okorrelerade

Okorrelerade is a term used in statistics to describe a pair of random variables that have zero linear relationship, meaning their covariance is zero. In plain terms, when two variables are uncorrelated, knowing the value of one variable gives no information about the expected linear change in the other.

Formally, for random variables X and Y with finite means EX and EY and finite variances σX² and σY², the covariance is Cov(X,Y) = E[(X−EX)(Y−EY)]. The correlation coefficient, or Pearson correlation, is ρ = Cov(X,Y) / (σX σY). The variables are considered uncorrelated if Cov(X,Y) = 0, which is equivalent to ρ = 0 when both variances are nonzero.

Uncorrelated does not imply independence. Independence means that the joint distribution factors as the product of marginals, which is a stronger condition than zero covariance. Zero correlation can occur even when X and Y are clearly dependent in a nonlinear way. A common example is X uniformly distributed on [−1,1] and Y = X²; then Cov(X,Y) = 0, so they are uncorrelated, but knowing X determines Y, so they are not independent. The special case where zero correlation implies independence is when (X,Y) have a joint normal distribution or, more generally, certain elliptical distributions.

In practice, uncorrelatedness is a weaker form of relationship often used in linear models and data whitening (e.g., principal component analysis yields uncorrelated components). It is estimated from data via the sample covariance and the sample correlation coefficient, and significance of zero correlation can be tested under normality assumptions.