python 最小二乘法实现线性回归

import numpy as np
import matplotlib.pyplot as plt

plt.rcParams['font.family'] = 'SimHei'  # 黑体

time = []
year = []
average_year_time = 0
average_year_year = 0

data = [[12, 1896], [11, 1900], [11, 1904], [10.8, 1908], [10.8, 1912], [10.8, 1920], [10.6, 1924], [10.8, 1928],[10.3, 1932], [10.3, 1936], [10.3, 1948], [10.4, 1952], [10.5, 1956], [10.2, 1960], [10.0, 1964], [9.95, 1968],[10.14, 1972], [10.06, 1976], [10.25, 1980], [9.99, 1984], [9.92, 1988], [9.96, 1992], [9.84, 1996],[9.87, 2000], [9.85, 2004], [9.69, 2008]]
length = len(data)

# plt.xlim(1896, 2008)
# plt.ylim(9, 12)  # 设置坐标区间

for i in data:
    time.append(i[0])
    year.append(i[1])

time = np.array(time)
year = np.array(year)

average_year = sum(year) / length  # year拔
average_time = sum(time) / length  # time拔

for i in data:
    average_year_time = average_year_time + i[0] * i[1]
    average_year_year = average_year_year + i[1] ** 2
average_year_time = average_year_time / length  # (year, time)拔
average_year_year = average_year_year / length  # (year, year)拔

w1 = (average_year_time - average_year * average_time) / (average_year_year - average_year * average_year)
w0 = average_time - w1 * average_year

# 线性回归：t = w0 + w1 * x
if w1 > 0:
    print('t={}+{}x'.format(w0, w1))
else:
    print('t={}{}x'.format(w0, w1))

t_2008 = w0 + w1 * 2008
t_1896 = w0 + w1 * 1896  # 回归直线的两个端点

plt.plot(np.array([1896, 2008]), np.array([t_1896, t_2008]), '-r', label='回归直线')

for i in data:
    plt.scatter(i[1], i[0], c='#DC143C', alpha=0.4)

plt.legend()
plt.show()