Linear Normal Models

These notes cover situations where we have a number of observations, each from a normal distribution, having a common variance, or standard deviation. We look at cases where the mean of the joint distribution belongs to a linear subspace, i.e. we are dealing with a linear normal model.

We use the theory of linear spaces and projections, together with the Maximum Likelihood method, to calculate estimates for the mean and the residual sum of squares for the model. We then consider nested models, and testing the hypotheses of model reduction, using the respective residual sum of squares to calculate the mean square ratio for used in the F-test.

The theory can be applied to many situations, such as testing for a particular common mean, linear regression, and analysis of variance of categorical data.