This lecture introduces linear regression as a supervised learning problem, focusing on parametric models and optimization techniques to find the optimal parameters. The instructor explains how to make predictions from labeled examples and demonstrates the process through a linear regression example. The lecture covers the concept of minimizing the sum of least squares to estimate the model parameters and emphasizes the importance of defining the model function. Additionally, it discusses the application of linear regression in predicting outcomes based on observations, highlighting the analytical approach to solving regression problems.