  The assumption that a parametric class of functions fits the data structure
sufficiently well is common in fitting curves and surfaces to regression data.
One then derives a parameter estimate resulting from a least squares fit, say,
and in a second step various kinds of chi^2 goodness of fit measures, to assess
whether the deviation between data and estimated surface is due to random noise
and not to systematic departures from the model. In this paper we show that
commonly-used chi^2-measures are invalid in regression models, particularly
when inhomogeneous noise is present. Instead we present a bootstrap algorithm
which is applicable in problems described by noisy versions of Fredholm
integral equations. of the first kind. We apply the suggested method to the
problem of recovering the luminosity density in the Milky Way from data of the
DIRBE experiment on board the COBE satellite.
