Python OOP Linear Regression

I need a clean, fully-object-oriented implementation of simple linear regression written from scratch in Python. The purpose of this model is to make the relationships between variables explicit and interpretable, rather than merely spitting out predictions. You will read the training data directly from the database I grant you access to, so a light SQL wrapper inside your code will be useful.

I expect a brief yet structured project proposal first—outline your class design, the main methods, and how you will validate the model’s fit and interpretability. Once we agree on the approach, you can proceed to coding.

Deliverables
• A self-contained Python 3.x module that defines the regression classes, handles database connection/ingest, trains, evaluates, and outputs coefficients
• Inline docstrings and a concise README explaining how to run and extend the code
• A short validation script or notebook that demonstrates coefficient calculation, R², and residual plots on a sample pull from the database

Acceptance criteria
The model must compile and run with only standard libraries plus NumPy. Results on the sample data should match analytical solutions within a small numerical tolerance, and your class interface should allow easy extension to multiple regression later.