source: trunk/yat/regression/Linear.h @ 1437

#ifndef _theplu_yat_regression_linear_
#define _theplu_yat_regression_linear_

// $Id: Linear.h 1437 2008-08-25 17:55:00Z peter $

/*
  Copyright (C) 2004, 2005, 2006, 2007 Jari Häkkinen, Peter Johansson
  Copyright (C) 2008 Peter Johansson

  This file is part of the yat library, http://dev.thep.lu.se/yat

  The yat library is free software; you can redistribute it and/or
  modify it under the terms of the GNU General Public License as
  published by the Free Software Foundation; either version 2 of the
  License, or (at your option) any later version.

  The yat library is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
  General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with this program; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
  02111-1307, USA.
*/

#include "OneDimensional.h"

#include <cmath>

namespace theplu {
namespace yat {
  namespace utility {
    class VectorBase;
  }
namespace regression {

  /**
     @brief linear regression.   
     
     Data are modeled as \f$ y_i = \alpha + \beta (x_i-m_x) +
     \epsilon_i \f$.
  */
  class Linear : public OneDimensional 
  {
  
  public:
    ///
    /// @brief The default constructor
    ///
    Linear(void);

    ///
    /// @brief The destructor 
    ///
    virtual ~Linear(void);
         
    /**
       The parameter \f$ \alpha \f$ is estimated as \f$
       \frac{1}{n}\sum y_i \f$
       
       @return the parameter \f$ \alpha \f$
    */
    double alpha(void) const;

    /**
       The standard deviation is estimated as \f$ \sqrt{\frac{s^2}{n}}
       \f$ where \f$ s^2 = \frac{\sum \epsilon^2}{n-2} \f$
       
       @return standard deviation of parameter \f$ \alpha \f$
    */
    double alpha_var(void) const;

    /**
       The parameter \f$ \beta \f$ is estimated as \f$
       \frac{\textrm{Cov}(x,y)}{\textrm{Var}(x)} \f$
       
       @return the parameter \f$ \beta \f$
    */
    double beta(void) const;

    /**
       The standard deviation is estimated as \f$ \frac{s^2}{\sum
       (x-m_x)^2} \f$ where \f$ s^2 = \frac{\sum \epsilon^2}{n-2} \f$

       @return standard deviation of parameter \f$ \beta \f$
    */
    double beta_var(void) const;

    /**
       Model is fitted by minimizing \f$ \sum{(y_i - \alpha - \beta
       (x-m_x))^2} \f$. By construction \f$ \alpha \f$ and \f$ \beta \f$
       are independent.
    */
    void fit(const utility::VectorBase& x, const utility::VectorBase& y) ;
    
    ///
    /// @return \f$ \alpha + \beta x \f$ 
    ///
    double predict(const double x) const;

    ///
    /// Function returning the coefficient of determination,
    /// i.e. fraction of variance explained by the linear model.
    ///
    double r2(void) const;

    /**
       \f$ \frac{\sum \epsilon_i^2}{N-2} \f$

       @return variance of residuals
    */
    double s2(void) const;

    /**
       The error of the model is estimated as \f$
       \textrm{alpha\_err}^2+\textrm{beta\_err}^2*(x-m_x)*(x-m_x)\f$
    
       @return estimated error of model in @a x
    */
    double standard_error2(const double x) const;


  private:
    ///
    /// Copy Constructor. (not implemented)
    ///
    Linear(const Linear&);

    double alpha_;
    double alpha_var_;
    double beta_;
    double beta_var_;
  };

}}} // of namespaces regression, yat, and theplu

#endif