The equation suggests that an increase in venue
numbers need not, by itself, raise player
losses per adult in an area. The result is counter-intuitive. To check on
its validity, we
investigated whether there might be a high degree of multi-collinearity
between any of the
regressors.
4.1.2 Multi-collinearity
One of the fundamental assumptions of OLS estimation of equations is that
the explanatory
variables are all independent of each other. OLS is efficient only if this
assumption is
satisfied. The correlation coefficients for the three explanatory variables,
the number of
EGMs, the number of hotels and the number of clubs (all divided by a
multiple of the
resident population) are shown
The sample correlations shown in the table are all greater
than 0.5 which is sufficiently large
to raise concerns about potential multi-collinearity between the three
regressors. The
correlation coefficient between EGM numbers and hotels is the highest among
the three,
at 0.7. To examine multi-collinearity more formally, eigenvalues of the
moment matrix over
a limited part of the sample range were examined. Only a limited part of the
sample was
considered because some of the 68 regions had missing observations or zero
values of club
and hotel numbers.
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