9.3 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.
  • OLS provides a point estimate of the BLP

Today

  • Robust Standard Error: quantify the uncertainty of OLS coefficients
  • Hypothesis testing with OLS coefficients
  • Bootstrapping

Looking Ahead

  • Regression is a foundational tool that can be applied to different contexts
  • The process of building a regression model looks different, depending on whether the goal is prediction, description, or explanation.