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##

Fitting

We now know enough symbol manipulation systems vocabulary to attempt
some real computation. There are still a few small bits and pieces
that we have to learn, but we'll learn about them on the go.

Assume that you have a set of *N* data points *y*_{i} and *x*_{i},
.
Furthermore assume that the dependence
between *y* and *x* is to be modelled by a linear relationship:

*y*(*x*) = *a* + *b x*

If points *y*_{i} have been measured with accuracy ,
then
the
merit function, whose minimum with respect to *a* and *b*yields the best fit is

In the following, we will evaluate expressions for *a* and *b* that
minimise ,
and the corresponding uncertainties, and .
We begin by doing it in Maxima. It is also in the
Maxima section that we discuss the relevant mathematics and
problems that, as you will see, affect Maple and Mathematica
as well (there are some
subtle bugs in all three). Since the general methodology, as well as
the general mechanics are going to be very similar in all three
systems, you should study all three sections that follow, in order
to gain a better understanding of how these things work in practice,
and what possible pitfalls you may encounter.

It is also in the following Maxima section that we write down
in an orderly fashion all
related results and formulas.
We will use these in the next chapter, which will discuss the
expanding Universe.

** Next:** Fitting in Maxima
** Up:** The Playsome Threesome: Maxima,
** Previous:** Differentiating a Function
*Zdzislaw Meglicki*

*2001-02-26*