/*
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* Copyright Nick Thompson, 2019
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* Use, modification and distribution are subject to the
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* Boost Software License, Version 1.0. (See accompanying file
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* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#ifndef BOOST_MATH_STATISTICS_LINEAR_REGRESSION_HPP
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#define BOOST_MATH_STATISTICS_LINEAR_REGRESSION_HPP
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#include <cmath>
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#include <algorithm>
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#include <utility>
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#include <boost/math/statistics/univariate_statistics.hpp>
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#include <boost/math/statistics/bivariate_statistics.hpp>
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namespace boost::math::statistics {
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template<class RandomAccessContainer>
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auto simple_ordinary_least_squares(RandomAccessContainer const & x,
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RandomAccessContainer const & y)
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{
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using Real = typename RandomAccessContainer::value_type;
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if (x.size() <= 1)
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{
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throw std::domain_error("At least 2 samples are required to perform a linear regression.");
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}
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if (x.size() != y.size())
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{
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throw std::domain_error("The same number of samples must be in the independent and dependent variable.");
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}
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auto [mu_x, mu_y, cov_xy] = boost::math::statistics::means_and_covariance(x, y);
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auto var_x = boost::math::statistics::variance(x);
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if (var_x <= 0) {
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throw std::domain_error("Independent variable has no variance; this breaks linear regression.");
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}
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Real c1 = cov_xy/var_x;
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Real c0 = mu_y - c1*mu_x;
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return std::make_pair(c0, c1);
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}
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template<class RandomAccessContainer>
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auto simple_ordinary_least_squares_with_R_squared(RandomAccessContainer const & x,
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RandomAccessContainer const & y)
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{
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using Real = typename RandomAccessContainer::value_type;
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if (x.size() <= 1)
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{
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throw std::domain_error("At least 2 samples are required to perform a linear regression.");
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}
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if (x.size() != y.size())
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{
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throw std::domain_error("The same number of samples must be in the independent and dependent variable.");
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}
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auto [mu_x, mu_y, cov_xy] = boost::math::statistics::means_and_covariance(x, y);
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auto var_x = boost::math::statistics::variance(x);
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if (var_x <= 0) {
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throw std::domain_error("Independent variable has no variance; this breaks linear regression.");
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}
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Real c1 = cov_xy/var_x;
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Real c0 = mu_y - c1*mu_x;
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Real squared_residuals = 0;
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Real squared_mean_deviation = 0;
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for(decltype(y.size()) i = 0; i < y.size(); ++i) {
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squared_mean_deviation += (y[i] - mu_y)*(y[i]-mu_y);
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Real ei = (c0 + c1*x[i]) - y[i];
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squared_residuals += ei*ei;
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}
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Real Rsquared;
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if (squared_mean_deviation == 0) {
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// Then y = constant, so the linear regression is perfect.
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Rsquared = 1;
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} else {
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Rsquared = 1 - squared_residuals/squared_mean_deviation;
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}
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return std::make_tuple(c0, c1, Rsquared);
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}
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}
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#endif
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