Linear Regression: Least Squares and Normal Equations

This lecture covers the concepts of least squares and normal equations in linear regression, focusing on finding the best-fit line for given data points. It discusses the uniqueness and existence of solutions, the importance of linear independence, and the process of determining the least squares solution. The instructor explains how to calculate the regression line and interpret the results using real-world examples, such as the number of Christian churches and murders in different cities. The lecture emphasizes the mathematical techniques involved in regression analysis and the significance of minimizing errors to obtain accurate predictions.