Linear regression

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Linear regression is a special case of regression analysis, which tries to explain the relationship between a dependent variable and one or more explanatory variables. Mathematical functions are used to predict or estimate the value of the dependent variables. In linear regression, these functions are linear.

Linear regression was the first type of regression analysis to be studied rigorously. This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters. What is more, the statistical properties of the resulting estimators are easier to determine.


  • Linear regression can be used to fit a predictive model to a set of observed values (data). This is useful, if the goal is prediction, or forecasting, or reduction. After developing such a model, if an additional value of X is then given without its accompanying value of y, the fitted model can be used to make a prediction of the value of y.

Linear regression models are often fitted using the least squares approach. Other ways of fitting exist; they include minimizing the "lack of fit" in some other norm (as with least absolute deviations regression), or minimizing a penalized version of the least squares loss function as in ridge regression. The least squares approach can also be used to fit models that are not linear. As ountlined above, the terms "least squares" and "linear model" are closely linked, but they are not synonyms.