在matplotlib中绘制最小二乘估计函数的等高线图

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# 定义数据集
x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 3, 5, 6, 8])

# 定义最小二乘估计函数
def least_squares(x, y):
    n = len(x)
    sum_x = np.sum(x)
    sum_y = np.sum(y)
    sum_xy = np.sum(x * y)
    sum_x2 = np.sum(x ** 2)
    
    # 计算最小二乘估计的系数
    a = (n * sum_xy - sum_x * sum_y) / (n * sum_x2 - sum_x ** 2)
    b = (sum_y - a * sum_x) / n
    
    return a, b

# 计算最小二乘估计的系数
a, b = least_squares(x, y)

# 定义绘制等高线图的函数
def plot_contour(a, b):
    # 创建网格点
    a_range = np.linspace(-10, 10, 100)
    b_range = np.linspace(-10, 10, 100)
    a_grid, b_grid = np.meshgrid(a_range, b_range)
    
    # 计算误差平方和
    error = np.sum((y - (a_grid * x + b_grid)) ** 2, axis=0)
    
    # 绘制等高线图
    plt.figure()
    plt.contour(a_grid, b_grid, error, levels=20)
    plt.xlabel('a')
    plt.ylabel('b')
    plt.title('Contour Plot of Least Squares Estimation')
    plt.colorbar(label='Error')
    plt.show()

# 调用绘制等高线图的函数
plot_contour(a, b)