Linear Regression from Scratch

Project Overview

This project implements basic linear regression from scratch using Python, providing a clear explanation of the underlying theory and mathematical concepts. It offers a practical demonstration of how linear regression works, emphasizing educational value and transparency in algorithmic design.

While libraries like scikit-learn make linear regression quick and efficient, this implementation focuses on manually coding the algorithm to gain deeper insights into its workings. The project also includes a comparison with scikit-learn's LinearRegression model to highlight differences in performance and ease of use.

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Key Features

• Provides a detailed walkthrough of linear regression concepts:
  • The role of coefficients and intercepts in predictions.
  • Gradient descent for optimizing error minimization.
  • Evaluation metrics such as R-squared for assessing model performance.
• Demonstrates data preprocessing techniques:
  • Encoding categorical variables.
  • Normalizing numerical data.
  • Splitting data into training and validation sets.
• Highlights the trade-offs between custom implementations and pre-built libraries.
• Includes debugging and error-analysis tools, such as R-squared convergence tracking and residual analysis.

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What Makes This Project Unique?

1. Educational Clarity:

   • The project prioritizes clarity and understanding over efficiency, making it suitable for those seeking to deepen their knowledge of linear regression.
   • Extensive comments and explanations accompany the code, ensuring the theoretical concepts are accessible.

2. Comparison with Standard Libraries:

   • The inclusion of scikit-learn's LinearRegression allows for a practical comparison, showcasing when and why industry-standard tools are advantageous.

3. Step-by-Step Implementation:

   • Offers a transparent look at gradient descent, matrix operations, and hyperparameter tuning, building a strong foundation for further exploration of machine learning techniques.

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Roadmap for Extensions

This project provides a foundation for future enhancements and explorations. Potential extensions include:

1. Exploring Regularization Methods:

   • Learn about advanced regression techniques, which are commonly used to prevent overfitting by adding penalties for large coefficients.

2. Improving Validation:

   • Improve the current train-validation split to test the model on multiple data subsets and improve evaluation.

3. Optimizing Gradient Descent:

   • Experiment with adjusting the learning rate or testing other simple optimization methods to see their impact on convergence speed.

4. Analyzing Errors:

   • Create simple plots of predicted vs. actual values to identify patterns or errors in the predictions and ensure the model assumptions hold.

5. Comparing with Other Models:

   • Experiment with alternative approaches, such as polynomial regression, to see how well they capture more complex relationships in the data.

6. Understanding Extensions to Neural Networks:

   • Explore how concepts from this project apply to neural networks, such as how weights and biases in a neural network generalize coefficients and intercepts.

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Getting Started

Prerequisites

• Python 3.x
• Libraries: pandas, numpy, matplotlib, scikit-learn

Dataset

The project uses the Food Delivery Times Prediction Dataset from Kaggle: Dataset Link

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How to Run the Code

1. Clone the repository and ensure all required libraries are installed.
2. Download the dataset and place it in the specified directory.
3. Run the script to:
   • Preprocess the dataset.
   • Train and compare models using both the custom implementation and scikit-learn.
   • Visualize convergence and R-squared values.

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Sample Outputs

• Custom Implementation: Reports R-squared, convergence details, and sample predictions.
• Scikit-learn Implementation: Provides R-squared and sample predictions for comparison.
• Visualization: Displays a plot of R-squared vs. iterations for the custom implementation.

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Acknowledgments

This project is designed to provide a comprehensive understanding of linear regression fundamentals. Special thanks to Kaggle for providing the dataset that forms the basis of this exploration.

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Contact

For suggestions or feedback, please reach out. Your input is valuable in enhancing this project and ensuring its relevance to the broader data science community.