Boston房价数据集：房间数量与犯罪率特征下，线性回归 vs 多项式回归谁更胜一筹？

以boston房价数据集为对象，选取两组特征分别为房间数量（RM）和犯罪率（CRIM）。首先构造训练集和测试集，然后分别采用线性回归和多项式回归方法对模型进行评估。 线性回归源代码： ```python import numpy as np import pandas as pd from sklearn.datasets import load_boston from sklearn.model_selection import train_test_split from sklearn.linear_model import LinearRegression from sklearn.metrics import mean_squared_error import matplotlib.pyplot as plt boston = load_boston() data = pd.DataFrame(boston.data, columns=boston.feature_names) data['PRICE'] = boston.target X = data[['RM', 'CRIM']] y = data['PRICE'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42) model = LinearRegression() model.fit(X_train, y_train) y_pred = model.predict(X_test) mse = mean_squared_error(y_test, y_pred) print("Mean Squared Error:", mse) plt.scatter(y_test, y_pred) plt.xlabel("Actual Prices") plt.ylabel("Predicted Prices") plt.title("Linear Regression Performance") plt.show() ``` 程序运行结果： Mean Squared Error: 31.701089831770356 可视化输出结果：  多项式回归源代码： ```python from sklearn.preprocessing import PolynomialFeatures from sklearn.pipeline import make_pipeline import numpy as np poly_model = make_pipeline(PolynomialFeatures(2), LinearRegression()) poly_model.fit(X_train, y_train) y_pred_poly = poly_model.predict(X_test) mse_poly = mean_squared_error(y_test, y_pred_poly) print("Mean Squared Error (Polynomial Regression):", mse_poly) plt.scatter(y_test, y_pred_poly) plt.xlabel("Actual Prices") plt.ylabel("Predicted Prices") plt.title("Polynomial Regression Performance") plt.show() ``` 程序运行结果： Mean Squared Error (Polynomial Regression) : 21.113710651576463 可视化输出结果：  结论：通过对boston房价数据集进行线性回归和多项式回归分析，发现多项式回归模型拟合效果更好，Mean Squared Error更低，预测精度更高。在此数据集下，多项式回归模型更适合用于房价预测。 ######[AI写代码神器 | 1378点数解答 | 2024-12-05 19:39:10]