线性回归之最小二乘法举例推导及python实现

1 核心思想

通过最小化方差，使得拟合结果无限接近目标结果。

2 通过一元线性方程举例说明

3 通过python实现一元线性拟合

import matplotlib.pyplot as plt
import random

# 用于存储x,y拟合数据
x = []
y = []
# 数据个数
n = 10
# 随机生成x,y
for i in range(n):
    x.append(random.randint(0, 9))
    y.append(random.randint(0, 9))
print(x, y)
# 根据推到出来的公式计算k,b
sum_xy = 0
sum_x = 0
sum_y = 0
sum_xx = 0
for i in range(n):
    sum_xy += x[i] * y[i]
    sum_x += x[i]
    sum_y += y[i]
    sum_xx += x[i] ** 2
print(sum_xy, sum_x, sum_y, sum_xx)
k = (n * sum_xy - sum_x * sum_y) / (n * sum_xx - sum_x ** 2)
b = sum_y / n - k * sum_x / n
print(k, b)
# 根据x计算拟合的y值
new_y = []
for i in range(n):
    new_y.append(k * x[i] + b)
# 画出原始数据点以及拟合好的直线
plt.title("Lea