Linear Regression: Basics and Geometric Interpretation

This lecture covers the basics of linear regression, focusing on Gaussian linear regression with a single covariate. The instructor explains the concept of response and explanatory variables, emphasizing the importance of understanding the linearity in parameters. The lecture delves into the design matrix, least squares estimation, and the geometric interpretation of linear regression. Various examples are used to illustrate the concepts, including the relationship between variables and the projection of observed data points onto a hyperplane. The instructor also discusses the assumptions and implications of full rank matrices in linear regression analysis.