Understanding Linear Regression: The Normal Equation and Matrix Multiplications Explained Understanding Linear Regression: The Normal Equation and Matrix Multiplications Explained Linear regression is a fundamental concept in machine learning and statistics, used to predict a target variable based on one or more input features. While gradient descent is a popular method for finding the best-fitting line, the normal equation offers a direct, analytical approach that doesn’t require iterations. This blog post will walk you through the normal equation step-by-step, explaining why and how it works, and why using matrices simplifies the process. Table of Contents Introduction to Linear Regression Gradient Descent vs. Normal Equation Step-by-Step Explanation of the Normal Equation Step 1: Add Column of Ones Step 2: Transpose of X (XT) Step 3: Matrix Multiplication (XTX) Step 4: Matrix Multiplication (XTy) Step 5: Inverse of XTX ((XTX)-1) Step 6: Final Multiplication to Get θ Why the Normal Equation Works Without Gradient Descent Advantages of Using Matrices Conclusion Introduction to Linear Regression Linear regression aims to fit a line to a dataset, predicting a target variable $y$ based on input features $x$. The model is defined as: $$ y = \theta_0 + \theta_1 x $$ For multiple features, it generalizes…
