Linear models

A linear model describes a relationship between one variable and another. The most common linear model you will be familiar with is:

$$y = mx + c$$ (1)

In GCSE Maths, this is referred to as the equation of a straight line. It describes a relationship between two variables, in this case $x$ and $y$, by using two constants, $m$, and $c$. i.e. we are predicting the behaviour of the variable $y$ as $x$ changes.

There are of course, many many other kinds of linear model, the only real constraint is that they describe a relationship between two variables.

A more formal notation:

$$\hat{f}(x) = w_0+w_1x$$ (2)

This describes the same model as straight-line, simply in terms of a function $\hat{f}$.