Fitting: unbalanced data point density and weights

Hello everybody,



I have a set of points {x,y}. When I plot them in a log-log scale they
apparently agree with a power dependence function F(x) = a*x^p. So, I am
fitting these points with this function.

(Details: Mathematica package, function NonlinearRegress, its description
for the help file: finds a least-squares fit to a list of data for a model
that is a not linear combination of the given basis functions; the
coefficients of the linear combination are the parameters of the fit).



The problem is that my data are evidently bad balanced: I have much more
points on the "left" side (small x value), their errors are also much
smaller (I use the errors to define weights, different for every point). On
the other side, the x-density of the "right" points is much smaller. The
points form a slight bow in the log-log scale - as the result, the fitted
function matches "perfectly" left points while the other points are badly
matched.

The question is: what to do to keep the data points appropriately balanced?
A friend of mine saw once an article about this subject, but you know: "gone
with the wind". ;)

Any advice? Should I present you a sketch of the problem?

(I hope this group fits to that subject).



Regards, Kris

.