In statistics, regression analysis examines the relation of a dependent variable (response variable) to specified independent variables (explanatory variables). The mathematical model of their relationship is the regression equation. The dependent variable is modeled as a random variable because of uncertainty as to its value, given values of the independent variables. A regression equation contains estimates of one or more unknown regression parameters ("constants"), which quantitatively link the dependent and independent variables. The parameters are estimated from given realisations of the dependent and independent variables.
Uses of regression include prediction (including forecasting of time-series data), modeling of causal relationships, and testing scientific hypotheses about relationships between variables.