Linear Regression From Scratch

This project aims to build a linear regression model using only mathematical theory and Python programming. The goal is to provide a clear understanding of the underlying principles of linear regression, including the model, objective function, and optimization techniques.

Project Overview

In this notebook, we will:

• Explain the concept of linear regression and its applications.
• Implement the linear regression algorithm from scratch, focusing on the mathematical foundations.
• Use gradient descent as the optimization technique to minimize the error in predictions.

Key Components

1. Model: The linear regression model predicts a continuous output variable based on one or more input features using the equation ( y = mx + b ), where:

   • ( y ) is the predicted output.
   • ( m ) is the weight (slope).
   • ( x ) is the input feature.
   • ( b ) is the bias (y-intercept).

2. Objective Function: The Mean Squared Error (MSE) is used to quantify the difference between the actual and predicted values. The goal is to minimize this error to improve the model's accuracy.

3. Optimizer: Gradient descent is employed to adjust the weights and bias iteratively, moving in the direction that reduces the error.

Getting Started

Prerequisites

• Python 3.x
• NumPy
• Matplotlib
• scikit-learn

Installation

You can install the required libraries using pip:

pip numpy matplotlib sckit-learn

Usage

1. Clone the repository:

git clone https://github.com/tozlukozmos/linear_regression_from_scratch.git
cd linear_regression_from_scratch

2. Open the Jupyter Notebook:

jupyter notebook linear_regression.ipynb

3. Run the cells in the notebook to see the implementation of the linear regression algorithm.

Acknowledgments

• Inspired by various online resources and tutorials on linear regression and machine learning.

1. How to implement Linear Regression from scratch with Python (https://www.youtube.com/watch?v=ltXSoduiVwY)
2. Linear Regression From Scratch in Python (Mathematical) (https://www.youtube.com/watch?v=VmbA0pi2cRQ)
3. Linear Regression (https://ml-cheatsheet.readthedocs.io/en/latest/linear_regression.html)
4. Gradient Descent (https://ml-cheatsheet.readthedocs.io/en/latest/gradient_descent.html)