Correlation

Correlation measures the direction and strength of association between two variables. It does not, by itself, establish that one variable causes changes in the other.

Pearson correlation coefficient: A statistic measuring the strength and direction of a linear relationship between two quantitative variables. It is the standard coefficient when both variables are quantitative and their relationship is approximately linear.
Random variable: A quantity whose possible values are associated with probabilities. Correlation summarizes how two variables vary jointly across observations.
Exploratory data analysis: The examination of datasets to find patterns, anomalies, and useful questions before formal modeling. Pairwise correlations are a common first summary of relationships among measured variables.
Causation: A relation in which changes in one factor bring about changes in another. An observed correlation alone cannot show that one variable causes the other.
Spearman's rank correlation coefficient: A statistic measuring the strength and direction of a monotonic relationship using ranked data. Ranking values lets correlation capture monotonic patterns that are not necessarily linear.
Scatter plot: A graph displaying paired numerical observations as points on two axes. The plotted pattern reveals shape, outliers, and clusters that a single coefficient can hide.
Feature selection: The process of choosing input variables for a predictive model. Correlations can flag redundant predictors, though they do not establish predictive usefulness on their own.
Mutual information: A measure of how much knowing one variable reduces uncertainty about another. Unlike correlation coefficients, it can detect many nonlinear forms of statistical dependence.
Kendall rank correlation coefficient: A rank-based statistic measuring association through concordant and discordant pairs. It measures whether pairs of observations tend to order together, offering an alternative to Spearman correlation.
Linear relationship: A relationship in which changes in one quantity are modeled by a straight-line function of another. Pearson correlation describes linear association, not every kind of dependence.

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