Econometrics HT 18

Chapter 5 : Deriving the OLS formula

By Lund University

Here we derive the OLS formula by minimizing the sum of squared residuals.

Deriving the OLS formula

This section presents the least squares principle mathematically as a minimization problem in two variables (intercept and slope). We will solve this problem analytically, which will result in the OLS formula. Based on the first order condition from the optimization problem, we can derive several important OLS results.

Deriving the OLS formula

Global minimum of RSS

Some OLS results

Problem: Minimize RSS by hand

Problem: Derivative of RSS

Problem: Deriving the OLS formula for a model with no intercept