📈 Simple Linear Regression

A hands-on exploration of Simple Linear Regression — one of the foundational algorithms in machine learning. This project implements the algorithm in two ways: using scikit-learn and from scratch using pure Python & NumPy.

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🎯 Objective

Understand the mechanics of simple linear regression by:

1. Building a model using scikit-learn — leveraging the industry-standard ML library.
2. Implementing from scratch — deriving and coding the algorithm manually to deepen understanding of the underlying math (gradient descent, cost function, etc.).

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📂 Project Structure

Simple linear regression/
├── simple_linear_regression_sklearn.ipynb   # Implementation using scikit-learn
├── simple_linear_regression_from_scratch.ipynb  # Implementation from scratch
└── README.md

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🔬 What's Covered

simple_linear_regression_sklearn.ipynb

• Loading and preparing data (NumPy arrays)
• Train/test split using train_test_split
• Fitting a LinearRegression model
• Making predictions on the test set
• Evaluating performance with MSE and R²
• Visualising results with a scatter plot + regression line

simple_linear_regression_from_scratch.ipynb

• Manual implementation of linear regression
• Understanding the math behind the model (slope, intercept, cost function)
• Building the model without any ML library
• Comparing results to the scikit-learn implementation

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📊 Sample Results (scikit-learn)

Metric	Value
Intercept (θ₀)	5.038
Slope (θ₁)	2.993
MSE	0.270
R² Score	0.998

An R² of 0.998 indicates an excellent fit — the model explains ~99.8% of the variance in the data.

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🛠️ Tech Stack

Tool	Purpose
Python 3	Programming language
NumPy	Numerical computing
Matplotlib	Data visualisation
scikit-learn	Machine learning library
Jupyter / Colab	Interactive notebook environment

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🚀 Getting Started

Prerequisites

pip install numpy matplotlib scikit-learn jupyter

Run the Notebooks

jupyter notebook

Then open either notebook to explore the implementations.

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📖 Key Concepts

• Simple Linear Regression: Models the relationship between a single independent variable X and a dependent variable y using a straight line: y = θ₀ + θ₁·X
• Mean Squared Error (MSE): Measures average squared difference between predicted and actual values — lower is better.
• R² Score: Indicates how well the model fits the data — closer to 1.0 is better.
• Train/Test Split: Divides data into training and testing subsets to evaluate generalisation.

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👤 Author

Zakaria Tanani — GitHub

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📝 License

This project is open source and available for educational purposes.