# source:trunk/yat/regression/Linear.h@1000

Last change on this file since 1000 was 1000, checked in by Jari Häkkinen, 15 years ago

trac moved to new location.

• Property svn:eol-style set to native
• Property svn:keywords set to Author Date Id Revision
File size: 3.2 KB
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1#ifndef _theplu_yat_regression_linear_
2#define _theplu_yat_regression_linear_
3
4// $Id: Linear.h 1000 2007-12-23 20:09:15Z jari$
5
6/*
7  Copyright (C) 2004, 2005, 2006 Jari Häkkinen, Peter Johansson
8  Copyright (C) 2007 Peter Johansson
9
10  This file is part of the yat library, http://trac.thep.lu.se/yat
11
12  The yat library is free software; you can redistribute it and/or
13  modify it under the terms of the GNU General Public License as
14  published by the Free Software Foundation; either version 2 of the
15  License, or (at your option) any later version.
16
17  The yat library is distributed in the hope that it will be useful,
18  but WITHOUT ANY WARRANTY; without even the implied warranty of
19  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
20  General Public License for more details.
21
22  You should have received a copy of the GNU General Public License
23  along with this program; if not, write to the Free Software
24  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
25  02111-1307, USA.
26*/
27
28#include "OneDimensional.h"
29
30#include <cmath>
31
32namespace theplu {
33namespace yat {
34  namespace utility {
35    class vector;
36  }
37namespace regression {
38
39  /**
40     @brief linear regression.
41
42     Data are modeled as \f$y_i = \alpha + \beta (x_i-m_x) + 43 \epsilon_i \f$.
44  */
45  class Linear : public OneDimensional
46  {
47
48  public:
49    ///
50    /// @brief The default constructor
51    ///
52    Linear(void);
53
54    ///
55    /// @brief The destructor
56    ///
57    virtual ~Linear(void);
58
59    /**
60       The parameter \f$\alpha \f$ is estimated as \f$61 \frac{1}{n}\sum y_i \f$
62
63       @return the parameter \f$\alpha \f$
64    */
65    double alpha(void) const;
66
67    /**
68       The standard deviation is estimated as \f$\sqrt{\frac{s^2}{n}} 69 \f$ where \f$s^2 = \frac{\sum \epsilon^2}{n-2} \f$
70
71       @return standard deviation of parameter \f$\alpha \f$
72    */
73    double alpha_var(void) const;
74
75    /**
76       The parameter \f$\beta \f$ is estimated as \f$77 \frac{\textrm{Cov}(x,y)}{\textrm{Var}(x)} \f$
78
79       @return the parameter \f$\beta \f$
80    */
81    double beta(void) const;
82
83    /**
84       The standard deviation is estimated as \f$\frac{s^2}{\sum 85 (x-m_x)^2} \f$ where \f$s^2 = \frac{\sum \epsilon^2}{n-2} \f$
86
87       @return standard deviation of parameter \f$\beta \f$
88    */
89    double beta_var(void) const;
90
91    /**
92       Model is fitted by minimizing \f$\sum{(y_i - \alpha - \beta 93 (x-m_x))^2} \f$. By construction \f$\alpha \f$ and \f$\beta \f$
94       are independent.
95    */
96    void fit(const utility::vector& x, const utility::vector& y) ;
97
98    ///
99    /// @return \f$\alpha + \beta x \f$
100    ///
101    double predict(const double x) const;
102
103    ///
104    /// Function returning the coefficient of determination,
105    /// i.e. fraction of variance explained by the linear model.
106    ///
107    double r2(void) const;
108
109    /**
110       \f$\frac{\sum \epsilon_i^2}{N-2} \f$
111
112       @return variance of residuals
113    */
114    double s2(void) const;
115
116    /**
117       The error of the model is estimated as \f$118 \textrm{alpha\_err}^2+\textrm{beta\_err}^2*(x-m_x)*(x-m_x)\f$
119
120       @return estimated error of model in @a x
121    */
122    double standard_error2(const double x) const;
123
124
125  private:
126    ///
127    /// Copy Constructor. (not implemented)
128    ///
129    Linear(const Linear&);
130
131    double alpha_;
132    double alpha_var_;
133    double beta_;
134    double beta_var_;
135  };
136
137}}} // of namespaces regression, yat, and theplu
138
139#endif
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