Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. A causal, complementary, parallel, or reciprocal relationship, especially a structural, functional, or qualitative correspondence between two comparable entities: a correlation between drug abuse and crime.
 n. Statistics The simultaneous change in value of two numerically valued random variables: the positive correlation between cigarette smoking and the incidence of lung cancer; the negative correlation between age and normal vision.
 n. An act of correlating or the condition of being correlated.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A reciprocal, parallel or complementary relationship between two or more comparable objects
 n. One of the several measures of the linear statistical relationship between two random variables, indicating both the strength and direction of the relationship.
from the GNU version of the Collaborative International Dictionary of English
 n. Reciprocal relation; corresponding similarity or parallelism of relation or law; capacity of being converted into, or of giving place to, one another, under certain conditions.
 n.
from The Century Dictionary and Cyclopedia
 n. Reciprocal relation; interdependence or interconnection.
 n. The act of bringing into orderly connection or reciprocal relation.
 n. In physiology, specifically, the interdependence of organs or functions; the reciprocal relations of organs.
 n. In geometry, such a relation between two planes that to each intersection of lines in either there corresponds in the other a line of junction between points corresponding to the intersecting lines in the first plane; also, a relation between two spaces such that to every point in either there corresponds a plane in the other, three planes in either intersecting in a point corresponding to the plane of the three points in the other space to which the three intersecting planes correspond; more generally, a relation between figures, propositions, etc., derivable from one another in an ndimensional space by interchanging points with (n—1) dimensional flats.
 n. In statistics, the relation of two or more variable quantities.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. a reciprocal relation between two or more things
 n. a statistic representing how closely two variables covary; it can vary from 1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation)
 n. a statistical relation between two or more variables such that systematic changes in the value of one variable are accompanied by systematic changes in the other
Etymologies
Examples

Historically, the dependency between two securities has been calculated using linear correlation or more generically correlation.

It is significant that in later times the term correlation has come to be applied more especially to the purely empirical constancies of relation, and has lost most of its functional significance.
Form and Function A Contribution to the History of Animal Morphology

Except the correlation is the opposite of conventional wisdom: the economy crashes after tax cuts and takes off after tax increases.

Except the correlation is the exact opposite of conventional wisdom  the economy crashes after tax cuts and takes off after tax increases.

But the correlation is a short term correlation – there is little to no correlation in the long term trends.

They concluded that because of our failure to prevail in Vietnam and because of Nixon's willingness to come to Moscow and make deals  the first SALT treaty and so on  with the Russians that what they called the correlation of forces in the world had shifted to their advantage and that they were now on the winning wicket.

These assertions are based on increases in correlation over time between general circulation model prognostications and observations as derived from a centred pattern correlation statistic.

The next correlation is where it starts to get a bit fuzzy to me.

Each bar code uses a special ink that recedes in correlation with passing time and a percentage graph indicating the remaining life of the veggie at hand.

The problem with correlation is that it often implies causation, but that does not necessarily "mean that cause and effect have been proven."
Geri Spieler: The Watchman's Rattle: Thinking Our Way Out of Extinction
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