Linear Regression in Machine Learning: OLS Derivation & Python Implementation from Scratch
Master linear regression in machine learning by understanding the underlying math and writing the Python code completely from scratch. In this comprehensive tutorial, we break down Ordinary Least Squares (OLS) regression using matrix math, vectors, and the normal equation.
Learn how to build, evaluate, and test a multiple linear regression model using real-world insurance datasets. We cover essential evaluation metrics like the Coefficient of Determination (R2), Residual Sum of Squares (RSS), Total Sum of Squares (TSS), and Mean Squared Error (MSE).
In this video, you will learn:
• Linear Algebra fundamentals (matrices, vectors, norms, and dot products).
• Estimating coefficients using the Normal Equation and handling Singular Matrices.
• Categorical Data Transformation (One-Hot Encoding) & fixing Multicollinearity.
• Testing model generalizability with Train/Test splits and avoiding overfitting.
• Evaluating performance using R-Squared (R2), RSS, TSS, and RMSE.
📌 Link to Dataset: https://www.kaggle.com/datasets/miric...
📌 OLS Normal Equation Mathematical Proof: https://statproofbook.github.io/P/mlr...
Prerequisites:
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1. Python Programming Tutorial: • 🐍 Python Coding Tutorial For Dummies | Bea...
2. Exploratory Data Analysis: • Exploratory Data Analysis (EDA) For Machin...
3. Role of Statistics in Data Analysis: • Hypothesis Testing in Python: T-Test, ANOV...
4. Introduction to Linear Regression: • Linear Regression Basics in Machine Learni...
Chapters:
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00:00 Function Approximation & Multiple Linear Regression Equation
01:15 Linear Algebra for Machine Learning (Matrices, Vectors, Norms)
06:24 Represent Data in Matrix & Vector Form
07:51 Matrix Dot Product Explained
10:34 Identity Matrix, Matrix Inverse & Square Matrices
13:25 The Normal Equation: Deriving Regression Coefficients
18:35 Coding a Linear Regression Model From Scratch in Python
22:10 What is a Singular Matrix? (Debugging Code Errors)
28:30 Bonus Data Science Tip
29:06 One-Hot Encoding Categorical Data & Multicollinearity
36:26 Train/Test Split: Testing Model Generalizability
38:19 Understanding Evaluation Metrics: R2, RSS, & TSS
42:03 Overfitting & Cross-Validation Techniques
45:09 What Exactly is the Coefficient of Determination (R2)?
47:50 Explaining MSE, RMSE, Variance & Standard Deviation
50:54 Simple Linear Regression vs Multiple Linear Regression
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Let’s Connect:
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GitHub: https://github.com/AmMoPy
Service Requests: https://ammopy.github.io/AmMoPy
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Soundtrack – Intro:
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Soundtrack – Outro:
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#linearregression #machinelearning #pythonprogramming #datascience #linearalgebra #olsregression #statistics #codingfromscratch
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