Defining a statistical model

The statistical model is usually written as

\[\begin{eqnarray*} y &=& \mbox{deterministic part + random error, or}\\ y &=& f(x) + \epsilon. \end{eqnarray*}\]

The deterministic component \(f(x)\) describes the relationship between the response and the predictor variables, this might take the form of a straight line or some other function.

The random error term will be described in some detail later in this course and usually a number of assumptions will be made about it’s distribution.

We can consider some statistical models for the examples we have already discussed.

When considering two variables we often use scatterplots to suggest the function or deterministic part of the model.