Getting to clustered standard errors for Multinomial Logit models

Starting from scratch — the geometry of ℝⁿ, through OLS standard errors under homoskedasticity, then heteroskedasticity, clustering, and finally the multinomial logit. Each part builds directly on the last.

• Part 1: The geometry in ℝⁿ, math and intuition of OLS and standard errors under homoskedasticity

  May 2026

  Y is a point in ℝⁿ. col(X) is a subspace. OLS projects Y onto it. Everything — β̂, σ̂², standard errors, degrees of freedom — follows from that single geometric fact.