linear regression. More...

#include </scratch/bob/jari/tmp/pristine/yat-0.10.x/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.

Detailed Description

linear regression.

Member Function Documentation

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

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

  @return the parameter \form#172

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

  @return the parameter \form#176

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 @a w) will be from the model
  value \form#211 and is typically
  divided into the conditional variance ( see s2() )
  given \form#62 and the squared standard error ( see
  standard_error2() ) of the model estimation in \form#62.

$E((Y|x - E(Y|x))^2|w) + E((E(Y|x) - \hat{y}(x))^2)$

  @return expected prediction error for a new data point in @a x
  with weight @a w.

double theplu::yat::regression::OneDimensionalWeighted::r2 ( void ) const

inherited

r2 is defined as $\frac{\sum w_i(y_i-\hat{y}_i)^2}{\sum w_i(y_i-m_y)^2}$ or the fraction of the variance explained by the regression model.

double theplu::yat::regression::LinearWeighted::s2 ( double w = 1 ) const

virtual

Noise level for points with weight w.

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

double theplu::yat::regression::LinearWeighted::standard_error2 ( const double x ) const

virtual

estimated error $y_{err} = \sqrt{ Var(\alpha) + Var(\beta)*(x-m)}$ .

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

Member Data Documentation

statistics::AveragerPairWeighted theplu::yat::regression::OneDimensionalWeighted::ap_

protectedinherited

Averager for pair of x and y

double theplu::yat::regression::OneDimensionalWeighted::chisq_

protectedinherited

Chi-squared.

Chi-squared is defined as the $\sum{w_i(\hat{y_i}-y_i)^2}$

The documentation for this class was generated from the following file:

/scratch/bob/jari/tmp/pristine/yat-0.10.x/yat/regression/LinearWeighted.h

Public Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

Member Data Documentation