11 The Linear Model
Learning Outcomes
At the end of this chapter you should be able to:
- state the basic univariate statistical model;
- identify the various parts of the model; and
- explain how special models arise from this.
11.1 Introduction
The rest of the unit consists of fitting univariate statistical models. The variables in a data set are classified as response/dependent variables, or explanatory/independent variables. Univariate in this case implies that the data contains only one response variable. In our case the response variable will be continuous.
11.2 Basic univariate linear statistical model
The response is usually denoted 
, 
. The general univariate statistical model is
![\[y_i = mean + \epsilon_i,\]](https://oercollective.caul.edu.au/app/uploads/quicklatex/quicklatex.com-81bca1df9e0a19ac62fc487969ac64ef_l3.png "Rendered by QuickLaTeX.com")
where 
represents the random variation or error term. The way the mean is specified determines the type of model that is being fitted.
We will consider this general model in special cases in the following chapters.
