= 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 ''ρ,,X,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^-1^Σd^-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 [[Analysis/Variance|variance]] and [[Analysis/Covariance|covariance]]: ''r = Corr(X,Y) = Cov(X,Y)/σ,,X,,σ,,Y,,''.




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CategoryRicottone