🚀 Logistic Regression from Scratch in Python

This project demonstrates how to build a logistic regression classifier from scratch using only NumPy—no machine learning libraries like scikit-learn were used for the algorithm itself. The goal is to understand and implement the underlying math, including the sigmoid function, gradient descent, and cross-entropy (log) loss.

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📚 What This Project Covers

• Logistic Regression fundamentals
• Implementation of the sigmoid activation function
• Loss function: Cross Entropy (Log Loss)
• Manual gradient descent optimization
• Accuracy evaluation on a real-world dataset (National Institute of Diabetes and Digestive and Kidney Diseases.)

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🧠 Math Behind It

The logistic regression algorithm is built upon:

Sigmoid Function

$$ \hat{y} = \frac{1}{1 + e^{-z}} $$

Cross-Entropy Loss

$$ L = -\frac{1}{N} \sum \left[ y \cdot \log(\hat{y}) + (1 - y) \cdot \log(1 - \hat{y}) \right] $$

• Gradient Descent for updating weights and bias.

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🧪 Dataset Used

• https://www.kaggle.com/datasets/mathchi/diabetes-data-set

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🛠️ Libraries Used

Only essential libraries were used:

numpy
pandas
scikit-learn (for data preprocessing and train-test split)