Peter Kempthorne continues MIT's 18.642, Topics in Mathematics with Applications in Finance, with a session on linear regression modeling. He works through the derivation of the ordinary least squares estimator, its mathematical formulation, and the interpretation of the Hat matrix as a projection operator. The lecture covers distributional assumptions under the normal linear model, inference procedures using t-tests and F-tests, and model diagnostics such as residual analysis and influence measures like leverage and Cook's distance. It closes by extending the framework to generalized least squares for handling correlated errors, connecting the statistical theory back to practical financial modeling concerns. The pace assumes familiarity with matrix algebra and probability, consistent with a graduate-level finance mathematics course, and Kempthorne moves methodically between derivations on the board and their interpretation for applied regression work.