The Linear Zero Functions Approach to Linear Models

In this paper we develop the theory of linear models using the properties of Linear Zero Functions. It is shown that all the major results on inference can be derived using these properties and simple vector space arguments. The general philosophy of the development is to enhance understanding of the problem by appealing to the intuition of the reader. A common feature of the results derived here is that they integrate the singular dispersion case into the mainstream. This is achieved without the use of heavy algebra. On the contrary, most of the derivations are simpler than the conventional ones. Nevertheless, the extension of some of the results to the singular dispersion case are new.