Linear regression is the first model every quant learns and the one interviewers return to most often, because almost every harder model is a variation on it. It is also the model behind some of the most important objects in finance: a stock’s market beta, a factor model’s loadings, and the hedge ratio in a pairs trade are all regression coefficients. This lesson defines the model, states the assumptions that make ordinary least squares (OLS) the right estimator, shows the closed-form solution and where it comes from, and works through two examples by hand: a clean fit with an $R^2$, and a market beta you could quote in an interview. We close with the pitfalls interviewers probe and the threads that lead into the rest of the course.
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