07.线性回归模型

import numpy as np
import matplotlib.pyplot as plt


# 实验数据 y = ax + b + ε
x = np.arange(1, 11, dtype=float)
y = 2 * x + 1 + np.random.normal(size=10)

# 最小二乘法:
# a = Σ(x - x_mean)(y - y_mean) / Σ(x - x_mean) ** 2
# b = y_mean - a * x_mean

x_mean, y_mean = np.mean(x), np.mean(y)
a = (x - x_mean).dot(y - y_mean) / (x - x_mean).dot(x - x_mean)
b = y_mean - a * x_mean

y_hat = a * x + b

plt.scatter(x , y)
plt.plot(x, y_hat, "r")
plt.show()