python多项式回归预测波士顿房价

好的，首先我们需要准备数据集。波士顿房价数据集可以在sklearn中直接导入，代码如下：

from sklearn.datasets import load_boston
import pandas as pd

boston = load_boston()
data = pd.DataFrame(boston.data, columns=boston.feature_names)
data['PRICE'] = boston.target

接下来，我们需要对数据进行预处理，包括将数据集分为训练集和测试集，以及进行归一化处理。代码如下：

from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

X = data.iloc[:, :-1].values
y = data.iloc[:, -1].values

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)

sc_X = StandardScaler()
sc_y = StandardScaler()
X_train = sc_X.fit_transform(X_train)
X_test = sc_X.transform(X_test)
y_train = sc_y.fit_transform(y_train.reshape(-1, 1)).reshape(-1)
y_test = sc_y.transform(y_test.reshape(-1, 1)).reshape(-1)

接下来，我们可以使用多项式回归模型对数据进行拟合和预测。代码如下：

from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures

poly_reg = PolynomialFeatures(degree=2)
X_poly_train = poly_reg.fit_transform(X_train)
X_poly_test = poly_reg.transform(X_test)

lin_reg = LinearRegression()
lin_reg.fit(X_poly_train, y_train)

y_pred = lin_reg.predict(X_poly_test)

最后，我们可以使用RMSE指标来评估模型的性能。代码如下：

from sklearn.metrics import mean_squared_error

rmse = np.sqrt(mean_squared_error(y_test, y_pred))
print('RMSE:', rmse)

完整代码如下：

from sklearn.datasets import load_boston
import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from sklearn.metrics import mean_squared_error

boston = load_boston()
data = pd.DataFrame(boston.data, columns=boston.feature_names)
data['PRICE'] = boston.target

X = data.iloc[:, :-1].values
y = data.iloc[:, -1].values

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)

sc_X = StandardScaler()
sc_y = StandardScaler()
X_train = sc_X.fit_transform(X_train)
X_test = sc_X.transform(X_test)
y_train = sc_y.fit_transform(y_train.reshape(-1, 1)).reshape(-1)
y_test = sc_y.transform(y_test.reshape(-1, 1)).reshape(-1)

poly_reg = PolynomialFeatures(degree=2)
X_poly_train = poly_reg.fit_transform(X_train)
X_poly_test = poly_reg.transform(X_test)

lin_reg = LinearRegression()
lin_reg.fit(X_poly_train, y_train)

y_pred = lin_reg.predict(X_poly_test)

rmse = np.sqrt(mean_squared_error(y_test, y_pred))
print('RMSE:', rmse)