python最小二乘法拟合直线

最小二乘法的推导可参考下面这个博客,推导非常详细.
https://my.oschina.net/keyven/blog/526010
首先画一个加入了噪声的散点图,函数是y=0.2x,加入噪声后如下图所示:

代码如下:

# -*- coding: utf-8 -*import numpy as npimport matplotlib.pyplot as pltx = np.linspace(0, 30, num=50)y = 0.2*x+[np.random.random() for _ in range(50)]if __name__ == '__main__':    plt.figure(figsize=(10, 5), facecolor='w')    plt.plot(x, y, 'ro', lw=2, markersize=6)    plt.grid(b=True, ls=':')    plt.xlabel(u'X', fontsize=16)    plt.ylabel(u'Y', fontsize=16)    plt.show()

我将上面这个代码保存为paint_scatter_plot.py这个名字,方便其他地方调用.
接下来画出拟合直线:

代码如下:

from  paint_scatter_plot import x,yimport numpy as np import matplotlib.pyplot as pltdef Least_squares(x,y):    x_ = x.mean()    y_ = y.mean()    m = np.zeros(1)    n = np.zeros(1)    k = np.zeros(1)    p = np.zeros(1)    for i in np.arange(50):        k = (x[i]-x_)* (y[i]-y_)        m += k        p = np.square( x[i]-x_ )        n = n + p    a = m/n    b = y_ - a* x_    return a,bif __name__ == '__main__':    a,b = Least_squares(x,y)    print a,b    y1 = a * x + b    plt.figure(figsize=(10, 5), facecolor='w')    plt.plot(x, y, 'ro', lw=2, markersize=6)    plt.plot(x, y1, 'r-', lw=2, markersize=6)    plt.grid(b=True, ls=':')    plt.xlabel(u'X', fontsize=16)    plt.ylabel(u'Y', fontsize=16)    plt.show()

代码运算结果: a = 0.19784577, b = 0.48503344 ,还是非常接近正确结果的.