Linear Regression in C

This project implements linear regression using the normal equation method in C. It includes matrix operations like multiplication, transposition, and inversion—essential components of solving for regression weights without external libraries.

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Files

• main.c: Entry point; tests the linear regression implementation on a sample dataset.
• model.h: Header file defining data structures and function declarations.
• model.c: Implements matrix operations and the linear regression algorithm.

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How It Works

1. Data Setup: main.c initializes a dataset with 4 samples and 3 features (including a bias term).
2. Training: Weights are computed using the normal equation:

   W = (X^T X)^(-1) X^T Y
   

3. Prediction: A test input is passed to the model to predict an output.
4. Output: The predicted value and learned weights are printed to the console.

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Building and Running

Compile the program using GCC:

gcc -o linear_regression main.c model.c -lm

Run the executable:

./linear_regression

Expected output:

Prediction for [1, 5, 9]: 14.000000
Learned Weights:
-0.000000 
1.000000 
1.000000 

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Core Concepts Used

• Matrix Multiplication
• Matrix Transposition
• Matrix Inversion (via Gauss-Jordan elimination)
• Dynamic Memory Management
• Struct-based data abstraction for matrices and models

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Sample Dataset

Bias	Feature1	Feature2	Output
1	2	3	5
1	3	5	8
1	1	1	2
1	4	6	10

The model learns the relationship:

y = 1 * x0 + 1 * x1 + 1 * x2

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License

This project is open source.