Pearson correlation coefficient

The Pearson correlation coefficient measures the strength and direction of a linear relationship between two quantitative variables, on a scale from −1 to 1.

Covariance: A measure of how two variables vary together, expressed in the product of their units. Pearson correlation standardizes covariance by both variables’ standard deviations.
Spearman's rank correlation coefficient: A rank-based measure of the strength and direction of a monotonic association between two variables. It detects monotonic relationships without requiring them to be linear.
Simple linear regression: A model describing a quantitative outcome as a linear function of one predictor. In this model, the coefficient summarizes standardized linear fit and determines the slope’s sign.
Correlation does not imply causation: The principle that statistical association alone does not establish a causal relationship. A nonzero Pearson coefficient cannot establish that one variable causes the other.
Linear relationship: A relationship between variables that can be represented by a straight-line pattern. Pearson correlation quantifies the direction and strength of this particular pattern.
Standard deviation: The square root of variance, measuring a variable’s typical distance from its mean. Dividing covariance by both standard deviations makes correlation unitless.
Kendall rank correlation coefficient: A rank-based association measure calculated from concordant and discordant pairs. It offers a rank-based alternative that is often interpreted through pair ordering.
Correlation and dependence: Statistical concepts describing whether and how values of random variables vary together. Pearson correlation is one specific measure of dependence, not a complete account of it.
Outlier: An observation unusually distant from the overall pattern of a dataset. A single extreme point can substantially change Pearson correlation.
Quantitative variable: A variable whose values represent numerical amounts on a meaningful scale. The coefficient is designed for pairs of quantitative variables.

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