# Partial Correlations

Peter Sibbald sibbald at qucis.queensu.ca
Mon Jul 24 21:07:57 EST 1995

```As a non-statistician who has used stats for years, here is a hopefully
simple explanation of correlation coefficients. There are two parts to
a CC: the value and the sign. The value indicates the strength of
the correlation. The sign indicates the slope of the relationship.
A correlation of +1.0 means that the slope is positive and the relation
ship is perfect (e.g. y=2x). A correlation of -1.0 means that the slope
is negative and the relationship is perfect (e.g. y=-x). A correlation
of 0.0 means that there is no relationship between x and y; this usually
looks like a random point cloud with no trends in it. In biology
perfect correlations (e.g. 1.0) are exceedingly rare. If you let
y=person's weight and x=person's height you might get a correlation
coefficient of 0.6 : taller people tend to be heavier but there are
some tall thin people and some short "gravitationally challenged"
people. If you let y=number of apples produced per tree and x=number
of caterpillars per tree you might get CC=-0.8 (more caterpillars,
fewer apples).

peter      sibbald at qucis.queensu.ca

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