多元线性回归 fortran

根据提供的引用内容，我们可以了解到Fortran2013版可以用于对离散数据进行多元线性回归。下面是一个简单的多元线性回归的Fortran代码示例：

program multiple_linear_regression
    implicit none
    integer, parameter :: dp = selected_real_kind(15, 307)
    integer :: i, j, k, n, m
    real(dp), dimension(:,:), allocatable :: x, y, xt, xtx, xtxi, b
    real(dp), dimension(:), allocatable :: xmean, ymean, xstd, ystd
    real(dp) :: r, ssr, sse, sst, yfit
    character(len=100) :: filename
    print *, "Enter the name of the data file:"
    read *, filename
    open(10, file=filename, status='old', action='read')
    read(10,*) n, m
    allocate(x(n,m), y(n))
    do i = 1, n
        read(10,*) (x(i,j), j=1,m), y(i)
    end do
    close(10)
    allocate(xt(m,n))
    do i = 1, n
        do j = 1, m
            xt(j,i) = x(i,j)
        end do
    end do
    allocate(xtx(m,m))
    do i = 1, m
        do j = 1, m
            xtx(i,j) = sum(xt(i,:)*x(:,j))
        end do
    end do
    allocate(xtxi(m,m))
    call matinv(xtx, xtxi)
    allocate(b(m))
    do i = 1, m
        b(i) = sum(y*xt(i,:))*xtxi(i,i)
    end do
    allocate(xmean(m), xstd(m), ymean, ystd)
    do i = 1, m
        xmean(i) = sum(x(:,i))/n
        xstd(i) = sqrt(sum((x(:,i)-xmean(i))**2)/(n-1))
        do j = 1, n
            x(j,i) = (x(j,i)-xmean(i))/xstd(i)
        end do
    end do
    ymean = sum(y)/n
    ystd = sqrt(sum((y-ymean)**2)/(n-1))
    do i = 1, n
        y(i) = (y(i)-ymean)/ystd
    end do
    sse = 0.0_dp
    ssr = 0.0_dp
    sst = 0.0_dp
    do i = 1, n
        yfit = 0.0_dp
        do j = 1, m
            yfit = yfit + b(j)*x(i,j)
        end do
        sse = sse + (y(i)-yfit)**2
        ssr = ssr + (yfit-ymean)**2
        sst = sst + (y(i)-ymean)**2
    end do
    r = sqrt(ssr/sst)
    print *, "Regression coefficients:"
    do i = 1, m
        print *, "b(",i,") = ", b(i)
    end do
    print *, "Coefficient of determination:"
    print *, "r = ", r
    print *, "Residual standard error:"
    print *, "s = ", sqrt(sse/(n-m))
    deallocate(x, y, xt, xtx, xtxi, b, xmean, xstd, ymean, ystd)
end program multiple_linear_regression