📝 OLS Regression Using Matrices and Its Properties

Here are links to several PDF handouts:

• Summation, Expectation, Variance, Covariance, and Correlation is a handout that provides several mathematical rules for working with sums, expectations, variances, covariances, and correlation.
• OLS Estimators and Their Properties is a handout that steps through estimating the OLS regression estimators and also derives some of the properties of those estimators
• Assumptions for OLS Regression and the Gauss-Markov Theorem is a handout that examines the assumptions underlying the Gauss-Markov theorem; the theorem showing that the OLS estimators are BLUE.
• Statistical Inference for the Regression Model is a handout working through how we carry out coefficient-level and model-level statistical inference.
• A Regression Example in Practice is a handout that walks through using matrix algebra to compute many of the things we are interested in as applied researchers. It also show the equivalent built-in R functions for obtaining this.

The handouts include more detail than I will cover in class. I will highlight some important ideas from each of them, and you can work through some of the mathematical derivation on your own if it is of interest.