CHAPTER 3 Normal Linear Models: Statistical Inference

Chapter 2 introduced least squares fitting of ordinary linear models. For n independent observations , with for μi = Eyi) and a model matrix and parameter vector , this model states that

numbered Display Equation

We now add to this model the assumption that {yi} have normal distributions. The model is then the normal linear model. This chapter presents the foundations of statistical inference about the parameters of the normal linear model.

We begin this chapter by reviewing relevant distribution theory for normal linear models. Quadratic forms incorporating normally distributed response variables and projection matrices generate chi-squared distributions. One such result, Cochran's theorem, is the basis of significance tests about in the normal linear model. Section 3.2 shows how the tests use the chi-squared quadratic forms to construct test statistics ...

Get Foundations of Linear and Generalized Linear Models now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.