korrelatsiooni

Korrelatsiooni, commonly referred to as correlation, is a statistical measure that describes the strength and direction of a relationship between two quantitative variables. The most widely used coefficient is Pearson's r, which assesses linear association and ranges from -1 to 1; +1 indicates a perfect positive linear relationship, -1 a perfect negative one, and 0 indicates no linear relationship.

Beyond linear relationships, rank-based measures such as Spearman's rho and Kendall's tau quantify monotonic associations using the ranks of the data. These coefficients also lie between -1 and 1 and are less sensitive to outliers and non-normal distributions than Pearson's r.

Calculation and interpretation: For a sample, Pearson's r is computed as the covariance of X and Y divided by the product of their standard deviations. In simple linear regression, the square of r is the coefficient of determination (R^2), representing the proportion of variance in one variable explained by the other.

Cautions: Correlation measures association, not causation. It can be affected by outliers, nonlinearity, and restricted data ranges. Confounding variables can create spurious correlations, and the presence of a correlation does not imply a direct causal link.

Applications and tools: Correlation is used in finance to study co-movements of asset returns, in psychology and epidemiology to explore associations between traits and outcomes, and in multivariate analysis to build correlation matrices. Partial correlation extends the idea by controlling for the influence of additional variables.