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\section*{Introduction}

In Module 1 we dealt with situation where a model could be fitted
exactly to
the data. It is always possible to find a model that fits the data
exactly. This is not, however, the most appropiate way of modeling the
data, especially if want to use the model to make predictions about
future events. It is also inefficient, since there are as many
parameters to calculate as there are data points. An efficient model
is one with the fewest parameters that still manages to describe the
behaviour of the data. The disadvantage of using a model with fewer
parameters than data points is that it will not pass through all the
data points, and so we find the model that is the `best fit' for the data.


The first problem shows you have to fit the `best' model of the form
$y=mx$ to the data. Within this problem we look at various ways of
selecting the `best' model. In the second problem we fit the `best'
model of the form $y=mx+b$. In the final problem, and in the projects
that your group will be assigned, you will first fit find and exact
fit model, then a two parameter non-linear model and finally fit a model
with more than two parameters. We will then compare the properties of these models.

In the process of completing these problems, we will see how to find
minimum and maximum values of functions, and see how to find
derivatives of functions in several variables.