8.3 Roadmap

Rear-View Mirror

• Statisticians create a population model to represent the world.
• Sometimes, the model includes an “outcome” random variable \(Y\) and “input” random variables \(X_1, X_2,...,X_k\).
• The joint distribution of \(Y\) and \(X_1, X_2,...,X_k\) is complicated.
• The best linear predictor (BLP) is the canonical way to summarize the relationship.

Today

• OLS regression is an estimator for the BLP
• We’ll discuss the mechanics of OLS

Looking Ahead

• To make regression estimates useful, we need measures of uncertainty (standard errors, tests…).
• The process of building a regression model looks different, depending on whether the goal is prediction, description, or explanation.