#include <yat/regression/Polynomial.h>

Inheritance diagram for theplu::yat::regression::Polynomial:

Public Member Functions
	Polynomial (size_t power)

	~Polynomial (void)
	Destructor.

const utility::Matrix &	covariance (void) const
	covariance of parameters

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

const utility::Vector &	fit_parameters (void) const

double	predict (const double x) const

double	s2 (void) const

double	standard_error2 (const double x) const

double	chisq (void) const
	Chi-squared. More...

double	prediction_error2 (const double x) const

std::ostream &	print (std::ostream &os, const double min, double max, const unsigned int n) const
	print output to ostream os More...

double	r2 (void) const

Protected Member Functions
double	variance (void) const

Protected Attributes
statistics::AveragerPair	ap_

double	chisq_

Detailed Description

Polynomial regression.

Data are modeled as $y = \alpha + \beta x + \gamma x^2 + ... + \delta x_i^{\textrm{power}} + \epsilon_i$

Constructor & Destructor Documentation

theplu::yat::regression::Polynomial::Polynomial ( size_t power )

explicit

Parameters

power degree of polynomial, e.g. 1 for a linear model

Member Function Documentation

double theplu::yat::regression::OneDimensional::chisq ( void ) const

inherited

Chi-squared.

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

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

virtual

Fit the model by minimizing the mean squared deviation between model and data.

Implements theplu::yat::regression::OneDimensional.

const utility::Vector& theplu::yat::regression::Polynomial::fit_parameters ( void ) const

Returns: parameters of the model

See Also: MultiDimensional

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

virtual

Returns: value in x of model

Implements theplu::yat::regression::OneDimensional.

double theplu::yat::regression::OneDimensional::prediction_error2 ( const double x ) const

inherited

The prediction error is defined as the expected squared deviation a new data point will have from value the model provides: $E(Y|x - \hat{y}(x))^2$ 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 $ .

Returns: expected squared prediction error for a new data point in x

std::ostream& theplu::yat::regression::OneDimensional::print	(	std::ostream &	os,
		const double	min,
		double	max,
		const unsigned int	n
	)		const

inherited

print output to ostream os

Printing estimated model to os in the points defined by min, max, and n. The values printed for each point is the x-value, the estimated y-value, and the estimated standard deviation of a new data poiunt will have from the y-value given the x-value (see prediction_error()).

Parameters

os	Ostream printout is sent to
n	number of points printed
min	smallest x-value for which the model is printed
max	largest x-value for which the model is printed

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

inherited

r2 is defined as $1 - \frac{Var(Y|x)}{Var(Y)}$ or the fraction of the variance explained by the regression model.

See Also: s2()

double theplu::yat::regression::Polynomial::s2 ( void ) const

virtual

$\frac{\sum \epsilon_i^2}{N-\textrm{DF}}$ where DF is number of parameters in model.

Returns: variance of residuals

Implements theplu::yat::regression::OneDimensional.

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

virtual

Returns: squared error of model value in x

Implements theplu::yat::regression::OneDimensional.

double theplu::yat::regression::OneDimensional::variance ( void ) const

protectedinherited

Variance of y

Member Data Documentation

statistics::AveragerPair theplu::yat::regression::OneDimensional::ap_

protectedinherited

Averager for pair of x and y

double theplu::yat::regression::OneDimensional::chisq_

protectedinherited

See Also: chisq()

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

yat/regression/Polynomial.h

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation