yat  0.14.5pre
Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
theplu::yat::regression::Polynomial Class Reference

Polynomial regression. More...

#include <yat/regression/Polynomial.h>

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

Public Member Functions

 Polynomial (size_t power)
 
 ~Polynomial (void)
 Destructor.
 
const utility::Matrixcovariance (void) const
 covariance of parameters
 
void fit (const utility::VectorBase &x, const utility::VectorBase &y)
 
const utility::Vectorfit_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
powerdegree 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
osOstream printout is sent to
nnumber of points printed
minsmallest x-value for which the model is printed
maxlargest 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:

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