Python线性回归标准方程

# -*- coding: utf-8 -*-
"""
Created on 2024.1.22

@author: rubyw
"""

import numpy as np
from numpy import genfromtxt
import matplotlib.pyplot as plt

data = np.genfromtxt('一元线性回归.csv', delimiter=',')
x_data = data[:, 0, np.newaxis]
y_data = data[:, 1, np.newaxis]
plt.scatter(x_data, y_data)
plt.show()

print(np.mat(x_data).shape)
print(np.mat(y_data).shape)
# 给样本添加偏置项
X_data = np.concatenate((np.ones((100, 1)), x_data), axis=1)
print(X_data.shape)

print(X_data[:3])


# 标准方程法求解回归参数
def weights(xArr, yArr):
    xMat = np.mat(xArr)
    yMat = np.mat(yArr)
    xTx = xMat.T * xMat  # 矩阵乘法
    # 计算矩阵的值,如果值为0，说明该矩阵没有逆矩阵
    if np.linalg.det(xTx) == 0.0:
        print("This matrix cannot do inverse")
        return
    # xTx.I为xTx的逆矩阵
    ws = xTx.I * xMat.T * yMat
    return ws


ws = weights(X_data, y_data)
print(ws)

# 画图
x_test = np.array([[20], [80]])
y_test = ws[0] + x_test * ws[1]
plt.plot(x_data, y_data, 'b.')
plt.plot(x_test, y_test, 'r')
plt.show()