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differences in petal width and length, which seem to be strongly correlated,
and there also looks to be a correlation of both sepal width and sepal length.
A correlation between petal and sepal length indicates only that both tend to
grow in size together, which seems logical and not particularly interesting.
If these were correlations between product purchases, however, a known
affinity for one class of product would increase the likelihood of affinity for
another, indicating value in marketing to those customers.
If you inspect the observed correlations in the flower data set more closely,
however, you see significant disparities within species that are not very
obviousinthescatterplotmatrix.
Figure2-2
showscorrelationmatrixcharts
for both the full data set and all three species individually. The correlations
observed across all of the species do not hold
within
all of the species. Petal
length and width are good indicators of species and so are correlated at the
global level. But once the species is known, one is not always an indicator of
likelihood of the other.
Figure 2-2:
A series of correlation matrices constructed in a spreadsheet
reveal how correlations between characteristics vary significantly within
subject groups. Here, subject groups are species of Iris flowers but could
also be customer profiles.
Thesamephenomenonoccursinbusiness.Forexample,statisticsmayshow
a correlation between comic book and sports biography purchases.
However, the correlation may simply be an indicator that the purchaser is a
young male. If it is already known that the purchaser is a man between the
age of 18 and 25, there may be no correlation whatsoever, and promoting
comics alongside sports bios here would be a waste of time.
Computers are very good at modeling these kinds of relationships and
computing the likelihood of other realities or behaviors given a set of known
facts. Given a case of
a, b, c,
a computer can communicate the likelihood
of
d, e, f
. However, without visualization of the nature of the underlying
