Correlation is covariance divided by the two standard deviations, so it is unitless and bounded in [-1, 1], while covariance carries the units of both variables and has no fixed scale. That is what makes correlation comparable across pairs; both only capture linear association.
Card 1 of 259. Answer: Correlation is covariance divided by the two standard deviations, so it is unitless and bounded in [-1, 1], while covariance carries the units of both variables and has no fixed scale. That is what makes correlation comparable across pairs; both only capture linear association.
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Covariance measures whether two variables move together, and correlation is covariance rescaled to a fixed range: corr(X, Y) = cov(X, Y) / (σX · σY). Covariance can be any number and carries the units of both variables; correlation is unitless and always between −1 and 1.
That is why correlation is the one you compare across pairs. The covariance between height in centimetres and weight in kilograms changes by a factor of 100 if you switch to metres; the correlation stays the same. A correlation of 0.8 means a strong positive linear relationship whatever the units.
Both only capture linear association and both are sensitive to outliers. A correlation of 0 does not mean the variables are independent, and neither measure says anything about causation. The covariance matrix is still the more useful object in practice: PCA, portfolio risk and the multivariate normal distribution are all built on it.
