#include <yat/regression/Naive.h>

Inheritance diagram for theplu::yat::regression::Naive:

Public Member Functions
	Naive (void)
	The default constructor.
virtual	~Naive (void)
	The destructor.
void	fit (const utility::VectorBase &x, const utility::VectorBase &y)
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

Naive Regression.

Data are modeled as $y_i = \alpha + \epsilon_i$

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

virtual

This function computes the best-fit for the naive model $ y = m $ from vectors x and y, by minimizing $\sum{(y_i-m)^2}$ .

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

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

virtual

The predicted value is the average $ m $

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