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What is a correlation coefficient?

What is a correlation coefficient? Here are some definitions.

Noun
  1. (statistics) Any of the several measures indicating the strength and direction of a linear relationship between two random variables.
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Examples
The correlation coefficient between the two curves is 0.909, which leads to the identification of pepper on Mars with certainty.
The correlation coefficient, r, measures the extent of the correlation between two variables.
The Kappa coefficient is the statistical parameter used for ordinal data and the intra-class correlation coefficient for continuum data.
We calculated a partial correlation coefficient that adjusted for both partners' ages.
For each genome and each kind of bias, we compute a correlation coefficient that expresses the strength of the bias for the genome.
The reliability coefficient may be interpreted as a correlation coefficient between this measurement and a hypothetical remeasurement taken under similar conditions.

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