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This lecture covers the fundamentals of linear regression, starting with a simple parametric model represented by a line. It progresses to line fitting with noise, training, and the solution for 1D linear regression. The lecture also delves into multivariate functions, gradients, and the transition to multi-input linear regression. The instructor explains the concepts of minimizing risk, derivatives, and gradients, emphasizing their importance in empirical risk minimization. The lecture concludes with a demonstration of linear regression in various scenarios, such as face completion tasks and age prediction from text.