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## RegularizedRegressionModel Class | Extreme Optimization Numerical Libraries for .NET Professional |

Extreme.DataAnalysis.Models

Extreme.DataAnalysis.Models

Extreme.Statistics

**Namespace:**Extreme.Statistics

**Assembly:**Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.1

The RegularizedRegressionModel type exposes the following members.

Use the RegularizedRegressionModel class to analyze a linear relationship between two or more numerical variables where the problem is ill-posed. A multiple linear regression model tries to express one variable, called the dependent variable, as a linear combination of one or more other variables called independent variables or predictors.

Regularized regression compensates for the ill-posed nature of the problem by trading some increase bias for a reduction in variance.

Two regularization methods are supported by the RegularizedRegressionModel class: the LASSO (least absolute shrinkage and selection operator) and elastic net. Ridge regression can be performed using the LinearRegressionModel class.

In ordinary least squares, the parameter values are computed by minimizing the sum of the squared residuals. In the LASSO, a multiple of the one-norm of the parameters is added to the objective function. The multiplier is specified as the RegularizationParameter property.

The elastic net is a generalization of the LASSO that also adds a multiple of the squared two-norm of the parameters to the objective function. The ratio of the coefficients is specified through the RegularizationRatio property. This is a value between 0 and 1. A value of 1 indicates LASSO (this is the default). A value of zero indicates ridge regression. However, the calculation of ridge regression coefficients in this fashion is not reliable.

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