In this section we briefly review the methods used in the standard linear regression method [14]. Along with presenting the necessary definitions and main results, we will also discuss several aspects that are specific to our particular problem of nuclear mass fits.
Let us assume
that we have a model describing
observables
in terms
parameters
, i.e.,
Each term in the sum of Eq. (2) is multiplied
by a weight factor . In this respect we can single out
two limiting situations of an exact and an inaccurate model:
In the nuclear mass fits discussed in the present paper, we
obviously have the case of an inaccurate model, by which typical
experimental errors are of the order of a few tens of keV
[15], but can also be as low as about 100eV [16], while
average deviations of mass models do not go below about 0.6MeV
[1]. In the case of several different kinds of observables
included in the fit, dependence of the results on weights is obvious,
see e.g. the recent comprehensive analysis in Ref. [5].
However, even if only nuclear masses are fitted, the 'natural' choice
of weights, , is only a choice, and many other choices
are possible, i.e. depending on whether one wants to put more weight
into the measured values of light or heavy, or stable or exotic nuclei.
We will illustrate this point in Sec. 3 below.