## Types in MathNet.Numerics.LinearRegression

Type MultipleRegression

Namespace MathNet.Numerics.LinearRegression

### Public Static Functions

#### Vector<T>DirectMethod<T>(Matrix<T> x, Vector<T> y, DirectRegressionMethod method)

Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals.
##### Parameters
###### `Matrix<T>` x

Predictor matrix X

###### `Vector<T>` y

Response vector Y

###### `DirectRegressionMethod` method

The direct method to be used to compute the regression.

##### Return
###### `Vector<T>`

Best fitting vector for model parameters β

#### Matrix<T>DirectMethod<T>(Matrix<T> x, Matrix<T> y, DirectRegressionMethod method)

Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals.
##### Parameters
###### `Matrix<T>` x

Predictor matrix X

###### `Matrix<T>` y

Response matrix Y

###### `DirectRegressionMethod` method

The direct method to be used to compute the regression.

##### Return
###### `Matrix<T>`

Best fitting vector for model parameters β

#### T[]DirectMethod<T>(IEnumerable<Tuple<T[], T>> samples, bool intercept, DirectRegressionMethod method)

Find the model parameters β such that their linear combination with all predictor-arrays in X become as close to their response in Y as possible, with least squares residuals. Uses the cholesky decomposition of the normal equations.
##### Parameters
###### `IEnumerable<Tuple<T[], T>>` samples

Sequence of predictor-arrays and their response.

###### `bool` intercept

True if an intercept should be added as first artificial predictor value. Default = false.

###### `DirectRegressionMethod` method

The direct method to be used to compute the regression.

##### Return
###### `T[]`

Best fitting list of model parameters β for each element in the predictor-arrays.

#### Vector<T>NormalEquations<T>(Matrix<T> x, Vector<T> y)

Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals. Uses the cholesky decomposition of the normal equations.
##### Parameters
###### `Matrix<T>` x

Predictor matrix X

###### `Vector<T>` y

Response vector Y

##### Return
###### `Vector<T>`

Best fitting vector for model parameters β

#### Matrix<T>NormalEquations<T>(Matrix<T> x, Matrix<T> y)

Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals. Uses the cholesky decomposition of the normal equations.
##### Parameters
###### `Matrix<T>` x

Predictor matrix X

###### `Matrix<T>` y

Response matrix Y

##### Return
###### `Matrix<T>`

Best fitting vector for model parameters β

#### T[]NormalEquations<T>(IEnumerable<Tuple<T[], T>> samples, bool intercept)

Find the model parameters β such that their linear combination with all predictor-arrays in X become as close to their response in Y as possible, with least squares residuals. Uses the cholesky decomposition of the normal equations.
##### Parameters
###### `IEnumerable<Tuple<T[], T>>` samples

Sequence of predictor-arrays and their response.

###### `bool` intercept

True if an intercept should be added as first artificial predictor value. Default = false.

##### Return
###### `T[]`

Best fitting list of model parameters β for each element in the predictor-arrays.

#### Matrix<T>QR<T>(Matrix<T> x, Matrix<T> y)

Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals. Uses an orthogonal decomposition and is therefore more numerically stable than the normal equations but also slower.
##### Parameters
###### `Matrix<T>` x

Predictor matrix X

###### `Matrix<T>` y

Response matrix Y

##### Return
###### `Matrix<T>`

Best fitting vector for model parameters β

#### Vector<T>QR<T>(Matrix<T> x, Vector<T> y)

Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals. Uses an orthogonal decomposition and is therefore more numerically stable than the normal equations but also slower.
##### Parameters
###### `Matrix<T>` x

Predictor matrix X

###### `Vector<T>` y

Response vector Y

##### Return
###### `Vector<T>`

Best fitting vector for model parameters β

#### T[]QR<T>(IEnumerable<Tuple<T[], T>> samples, bool intercept)

Find the model parameters β such that their linear combination with all predictor-arrays in X become as close to their response in Y as possible, with least squares residuals. Uses an orthogonal decomposition and is therefore more numerically stable than the normal equations but also slower.
##### Parameters
###### `IEnumerable<Tuple<T[], T>>` samples

Sequence of predictor-arrays and their response.

###### `bool` intercept

True if an intercept should be added as first artificial predictor value. Default = false.

##### Return
###### `T[]`

Best fitting list of model parameters β for each element in the predictor-arrays.

#### Vector<T>Svd<T>(Matrix<T> x, Vector<T> y)

Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals. Uses a singular value decomposition and is therefore more numerically stable (especially if ill-conditioned) than the normal equations or QR but also slower.
##### Parameters
###### `Matrix<T>` x

Predictor matrix X

###### `Vector<T>` y

Response vector Y

##### Return
###### `Vector<T>`

Best fitting vector for model parameters β

#### Matrix<T>Svd<T>(Matrix<T> x, Matrix<T> y)

Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals. Uses a singular value decomposition and is therefore more numerically stable (especially if ill-conditioned) than the normal equations or QR but also slower.
##### Parameters
###### `Matrix<T>` x

Predictor matrix X

###### `Matrix<T>` y

Response matrix Y

##### Return
###### `Matrix<T>`

Best fitting vector for model parameters β

#### T[]Svd<T>(IEnumerable<Tuple<T[], T>> samples, bool intercept)

Find the model parameters β such that their linear combination with all predictor-arrays in X become as close to their response in Y as possible, with least squares residuals. Uses a singular value decomposition and is therefore more numerically stable (especially if ill-conditioned) than the normal equations or QR but also slower.
##### Parameters
###### `IEnumerable<Tuple<T[], T>>` samples

Sequence of predictor-arrays and their response.

###### `bool` intercept

True if an intercept should be added as first artificial predictor value. Default = false.

##### Return
###### `T[]`

Best fitting list of model parameters β for each element in the predictor-arrays.