Linear Algebra for Financial Data

Least Squares Regression on Stock Returns

This project demonstrates how core linear algebra concepts can be applied to real-world financial data using least squares regression.

The notebook formulates linear regression explicitly as a matrix equation Ax = b and solves it using linear algebra, not black-box machine learning libraries.

This is an educational, beginner-friendly project intended to bridge linear algebra theory and practical data analysis.

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What This Project Does

• Models percentage price change (change_pct) as a linear combination of market features
• Constructs a design matrix (A) and target vector (b)
• Solves an overdetermined system using the least-squares solution
• Interprets regression coefficients in a financial context

The focus is on understanding, not prediction performance.

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Why This Project Is Useful

If you are learning linear algebra and wondering:

• Where does Ax = b show up in real problems?
• What does least squares actually do geometrically?
• How do regression coefficients relate to real data?

This notebook answers those questions with a concrete financial example.

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Notebook File

linear_algebra_least_squares_finance.ipynb

Run the notebook top to bottom.
Each step explains both the math and the code.

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Dataset

This project uses trending stock data from Yahoo Finance.

Dataset source:
https://huggingface.co/datasets/ronantakizawa/trending-stocks-yahoo-finance

All credit for the dataset goes to the original creator.

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Environment Setup

1. Create a Conda Virtual Environment (Python ≥ 3.10)

conda create -n linear-algebra-finance python=3.10

conda activate linear-algebra-finance

2. Install Dependencies

This repository includes a requirements.txt file.

pip install -r requirements.txt

3. Open the Notebook

You can use:

• VS Code
• Cursor
• Any IDE that supports Jupyter Notebooks

Make sure to select the conda environment kernel linear-algebra-finance when running the notebook.

Key Concepts Covered

• Linear systems and matrix multiplication
• Overdetermined systems
• Least squares and projections
• Interpreting regression coefficients
• Bias (intercept) terms in linear models No prior machine learning knowledge is required.

Learning Credits

This project is inspired by concepts from:

Linear Algebra for Machine Learning and Data Science by DeepLearning.AI

https://learn.deeplearning.ai/specializations/mathematics-for-machine-learning-and-data-science/overview

Notes and Limitations

• The model assumes linear relationships
• Features are not standardized
• No train/test split is used

These choices are intentional to keep the focus on linear algebra fundamentals, not model optimization.

Who This Project Is For

• Beginners learning linear algebra
• Students applying math to real data for the first time
• Anyone curious how regression emerges from linear algebra