Summary: LEAST SQUARES DATA FITTING
Experiments generally have error or uncertainty in mea-
suring their outcome. Error can be human error, but it is
more usually due to inherent limitations in the equipment
being used to make measurements. Uncertainty can be
due to lack of precise de...nition or of human variation
in what is being measured. (For example, how do you
measure how much you like something?)
We often want to represent the experimental data by
some functional expression. Interpolation is often un-
satisfactory because it fails to account for the error or
uncertainty in the data.
We may know from theory that the data is taken from a
particular form of function (e.g. a quadratic polynomial),
or we may choose to use some particular type of formula
to represent the data.
Consider the following data.
Table 1: Empirical data
xi yi xi yi