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Fotran source code to calculate a coefficent of determination for simple linear regression.
!****************************************************
! 単回帰分析(線形回帰)決定係数計算
!
! date name version
! 2019.03.31 mk-mode.com 1.00 新規作成
!
! Copyright(C) 2019 mk-mode.com All Rights Reserved.
!****************************************************
!
module const
! SP: 単精度(4), DP: 倍精度(8)
integer, parameter :: SP = kind(1.0)
integer(SP), parameter :: DP = selected_real_kind(2 * precision(1.0_SP))
end module const
module comp
use const
implicit none
private
public :: calc_reg_line, r_2
contains
! 単回帰直線計算
!
! :param(in) real(8) x(:): 説明変数配列
! :param(in) real(8) y(:): 目的変数配列
! :param(out) real(8) a: 切片
! :param(out) real(8) b: 傾き
! :param(out) real(8) r: 相関係数
subroutine calc_reg_line(x, y, a, b, r)
implicit none
real(DP), intent(in) :: x(:), y(:)
real(DP), intent(out) :: a, b, r
integer(SP) :: size_x, size_y, i
real(DP) :: sum_x, sum_y, sum_xx, sum_xy
real(DP) :: mean_x, mean_y, cov, var_x, var_y
size_x = size(x)
size_y = size(y)
if (size_x == 0 .or. size_y == 0) then
print *, "[ERROR] array size == 0"
stop
end if
if (size_x /= size_y) then
print *, "[ERROR] size(X) != size(Y)"
stop
end if
! 単回帰直線
sum_x = sum(x)
sum_y = sum(y)
sum_xx = sum(x * x)
sum_xy = sum(x * y)
a = (sum_xx * sum_y - sum_xy * sum_x) &
& / (size_x * sum_xx - sum_x * sum_x)
b = (size_x * sum_xy - sum_x * sum_y) &
& / (size_x * sum_xx - sum_x * sum_x)
! 相関係数
mean_x = sum(x) / size_x
mean_y = sum(y) / size_x
cov = sum((x - mean_x) * (y - mean_y))
var_x = sum((x - mean_x) * (x - mean_x))
var_y = sum((y - mean_y) * (y - mean_y))
r = (cov / sqrt(var_x)) / sqrt(var_y)
end subroutine calc_reg_line
! 決定係数 (公式使用)
!
! :param(in) x: 説明変数配列
! :param(in) y: 目的変数配列
! :param(in) b: 回帰直線の傾き
! :return r_2: 残差の変動
function r_2(x, y, b)
implicit none
real(DP), intent(in) :: x(:), y(:), b
real(DP) :: r_2
real(DP) :: sum_x, sum_y, sum_y2, sum_xy
integer(SP) :: n
n = size(x)
sum_x = sum(x)
sum_y = sum(y)
sum_y2 = sum(y * y)
sum_xy = sum(x * y)
r_2 = b * (sum_xy - sum_x * sum_y / n) &
& / (sum_y2 - sum_y * sum_y / n)
end function r_2
end module comp
program coefficient_of_determination_line
use const
use comp
implicit none
character(9), parameter :: F_INP = "input.txt"
integer(SP), parameter :: UID = 10
real(DP) :: a, b, r
real(DP) :: y_b, s_r, s_y2, s_e
integer(SP) :: n, i
character(20) :: f
real(DP), allocatable :: x(:), y(:), y_e(:)
! IN ファイル OPEN
open (UID, file = F_INP, status = "old")
! データ数読み込み
read (UID, *) n
! 配列メモリ確保
allocate(x(n))
allocate(y(n))
allocate(y_e(n))
! データ読み込み
do i = 1, n
read (UID, *) x(i), y(i)
end do
write (f, '("(A, ", I0, "F8.2, A)")') n
print f, "説明変数 X = (", x, ")"
print f, "目的変数 Y = (", y, ")"
print '(A)', "---"
! IN ファイル CLOSE
close (UID)
! 単回帰直線
call calc_reg_line(x, y, a, b, r)
print '(A, F12.8)', " 切片 a = ", a
print '(A, F12.8)', " 傾き b = ", b
print '(A, F12.8)', "相関係数 r = ", r
! 決定係数
y_e = a + b * x ! 推定値
y_b = sum(y) / size(y) ! 標本値 Y (目的変数)の平均
s_r = sum((y_e - y_b)**2) ! 推定値の変動
s_y2 = sum((y - y_b)**2) ! 標本値の変動
s_e = sum((y - y_e)**2) ! 残差の変動
print '(A)', "決定係数"
! 解法-1. 決定係数 (= 推定値の変動 / 標本値の変動)
print '(A, F20.16)', " R2 (1) = ", s_r / s_y2
! 解法-2. 決定係数 (= 1 - 残差の変動 / 標本値の変動)
print '(A, F20.16)', " R2 (2) = ", 1.0 - s_e / s_y2
! 解法-3. 決定係数 (公式使用(解法-1,2の変形))
print '(A, F20.16)', " R2 (3) = ", r_2(x, y, b)
! 解法-4. 決定係数 (= 相関係数の2乗)
print '(A, F20.16)', " R2 (4) = ", r * r
! 配列メモリ解放
deallocate(x)
deallocate(y)
deallocate(y_e)
end program coefficient_of_determination_line
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