python3 實現線性迴歸(繪圖說明)

線性迴歸是最基本的預測, 先隨機生成一堆大概線性相關的數據,

然後通過最小二乘法算出斜率和偏移值, 線性模型就能求出來了, 也能預測數據了 

import numpy as np
import matplotlib.pyplot as plt

#數據集大小, 數據越多 a b就越準確

dataset_size = 100000
#干擾幅度, 干擾越小, ab越準確
amplitute = 200
#預測 y = 2x+3 的線性函數
x = np.random.randint(0,1000,dataset_size)
y = 2 * x + 3 + np.random.normal(size=dataset_size)*amplitute
print(x[:10])
print(y[:10])


plt.scatter(x[:50],y[:50])
plt.axis([0,3000,0,3000])
plt.show()

 

輸出結果: 
[865 603 390 894 593 818  18 304 402 708]
[ 1528.27202848   955.29457768   854.84928664  1621.34212968  1309.90961998
  1617.55872572   215.46963559   502.5849728    606.06870139  1862.69632193]

 

最小二乘法實現, 具體推到大家可以網上搜一下

 

#這裏使用最小二乘法求解線性迴歸的參數
x_mean = np.mean(x)
y_mean = np.mean(y)
​
m1 = 0   #分母
m2 = 0   #分子
for x_i, y_i in zip(x, y):
    m1 += (x_i - x_mean) * (y_i - y_mean)
    m2 += (x_i - x_mean) ** 2

a = m1/m2
b = y_mean - a*x_mean
print(a,b)

2.00067632091 3.07374278432

y_line = a*x + b
print(a,b)
plt.scatter(x[:50],y[:50])
plt.plot(x, y_line, color='r')
plt.axis([0,4000,0,4000])
plt.show()

2.00961672756 3.47528458815

線性迴歸就完了