Ordinary Least Squares (OLS) Derivation & Properties

Derive and apply ordinary least squares for an intercept and one predictor. Calculate coefficients, audit normal equations, study centering and unit changes, and examine the scope of the BLUE theorem. Prerequisites: the SLR model, differentiation and matrix projection. Original calculations and proof checks extend to reverse regression, constrained fits and estimator-comparison limits.

Further reading: NIST least squares, Gauss–Markov theorem.