Michael Daly wrote:

On 15-Jun-2005, Peter wrote:


When two variables are correlated it means that they have
a tendency to vary in the same manner, not that there is a one-to-one
correspondence in each particular case.


Fine - I'm using the term correctly.

No, you're not. What you said before was "there is no correlation
between overall length and waterline length in kayaks."

If that were true it would mean that knowing the overall length would
not give us any hint about the waterline length - that is it would be
similar to my telling you my astrological sign and asking you to guess
my weight. But in fact the overall and waterline lengths of boats are
quite highly correlated and boats that are 18' long overall will almost
always have waterline lengths greater than boats that are 14' long. The
correlation isn't perfect (correlation coefficient of 1.0), but it is
very high (correlation coefficient is probably around 0.95). An example
graph of skin fold thickness vs. body fat, two highly correlated
variables, is shown at:
http://www.sportsci.org/resource/stats/correl.html
In this case the correlation coefficient is 0.9 indicating a high degree
of correlation, but you'll notice that there's quite a bit of scatter;
i.e. there are many examples of specific individuals who may have a
greater skin fold thickness than someone else while having a lower body
fat percentage. In the same way, there would be some scatter if we
plotted kayak overall lengths vs. their waterline lengths, but we'd
clearly see that the *tendency* is for the longer boats overall to also
have long waterline lengths.

When you compare kayaks,
you will see that some have overhanging stem and/or stern, others have
plumb stem and/or stern while others still have raked ends. Thus, you
can find kayaks of the same overall length with very different waterline
lengths. It is not automatically true that if a kayak has a longer
overall length it necessarily has a longer waterline length.

And of course no one has ever argued otherwise - you're just rambling on
debating strawmen. If you're going to use the term "correlation" then
it would be good if you knew what it meant.