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单词 regression
释义
regression

Mathematics
  • A statistical procedure to determine the relationship between a dependent variable and one or more explanatory variables. The purpose is normally to enable the value of the dependent variable to be predicted from given values of the explanatory variables. It is multiple regression if there are two or more explanatory variables. Usually the model supposes that Y, where Y is the dependent variable, is given by some formula involving certain unknown parameters. In multiple linear regression, with k explanatory variables X1, X2,…, Xk, then

    Y=b0+b1X1+b2X2++bkXk+ε.

    Here b0, b1,…, bk are the regression coefficients and ε‎ denotes the error term. See also least squares.


Statistics
  • A word introduced by Galton that derives from his phrase ‘regression towards the mean’. It is often used as shorthand for linear regression or multiple regression models. In these models the expected value of one variable Y is presumed to be dependent on one or more other variables (x1, x2,…). The variable Y is variously known as the response variable, dependent variable, or outcome variable. The x-variables are variously known as antecedent variables, background variables, predictor variables, explanatory variables, controlled variables, or, potentially confusingly, independent variables. In the context of a factorial experiment (see factorial design) the x-variables are factors. See linear regression.


Economics
  • A tool for numerical data analysis that summarizes the relationship among the variables in a data set as an equation, where the variable of interest, or the dependent variable, is expressed as a function of one or several explanatory variables. The name regression originates from the phenomenon of regression to the average in heights of children compared to the heights of their parents, described by Francis Galton (1822–1911) in the 1870s. See also linear regression; multiple regression; nonlinear regression.


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