# source:trunk/yat/regression/Linear.h@726

Last change on this file since 726 was 726, checked in by Peter, 16 years ago

fixes #165 added test checking Linear Regression is equivalent to Polynomial regression of degree one.

• Property svn:eol-style set to native
• Property svn:keywords set to Author Date Id Revision
File size: 3.3 KB
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1#ifndef _theplu_yat_regression_linear_
2#define _theplu_yat_regression_linear_
3
4// $Id: Linear.h 726 2007-01-04 14:38:56Z peter$
5
6/*
7  Copyright (C) The authors contributing to this file.
8
9  This file is part of the yat library, http://lev.thep.lu.se/trac/yat
10
11  The yat library is free software; you can redistribute it and/or
12  modify it under the terms of the GNU General Public License as
13  published by the Free Software Foundation; either version 2 of the
15
16  The yat library is distributed in the hope that it will be useful,
17  but WITHOUT ANY WARRANTY; without even the implied warranty of
18  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
19  General Public License for more details.
20
21  You should have received a copy of the GNU General Public License
22  along with this program; if not, write to the Free Software
23  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
24  02111-1307, USA.
25*/
26
27#include "OneDimensional.h"
28
29#include <cmath>
30
31namespace theplu {
32namespace yat {
33  namespace utility {
34    class vector;
35  }
36namespace regression {
37
38  /**
39     @brief linear regression.
40
41     Data are modeled as \f$y_i = \alpha + \beta (x_i-m_x) + 42 \epsilon_i \f$.
43  */
44  class Linear : public OneDimensional
45  {
46
47  public:
48    ///
49    /// @brief The default constructor
50    ///
51    Linear(void);
52
53    ///
54    /// @brief The destructor
55    ///
56    virtual ~Linear(void);
57
58    /**
59       The parameter \f$\alpha \f$ is estimated as \f$60 \frac{1}{n}\sum y_i \f$
61
62       @return the parameter \f$\alpha \f$
63    */
64    double alpha(void) const;
65
66    /**
67       The standard deviation is estimated as \f$\sqrt{\frac{s^2}{n}} 68 \f$ where \f$s^2 = \frac{\sum \epsilon^2}{n-2} \f$
69
70       @return standard deviation of parameter \f$\alpha \f$
71    */
72    double alpha_var(void) const;
73
74    /**
75       The parameter \f$\beta \f$ is estimated as \f$76 \frac{\textrm{Cov}(x,y)}{\textrm{Var}(x)} \f$
77
78       @return the parameter \f$\beta \f$
79    */
80    double beta(void) const;
81
82    /**
83       The standard deviation is estimated as \f$\frac{s^2}{\sum 84 (x-m_x)^2} \f$ where \f$s^2 = \frac{\sum \epsilon^2}{n-2} \f$
85
86       @return standard deviation of parameter \f$\beta \f$
87    */
88    double beta_var(void) const;
89
90  /**
91       Chi-squared is calculated as \f$\sum 92 (y_i-\alpha-\beta(x_i-m_x))^2 \f$
93    */
94    double chisq(void) const;
95
96    /**
97       Model is fitted by minimizing \f$\sum{(y_i - \alpha - \beta 98 (x-m_x))^2} \f$. By construction \f$\alpha \f$ and \f$\beta \f$
99       are independent.
100    */
101    void fit(const utility::vector& x, const utility::vector& y) ;
102
103    ///
104    /// @return \f$\alpha + \beta x \f$
105    ///
106    double predict(const double x) const;
107
108    ///
109    /// Function returning the coefficient of determination,
110    /// i.e. fraction of variance explained by the linear model.
111    ///
112    double r2(void) const;
113
114    /**
115       The error of the model is estimated as \f$\sqrt{ 116 \textrm{alpha\_err}^2+\textrm{beta\_err}^2*(x-m_x)*(x-m_x)}\f$
117
118       @return estimated error of model in @a x
119    */
120    double standard_error(const double x) const;
121
122
123  private:
124    ///
125    /// Copy Constructor. (not implemented)
126    ///
127    Linear(const Linear&);
128
129    double s2(void) const;
130
131    double alpha_;
132    double alpha_var_;
133    double beta_;
134    double beta_var_;
135    double chisq_;
136    double r2_; // coefficient of determination
137  };
138
139}}} // of namespaces regression, yat, and theplu
140
141#endif
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