theplu::yat::regression::Polynomial Class Reference

#include <yat/regression/Polynomial.h>

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

List of all members.

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.

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

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

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::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::chisq ( void ) const [inherited]

Chi-squared.

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

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::OneDimensional::variance ( void ) const [protected, inherited]

Variance of y

Member Data Documentation

statistics::AveragerPair theplu::yat::regression::OneDimensional::ap_ [protected, inherited]

Averager for pair of x and y

double theplu::yat::regression::OneDimensional::chisq_ [protected, inherited]

See also:: chisq()

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

yat/regression/Polynomial.h


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.
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
double	r2 (void) const
Protected Member Functions
double	variance (void) const
Protected Attributes
statistics::AveragerPair	ap_
double	chisq_