在Python中绘制回归线、置信区间和预测区间

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error

x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 5, 4, 5])

model = LinearRegression()
model.fit(x.reshape(-1, 1), y)
slope = model.coef_[0]
intercept = model.intercept_

plt.scatter(x, y)
plt.plot(x, slope * x + intercept, color='red')
plt.xlabel('x')
plt.ylabel('y')
plt.show()

y_pred = model.predict(x.reshape(-1, 1))
residuals = y - y_pred

residual_std = np.std(residuals)
confidence_interval = 1.96 * residual_std

prediction_interval = 2.58 * residual_std