When
no dedicated weighted least-squares procedure is available,
mis-applying a case-weighting strategy as a method of implementing
a weighted least-squares regression analysis can lead to gross
inaccuracies. The magnitudes of many of the obtained estimates
depend strongly on the absolute magnitudes of the weights
applied during fitting and, in aaddition, several of the crucial
regression estimates are incorrect. Among all possible rescalings,
the most successful weights are those that have been rescaled
so that they sum to the original sample size. However, even
with the application of these rescaled weights, estimation
of the residual variance remains problematic. A simple adjstment
is provided.

Discusses
problems with the R2 statistic when it is used in
regression models that are fit by weighted least-squares. We
show how
a reliance on the R2 statistic can lead to an overly
optimistic interpretation of the proportion of variance accounted
for,
in the regression. We propose a modification of the estimator
and demonstrate its utility with an example.