创建散点图

# 创建散点图
plt.figure(figsize=(10, 6))
plt.scatter(df['成本'], df['价格'], color='blue', label='Data Spot')
plt.title('Cost vs Price')
plt.xlabel('Cost')
plt.ylabel('Price')
plt.legend()
plt.grid(True)
plt.show()
plt.savefig('test.jpg')

实现梯度下降算法来优化线性回归模型的参数

def gradient_descent(X, y, learning_rate=0.01, iterations=100):
    """
    实现梯度下降算法来优化线性回归模型的参数。
    """
    m = len(y)
    X = np.hstack((np.ones((m, 1)), X))  # 添加一列 1 作为偏置项
    theta = np.zeros(X.shape[1])
    loss_history = []

    for _ in range(iterations):
        predictions = X.dot(theta)
        errors = predictions - y
        gradient = X.T.dot(errors) / m
        theta -= learning_rate * gradient
        loss = np.mean(errors ** 2) / 2
        loss_history.append(loss)

    return theta, loss_history

准备数据

X = df[['成本']]

y = df['价格']

使用梯度下降优化参数

theta, _ = gradient_descent(X, y, iterations=1000)

绘制回归拟合图

plt.figure(figsize=(10, 6))

plt.scatter(X, y, color='blue', label='Data Spot')

plt.plot(X, theta[0] + theta[1] * X, color='red', label='Fitting line')

plt.title('Cost vs Price')

plt.xlabel('Cost')

plt.ylabel('Price')

plt.legend()

plt.grid(True)

plt.show()

显示回归方程

print(f"The regression equation is: Price = {theta[0]:.2f} + {theta[1]:.2f} * Cost")

分析迭代次数对性能的影响

# 分析迭代次数对性能的影响
iteration_counts = [50, 100, 200, 500, 1000,2000]
losses = []

for iterations in iteration_counts:
    _, loss_history = gradient_descent(X, y, iterations=iterations)
    losses.append(loss_history[-1])

# 绘制结果
plt.figure(figsize=(10, 6))
plt.plot(iteration_counts, losses, marker='o')
plt.title('Loss vs. Iteration')
plt.xlabel('Iterations')
plt.ylabel('Loss Value')
plt.grid(True)
plt.show()