An Intuitive Geometric Approach to the Gauss Markov Theorem

ABSTRACT

Algebraic proofs of Gauss–Markov theorem are very disappointing from an intuitive point of view. An alternative is to use geometry that emphasizes the essential statistical ideas behind the result. This article presents a truly geometrical intuitive approach to the theorem, based only in simple geometrical concepts, like linear subspaces and orthogonal projections.

KEYWORDS:

• Dispersion cloud of points
• Gauss–Markov estimator
• Orthogonal projection