First recorded in 1555–65, correlation is from the Medieval Latin word correlātiōn- (stem of correlātiō). See cor-, relation

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.