Chapter 2 introduced least squares fitting of ordinary linear models. For *n* independent observations , with for *μ*_{i} = *E*( *y _{i}*) and a model matrix and parameter vector , this model states that

We now add to this model the assumption that {*y _{i}*} have normal distributions. The model is then the

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 ...

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