Correlation
Correlation is a measure of how two variables are linearly related.
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Description
For two random variables X and Y, correlation is usually notated as either Corr(X,Y) or ρX,Y.
For a random vector x, the correlation matrix is usually notated Ρ. (Note this is a capital rho, not a P, although the two are virtually indistinguishable.) Given a covariance matrix Σ, let d = √diag(Σ) i.e. a vector of standard deviations. Ρ = d-1Σd-1 and Σ = dΡd.
Pearson's r
Pearson's r, also called the Pearson correlation coefficient, is a type of correlation that is applicable to continuous random variables.
The correlation of X and Y is calculated in terms of variance and covariance: r = Corr(X,Y) = Cov(X,Y)/σXσY.