To evaluate the approach we used two methods. The first one is to run
the 
test to assess the correlation between our experiments
and the theoretical terms. Then we ran more experiments (a different set
of experiments) to see whether we can estimate the outcomes of these
new experiments with our old formulas (and hence with the old
constants).
The test, for all of the three measurements (setup,
querying, selection), showed that the estimated values and the actual
values obtained from the experiments were highly correlated.
We ran 1000 extra experiments and obtained the same times with the
similar methods used in the previous set of experiments (the starfield
display was always active in this set of experiments). We had a random
combination of the following values for our experiments: point size
varied between 
to 
, jump size varied from 1 to 50,
screen size varied from 
to 
(with range sliders of size
250 pixels a user interface with a starfield of pixels
nearly fills the screen), and the slider sizes varied from 150 to
250. The only values that were fixed during these new set of
experiments (i.e., same values with the previous set of experiments)
were the dataset sizes and the attribute counts (as it is practically
impossible to generate all the possible (random) datasets (either in
terms of time or space) on the fly for these new set of
experiments). The differences between the estimates and the actual
times were obtained. The average deviation observed for setup time was
9.50 percent; for selection, 3.97 percent; for querying, 16.63
percent.