A desk that publishes a CAPM beta with a -stat of 3.2 is making a claim about sampling uncertainty. That claim is only as good as the classical linear regression assumptions behind ordinary least squares. This note restates those assumptions — Greene's A1–A6 — and the Gauss–Markov theorem that makes OLS best linear unbiased under them, then maps each systematic failure in financial data to the later stage of this unit that rebuilds the model. The payoff is a failure-mode map: when a residual plot or ACF looks wrong, you know which tool to reach for next rather than silently trusting default software standard errors.
Learning objectives. By the end of this note you should be able to:
- state the classical linear regression model in matrix form and list Greene's assumptions A1–A6;
- prove (or reproduce) that under A1–A5, , and state the Gauss–Markov theorem;
- explain what each assumption buys for estimation versus what it buys for exact finite-sample inference;
- map heteroscedasticity, serial correlation, nonstationarity, and endogeneity to the corresponding later topics in this unit;
- read a CAPM-style residual plot and say which assumption is under threat.
In this lesson
- The classical linear regression model
- OLS and the Gauss–Markov theorem
- Where finance breaks the assumptions
- Failure-mode map for the unit
Before you start
- Simple Linear Regression: OLS Estimators and Geometry
- Multiple Linear Regression
- Inference in Simple Linear Regression
The full lesson, with worked examples and exercise solutions, is for members.
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