python matplotlib 散点图的拟合直线的简单示例

# sample points
X = [0, 5, 10, 15, 20]
Y = [0, 7, 10, 13, 20]
 
 
# solve for a and b
def best_fit(X, Y):
    xbar = sum(X) / len(X)
    ybar = sum(Y) / len(Y)
    n = len(X)  # or len(Y)
 
    numer = sum([xi * yi for xi, yi in zip(X, Y)]) - n * xbar * ybar
    denum = sum([xi ** 2 for xi in X]) - n * xbar ** 2
 
    b = numer / denum
    a = ybar - b * xbar
 
    print('best fit line:\ny = {:.2f} + {:.2f}x'.format(a, b))
 
    return a, b
 
 
# solution
a, b = best_fit(X, Y)
# best fit line:
# y = 0.80 + 0.92x
 
# plot points and fit line
import matplotlib.pyplot as plt
 
plt.scatter(X, Y)
yfit = [a + b * xi for xi in X]
plt.plot(X, yfit)
plt.show()

用Scripy实现最小二乘法与股票K线回归例子

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import leastsq
 
##样本数据(Xi,Yi)，需要转换成数组(列表)形式
Xi = np.array([160, 165, 158, 172, 159, 176, 160, 162, 171])
Yi = np.array([58, 63, 57, 65, 62, 66, 58, 59, 62])
 
 
##需要拟合的函数func :指定函数的形状 k= 0.42116973935 b= -8.28830260655
def func(p, x):
    k, b = p
    return k * x + b
 
 
##偏差函数：x,y都是列表:这里的x,y更上面的Xi,Yi中是一一对应的
def error(p, x, y):
    return func(p, x) - y
 
 
# k,b的初始值，可以任意设定,经过几次试验，发现p0的值会影响cost的值：Para[1]
p0 = [1, 20]
# 把error函数中除了p0以外的参数打包到args中(使用要求)
Para = leastsq(error, p0, args=(Xi, Yi))
print(Para)
# 读取结果
k, b = Para[0]
print("k=", k, "b=", b)
# 画样本点
plt.figure(figsize=(8, 6))  ##指定图像比例：8：6
plt.scatter(Xi, Yi, color="green", label="source", linewidth=2)
# 画拟合直线
x = np.linspace(150, 190, 100)  ##在150-190直接画100个连续点
y = k * x + b  ##函数式
plt.plot(x, y, color="red", label="target", linewidth=2)
plt.legend()  # 绘制图例
plt.show()