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A model with exactly one explanatory variable is a simple linear regression; a model with two or more explanatory variables is a multiple linear regression. [1] This term is distinct from multivariate linear regression, which predicts multiple correlated dependent variables rather than a single dependent variable. [2]
The general linear model is a generalization of multiple linear regression to the case of more than one dependent variable. If Y , B , and U were column vectors , the matrix equation above would represent multiple linear regression.
In linear regression, the model specification is that the dependent variable, is a linear combination of the parameters (but need not be linear in the independent variables). For example, in simple linear regression for modeling n {\displaystyle n} data points there is one independent variable: x i {\displaystyle x_{i}} , and two parameters, β ...
The least squares regression line is a method in simple linear regression for modeling the linear relationship between two variables, and it serves as a tool for making predictions based on new values of the independent variable. The calculation is based on the method of the least squares criterion. The goal is to minimize the sum of the ...
The following outline is provided as an overview of and topical guide to regression analysis: Regression analysis – use of statistical techniques for learning about the relationship between one or more dependent variables ( Y ) and one or more independent variables ( X ).
If this number is large, the regression gives a good fit, and there is little point in searching for additional variables. Other regression equations on different data sets are said to be less satisfactory or less powerful if their R 2 {\displaystyle R^{2}} is lower.
In econometrics, the seemingly unrelated regressions (SUR) [1]: 306 [2]: 279 [3]: 332 or seemingly unrelated regression equations (SURE) [4] [5]: 2 model, proposed by Arnold Zellner in (1962), is a generalization of a linear regression model that consists of several regression equations, each having its own dependent variable and potentially ...
For example, a four-way discrete variable of blood type with the possible values "A, B, AB, O" would be converted to separate two-way dummy variables, "is-A, is-B, is-AB, is-O", where only one of them has the value 1 and all the rest have the value 0. This allows for separate regression coefficients to be matched for each possible value of the ...