Peter Kempthorne continues his regression analysis lecture for MIT's 18.642, Topics in Mathematics with Applications in Finance. The session builds on linear regression theory, covering hypothesis testing, parameter estimation, and model diagnostics before moving into regularized methods such as ridge, lasso, and principal components regression. Kempthorne applies these tools to finance problems, including ETF sector regressions and an empirical test of the Capital Asset Pricing Model, discussing how residual distribution issues and regime changes complicate the standard model. Running 83 minutes, the lecture mixes theoretical derivation with worked examples drawn from market data, aimed at students who already have the basics of regression and want to see where the method breaks down in practice.