Correlation coefficient

A numerical measure of the strength and direction of association between two variables. Different coefficients capture different forms of association, including linear and rank-based relationships.

Statistical association: A relationship in which the distribution of one variable varies with another. Correlation coefficients quantify association without, by themselves, establishing causation.
Pearson correlation coefficient: A measure of linear association equal to covariance divided by the product of standard deviations. It is the standard coefficient when the target is linear association between numerical variables.
Exploratory data analysis: The examination of data using summaries and visualizations to identify patterns and anomalies. Pairwise coefficients offer compact summaries before a model is chosen.
Causation: A relationship in which changes to one factor produce changes in another. An observed correlation alone cannot establish that one variable causes the other.
Covariance: A measure of how two variables vary together, expressed in the product of their units. Pearson’s coefficient standardizes covariance to make its scale independent of measurement units.
Spearman's rank correlation coefficient: A measure of monotonic association calculated as the Pearson correlation of ranked values. Ranking values makes the measure responsive to ordered trends beyond straight-line relationships.
Scatter plot: A graph that displays paired numerical observations as points on two axes. Its shape exposes nonlinear patterns and outliers that a single coefficient can conceal.
Nonlinear correlation: Association following a curved or otherwise nonstraight pattern between variables. A zero Pearson coefficient can coexist with strong nonlinear dependence.
Standard deviation: A measure of the spread of values around their mean, expressed in the variable’s units. Pearson’s coefficient divides covariance by both variables’ standard deviations.
Kendall rank correlation coefficient: A rank-based measure comparing concordant and discordant pairs of observations. It measures ordering agreement through pairs rather than differences between ranks.

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