---
name: "mlpack_regression_LinearRegression"
section: "3"
platform: "linux"
package: "mlpack-doc"
version: "1.0.10-1"
release: "Debian 8 (Jessie)"
platforms: ["linux"]
url: "https://new.carta.tech/mlpack_regression_LinearRegression"
---

# mlpack\_regression\_LinearRegression(3)

A simple linear regression algorithm using ordinary least squares.

## NAME

mlpack::regression::LinearRegression -

A simple linear regression algorithm using ordinary least squares.

## SYNOPSIS

### Public Member Functions

**LinearRegression** (const arma::mat &predictors, const arma::vec &responses, const double **lambda**=0)\
 *Creates the model.*  **LinearRegression** (const std::string &filename)\
 *Initialize the model from a file.*  **LinearRegression** (const **LinearRegression** &linearRegression)\
 *Copy constructor.*  **LinearRegression** ()\
 *Empty constructor.*  double **ComputeError** (const arma::mat &points, const arma::vec &responses) const \
 *Calculate the L2 squared error on the given predictors and responses using this linear regression model.*  double **Lambda** () const \
 *Return the Tikhonov regularization parameter for ridge regression.*  double & **Lambda** ()\
 *Modify the Tikhonov regularization parameter for ridge regression.*  const arma::vec & **Parameters** () const \
 *Return the parameters (the b vector).*  arma::vec & **Parameters** ()\
 *Modify the parameters (the b vector).*  void **Predict** (const arma::mat &points, arma::vec &predictions) const \
 *Calculate y\_i for each data point in points.*  std::string **ToString** () const \

### Private Attributes

double **lambda**\
 *The Tikhonov regularization parameter for ridge regression (0 for linear regression).*  arma::vec **parameters**\
 *The calculated B.*

## Detailed Description

A simple linear regression algorithm using ordinary least squares.

Optionally, this class can perform ridge regression, if the lambda parameter is set to a number greater than zero.

Definition at line 35 of file linear\_regression.hpp.

## Constructor & Destructor Documentation

### mlpack::regression::LinearRegression::LinearRegression (const arma::mat &predictors, const arma::vec &responses, const doublelambda = `0`)

Creates the model.

**Parameters:**

*predictors* X, matrix of data points to create B with. \
 *responses* y, the measured data for each point in X

### mlpack::regression::LinearRegression::LinearRegression (const std::string &filename)

Initialize the model from a file.

**Parameters:**

*filename* the name of the file to load the model from.

### mlpack::regression::LinearRegression::LinearRegression (const LinearRegression &linearRegression)

Copy constructor.

**Parameters:**

*linearRegression* the other instance to copy parameters from.

### mlpack::regression::LinearRegression::LinearRegression ()` [inline]`

Empty constructor.

Definition at line 65 of file linear\_regression.hpp.

## Member Function Documentation

### double mlpack::regression::LinearRegression::ComputeError (const arma::mat &points, const arma::vec &responses) const

Calculate the L2 squared error on the given predictors and responses using this linear regression model. This calculation returns

.PP where $ y $ is the responses vector, $ X $ is the matrix of predictors, and $ B $ is the parameters of the trained linear regression model.

As this number decreases to 0, the linear regression fit is better.

**Parameters:**

*predictors* Matrix of predictors (X). \
 *responses* Vector of responses (y).

### double mlpack::regression::LinearRegression::Lambda () const` [inline]`

Return the Tikhonov regularization parameter for ridge regression.

Definition at line 101 of file linear\_regression.hpp.

References lambda.

### double& mlpack::regression::LinearRegression::Lambda ()` [inline]`

Modify the Tikhonov regularization parameter for ridge regression.

Definition at line 103 of file linear\_regression.hpp.

References lambda.

### const arma::vec& mlpack::regression::LinearRegression::Parameters () const` [inline]`

Return the parameters (the b vector).

Definition at line 96 of file linear\_regression.hpp.

References parameters.

### arma::vec& mlpack::regression::LinearRegression::Parameters ()` [inline]`

Modify the parameters (the b vector).

Definition at line 98 of file linear\_regression.hpp.

References parameters.

### void mlpack::regression::LinearRegression::Predict (const arma::mat &points, arma::vec &predictions) const

Calculate y\_i for each data point in points.

**Parameters:**

*points* the data points to calculate with. \
 *predictions* y, will contain calculated values on completion.

### std::string mlpack::regression::LinearRegression::ToString () const

## Member Data Documentation

### double mlpack::regression::LinearRegression::lambda` [private]`

The Tikhonov regularization parameter for ridge regression (0 for linear regression).

Definition at line 119 of file linear\_regression.hpp.

Referenced by Lambda().

### arma::vec mlpack::regression::LinearRegression::parameters` [private]`

The calculated B. Initialized and filled by constructor to hold the least squares solution.

Definition at line 113 of file linear\_regression.hpp.

Referenced by Parameters().

## Author

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