线性回归：从拟合直线到解释预测误差

import numpy as np
from sklearn.linear_model import LinearRegression, Ridge
from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score
from sklearn.model_selection import train_test_split

rng = np.random.default_rng(42)
input_mb = rng.uniform(5, 100, 300)
file_count = rng.integers(1, 80, 300)
duration = 1.8 * input_mb + 0.7 * file_count + 15 + rng.normal(0, 12, 300)
X = np.column_stack([input_mb, file_count])
X_train, X_test, y_train, y_test = train_test_split(
    X, duration, test_size=0.25, random_state=42,
)

for model in (LinearRegression(), Ridge(alpha=10.0)):
    model.fit(X_train, y_train)
    prediction = model.predict(X_test)
    print(type(model).__name__)
    print("coefficients:", np.round(model.coef_, 3))
    print("MAE:", round(mean_absolute_error(y_test, prediction), 2))
    print("RMSE:", round(np.sqrt(mean_squared_error(y_test, prediction)), 2))
    print("R2:", round(r2_score(y_test, prediction), 3))
    print("mean residual:", round(float(np.mean(y_test - prediction)), 3))

import matplotlib.pyplot as plt

prediction = model.predict(X_test)
residual = y_test - prediction
figure, axis = plt.subplots(figsize=(6, 4))
axis.scatter(prediction, residual, alpha=0.6)
axis.axhline(0, color="black", linewidth=1)
axis.set(xlabel="Prediction", ylabel="Residual", title="Residual check")
figure.tight_layout()
figure.savefig("residuals.png", dpi=150)
plt.close(figure)

from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler

X_correlated = np.column_stack(
    [input_mb, file_count, input_mb * 1.02 + rng.normal(0, 1, len(input_mb))]
)
X_train_c, X_test_c, y_train_c, y_test_c = train_test_split(
    X_correlated, duration, test_size=0.25, random_state=42,
)

ridge = make_pipeline(StandardScaler(), Ridge(alpha=10.0))
ridge.fit(X_train_c, y_train_c)
print("test MAE:", round(mean_absolute_error(y_test_c, ridge.predict(X_test_c)), 2))
print("scaled coefficients:", np.round(ridge.named_steps["ridge"].coef_, 3))