最小二乘法拟合二维线

simple linear regression 基于最小化二次误差,纯Python实现非常简单(检查±和以上链接上的等式):

def linear_fit(x, y):
    """For set of points `(xi, yi)`, return linear polynomial `f(x) = k*x + m` that
    minimizes the sum of quadratic errors.
    """
    meanx = sum(x) / len(x)
    meany = sum(y) / len(y)
    k = sum((xi-meanx)*(yi-meany) for xi,yi in zip(x,y)) / sum((xi-meanx)**2 for xi in x)
    m = meany - k*meanx
    return k, m

对于您的示例输入:

>>> x = [1,2,3,4,6,7]
>>> y = [5,4,3,2,-2,-1]
>>> linear_fit(x, y)
(-1.1614906832298135, 6.285714285714285)