The Gram-Schmidt Construction as a Basis for Linear Models

Abstract

The Gram-Schmidt construction, with a little extension, can be used to establish results in linear algebra, multiple regression analysis, and the theory of linear models. This article describes and illustrates how it serves to develop the basic results required for statistical inference in the Gauss–Markov model. For upper-level theory courses, the method’s advantage is that it requires less background and fewer results in linear algebra than are usually required. For applications-oriented courses, it makes it possible to describe relations and computations simply and explicitly.

• Estimability
• Least squares
• Linear equations
• Orthogonal projection