13.线性回归

实现 Simple Linear Regression

import numpy as np
import matplotlib.pyplot as plt

x = np.arange(1, 6, dtype=float)
y = np.array([1., 3., 2., 3., 5.])

plt.scatter(x, y)
plt.axis([0, 6, 0, 6])

 

 

x_mean = np.mean(x)
y_mean = np.mean(y)

num = 0.0
d = 0.0
for x_i, y_i in zip(x, y):
    num += (x_i - x_mean) * (y_i - y_mean)
    d += (x_i - x_mean)**2

a = num / d
b = y_mean -a * x_mean

 

求 a b 的向量化方式

# 求出数据集和标签的均值

x_mean = np.mean(x)
y_mean = np.mean(y)

# 向量化求解a b

num = (x_train - x_mean).dot(y_train - y_mean)
d = (x_train - x_mean).dot(x_train - x_mean)

a = num / d
b = y_mean -a * x_mean

y_hat = a * x + b
y_hat

array([1.2, 2. , 2.8, 3.6, 4.4])

plt.scatter(x, y)
plt.plot(x, y_hat, color="r")
plt.axis([0, 6, 0, 6])

 

 

x_predict = 6
y_predict = a * x_predict + b
y_predict

5.2