Linear regression

In statistics, linear regression is a method of estimating the conditional expected value of one variable y given the values of some other variable or variables x. The variable of interest, y, is conventionally called the "dependent variable". The terms "endogenous variable" and "output variable" are also used. The other variables x are called the "independent variables". The terms "exogenous variables" and "input variables" are also used. The dependent and independent variables may be scalars or vectors. If the independent variable is a vector, one speaks of multiple linear regression.

Related Topics:
Statistics - Expected value - Dependent variable - Independent variable - Scalar - Vector - Multiple linear regression

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The term independent variable suggests that its value can be chosen at will, and the dependent variable is an effect, i.e., causally dependent on the independent variable, as in a stimulus-response model. Although many linear regression models are formulated as models of cause and effect, the direction of causation may just as well go the other way, or indeed there need not be any causal relation at all.

Related Topics:
Stimulus-response model - Causal

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Regression, in general, is the problem of estimating a conditional expected value. Linear regression is called "linear" because the relation of the dependent to the independent variables is assumed to be a linear function of some parameters. Regression models which are not a linear function of the parameters are called nonlinear regression models. A neural network is an example of a nonlinear regression model.

Related Topics:
Linear function - Nonlinear regression - Neural network - Model

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Still more generally, regression may be viewed as a special case of density estimation. The joint distribution of the dependent and independent variables can be constructed from the conditional distribution of the dependent variable and the marginal distribution of the independent variables. In some problems, it is convenient to work in the other direction: from the joint distribution, the conditional distribution of the dependent variable can be derived.

Related Topics:
Density estimation - Joint distribution - Conditional distribution - Marginal distribution

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