[kawr-uh-ley-shuhn, kor-]
mutual relation of two or more things, parts, etc.: Studies find a positive correlation between severity of illness and nutritional status of the patients. similarity, correspondence, matching; parallelism, equivalence; interdependence, interrelationship, interconnection.
the act of correlating or state of being correlated.
Statistics. the degree to which two or more attributes or measurements on the same group of elements show a tendency to vary together.
Physiology. the interdependence or reciprocal relations of organs or functions.
Geology. the demonstrable equivalence, in age or lithology, of two or more stratigraphic units, as formations or members of such.
Also, especially British, corelation.

1555–65; < Medieval Latin correlātiōn- (stem of correlātiō). See cor-, relation

correlational, adjective
intercorrelation, noun
miscorrelation, noun
noncorrelation, noun

The word correlation is a wonderful example of a word that started out as a general term and proved to be so useful in various fields of study that it developed more specialized senses over time.
Correlation has been in the English language since the 16th century. Its French cousin, corrélation, comes from Latin which literally means “restoring things together.” In English, we use it to describe a mutual relation between two things. Correlation is not to be confused with the word corollary, which is derived from an entirely different Latin root, corrollārium, a kind of ancient Roman gratuity, a “little something extra.”
In the 19th century, scholars of various disciplines adopted the term correlation to their specific areas of interest. In statistics, a correlation between two variables can be described as a numerical value. The words “positive,” “negative,” “strong,” and “direct” are often used as modifiers before correlation in this context. In the fields of biology and geology, researchers use correlation to help understand and describe various features of physiology and rock formations respectively. With the original meaning still in popular use, correlation is not just for mathematicians and scientists. Just be aware that if you casually mention correlation (in the general sense) to math enthusiasts, their initial responses might be to visualize a graph.

—Pearson correlation coefficient: a value between -1 and +1 that represents the relationship between two variables.

“There's not a direct correlation between poverty and violence and conflict and terrorism.“
—Barack Obama, “in Strasbourg Town Hall“ American Rhetoric (delivered April 3, 2009)
“Researchers compute correlation coefficients when they want to know how two variables are related to each other.“
—Timothy C. Urdan, Statistics in Plain English (2005)
“By the expression ‘Correlation of the Organs,’ is understood the state of mutual dependence of the organs, after their division of labor has been brought about by the process of evolution; each has its own particular function to perform, but the fulfilment of this function is not sufficient for its existence, since rather it would be unable to perform its own function without the aid it derives from the other organs.“
—Thomas H. Montgomery, Jr., “Organic Variation as a Criterion of Development“ Journal of Morphology, Vol. XII (1897)
“From correlation of the rock sequences exposed at different localities, geologists can reconstruct a geologic history over a billion years long.“
—Frank Press, et. al, Understanding Earth (2004) Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
correlation (ˌkɒrɪˈleɪʃən)
1.  a mutual or reciprocal relationship between two or more things
2.  the act or process of correlating or the state of being correlated
3.  statistics the extent of correspondence between the ordering of two variables. Correlation is positive or direct when two variables move in the same direction and negative or inverse when they move in opposite directions
[C16: from Medieval Latin correlātiō, from com- together + relātiō,relation]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin & History

1561, from M.Fr. corrélation, from com- "together" + relation (see relation).
Online Etymology Dictionary, © 2010 Douglas Harper
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