Multiple linear regression

EN Texto em inglês Ainda não há artigo no seu idioma: trecho em inglês.

Multiple linear regression, also known as multivariable linear regression, is a generalization of simple linear regression to the case of more than one independent variable. The basic model for multiple linear regression is Y i = β 0 + β 1 X i 1 + β 2 X i 2 + … + β p X i p + ϵ i {\displaystyle Y_{i}=\beta _{0}+\beta _{1}X_{i1}+\beta _{2}X_{i2}+\ldots +\beta _{p}X_{ip}+\epsilon _{i}} for each observation i = 1 , … , n {\textstyle i=1,\ldots ,n} . In the formula above we consider n observations of one dependent variable and p independent variables. Thus, Yi is the ith observation of the dependent variable, Xij is ith observation of the jth independent variable, j = 1, 2, ..., p. The values βj represent parameters to be estimated, and εi is the ith independent identically distributed normal error. Nearly all real-world regression models involve multiple predictors, and basic descriptions of linear regression are often phrased in terms of the multiple regression model. Note, however, that in these cases the response variable y is still a scalar. Multiple linear regression is a special case, restricted to one dependent variable, of general linear models (also known as multivariate linear regression), which predicts multiple correlated dependent variables.