notebook
├── README.md                              # Project documentation

---

🧑‍💻 Author

Edwin Kofi Afful
📍 Computer Science & Engineering Student
💡 Passionate about AI, Quantum Computing, and Machine Learning

---

🌟 Acknowledgments

Inspired by Andrew Ng’s Machine Learning Specialization and DeepLearning.AI resources.
Built as part of foundational practice for understanding gradient-based optimization.