Fortran source code to calculate a coefficent of determination for simple 2D regression.

coefficient_of_determination_2d.f95

!****************************************************
! 単回帰分析（2次曲線回帰）の決定係数計算！
!
!   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_curve

contains
  ! 単回帰曲線（2次回帰）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: 係数 a
  ! :param(out) real(8)    b: 係数 b
  ! :param(out) real(8)    b: 係数 c
  subroutine calc_reg_curve(x, y, a, b, c)
    implicit none
    real(DP), intent(in)  :: x(:), y(:)
    real(DP), intent(out) :: a, b, c
    integer(SP) :: size_x, size_y, i
    real(DP)    :: m_x, m_x2, m_x3, m_x4, m_xy, m_x2y, m_y
    real(DP)    :: s_xx, s_xy, s_xx2, s_x2x2, s_x2y

    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

    m_x    = sum(x) / size_x              ! avg(X)
    m_y    = sum(y) / size_y              ! avg(Y)
    m_x2   = sum(x * x) / size_x          ! avg(X^2)
    m_x3   = sum(x * x * x) / size_x      ! avg(X^3)
    m_x4   = sum(x * x * x * x) / size_x  ! avg(X^4)
    m_xy   = sum(x * y) / size_x          ! avg(X * Y)
    m_x2y  = sum(x * x * y) / size_x      ! avg(X-2 * Y)
    s_xx   = m_x2 - m_x * m_x             ! Sxx
    s_xy   = m_xy - m_x * m_y             ! Sxy
    s_xx2  = m_x3 - m_x * m_x2            ! Sxx2
    s_x2x2 = m_x4 - m_x2 * m_x2           ! Sx2x2
    s_x2y  = m_x2y - m_x2 * m_y           ! Sx2y
    b = s_xy * s_x2x2 - s_x2y * s_xx2
    b = b / (s_xx * s_x2x2 - s_xx2 * s_xx2)
    c = s_x2y * s_xx - s_xy * s_xx2
    c = c / (s_xx * s_x2x2 - s_xx2 * s_xx2)
    a = m_y - b * m_x - c * m_x2
  end subroutine calc_reg_curve
end module comp

program coefficient_of_determination_2d
  use const
  use comp
  implicit none
  character(9), parameter :: F_INP = "input.txt"
  integer(SP),  parameter :: UID   = 10
  real(DP)      :: a, b, c
  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)

  ! 単回帰曲線
  call calc_reg_curve(x, y, a, b, c)
  print '(A, F12.8)', "         a = ", a
  print '(A, F12.8)', "         b = ", b
  print '(A, F12.8)', "         c = ", c

  ! 決定係数
  y_e  = a + b * x + c * x * 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

  ! 配列メモリ解放
  deallocate(x)
  deallocate(y)
  deallocate(y_e)
end program coefficient_of_determination_2d