`Consider the following problem. We have a set of 21 data points,
representing measurements of a rocket altitude during flight at 21
consecutive time moments. We know that, in an uniformly accelerated motion,
the altitude as a function of time is given by
`

t h(t) t h(t) t h(t) ------------ ------------ ------------ 0.0 -0.2173 0.7 3.3365 1.4 6.3312 0.1 1.0788 0.8 1.9122 1.5 6.3549 0.2 0.1517 0.9 3.0594 1.6 8.5257 0.3 0.1307 1.0 3.7376 1.7 8.7116 0.4 1.4589 1.1 3.3068 1.8 8.2902 0.5 2.9535 1.2 3.7606 1.9 11.4596 0.6 2.4486 1.3 6.6112 2.0 11.2895

`Note that we have 21 data points to determine 3 parameters; the data is
corrupted by measurement errors (for example, the first altitude is negative!).
We will use the redundancy in the data to ``smooth out'' these
measurement errors; see Figure for the distribution of data
points and the parametrized curve.
`

`At each time moment , we are given the measured height
(in the data set); the height obtained by the formula ()
is
. Therefore, the formula ()
``approximates'' the measured height at time with an error
`

`We want the values , and chosen such that the
differences between the model and the measurements
are small. Therefore, we impose that
the sum of squares of errors is minimized
`