python最小二乘法拟合直线

约定不等于承诺〃 2022-06-12 11:15 381阅读 0赞

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][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:

![SouthEast][]  
代码如下:

# -*- coding: utf-8 -*
    import numpy as np
    import matplotlib.pyplot as plt
    x = 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:  
![SouthEast 1][]  
代码如下:

from  paint_scatter_plot import x,y
    import numpy as np 
    import matplotlib.pyplot as plt
    def 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,b
    if __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.

[https_my.oschina.net_keyven_blog_526010]: https://my.oschina.net/keyven/blog/526010
[SouthEast]: /images/20220612/2e86c6e6f8134a00a83b736d0bc3dc42.png
[SouthEast 1]: /images/20220612/122a7acc78574c659748fffd07e83eb8.png