linear regression. More...

#include <yat/regression/LinearWeighted.h>

Inheritance diagram for theplu::yat::regression::LinearWeighted:

Public Member Functions
	LinearWeighted (void)
	The default constructor.

virtual	~LinearWeighted (void)
	The destructor.

double	alpha (void) const

double	alpha_var (void) const

double	beta (void) const

double	beta_var (void) const

void	fit (const utility::VectorBase &x, const utility::VectorBase &y, const utility::VectorBase &w)

double	predict (const double x) const

double	s2 (double w=1) const

double	standard_error2 (const double x) const

double	prediction_error2 (const double x, const double w=1.0) const

double	r2 (void) const

Protected Attributes
statistics::AveragerPairWeighted	ap_

double	chisq_
	Chi-squared. More...

Detailed Description

linear regression.

Member Function Documentation

double theplu::yat::regression::LinearWeighted::alpha ( void ) const

$ alpha $ is estimated as $\frac{\sum w_iy_i}{\sum w_i}$

Returns: the parameter $\alpha$

double theplu::yat::regression::LinearWeighted::alpha_var ( void ) const

Variance is estimated as $\frac{s^2}{\sum w_i}$

See Also: s2()

Returns: variance of parameter $\alpha$

double theplu::yat::regression::LinearWeighted::beta ( void ) const

$ beta $ is estimated as $\frac{\sum w_i(y_i-m_y)(x_i-m_x)}{\sum w_i(x_i-m_x)^2}$

Returns: the parameter $\beta$

double theplu::yat::regression::LinearWeighted::beta_var ( void ) const

Variance is estimated as $\frac{s^2}{\sum w_i(x_i-m_x)^2}$

See Also: s2()

Returns: variance of parameter $\beta$

void theplu::yat::regression::LinearWeighted::fit	(	const utility::VectorBase &	x,
		const utility::VectorBase &	y,
		const utility::VectorBase &	w
	)

virtual

This function computes the best-fit linear regression coefficients $(\alpha, \beta)$ of the model $y = \alpha + \beta (x-m_x)$ from vectors x and y, by minimizing $\sum{w_i(y_i - \alpha - \beta (x-m_x))^2}$ , where $ m_x $ is the weighted average. By construction $\alpha$ and $\beta$ are independent.

Implements theplu::yat::regression::OneDimensionalWeighted.

double theplu::yat::regression::LinearWeighted::predict ( const double x ) const

virtual

Function predicting value using the linear model: $y =\alpha + \beta (x - m)$

Implements theplu::yat::regression::OneDimensionalWeighted.

double theplu::yat::regression::OneDimensionalWeighted::prediction_error2	(	const double	x,
		const double	w = `1.0`
	)		const

inherited

The prediction error is defined as expected squared deviation a new data point (with weight w) will be from the model value $E((Y|x - \hat{y}(x))^2|w)$ and is typically divided into the conditional variance ( see s2() ) given $ x $ and the squared standard error ( see standard_error2() ) of the model estimation in $ x $ .