02-07 多元线性回归(波士顿房价预测)

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多元线性回归(波士顿房价预测)

1、导入模块

import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.font_manager import FontProperties
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
%matplotlib inline
font = FontProperties(fname='/Library/Fonts/Heiti.ttc')

2、获取数据

df = pd.read_csv('housing-data.txt', sep='\s+', header=0)
X = df.iloc[:, :-1].values
y = df['MEDV'].values
# 将数据分红训练集（0.7）和测试集（0.3）
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)

3、训练模型

lr = LinearRegression()
# 训练模型
lr.fit(X_train, y_train)
# 预测训练集数据
y_train_predict = lr.predict(X_train)
# 预测测试集数据
y_test_predict = lr.predict(X_test)

4、可视化

# y_train_predict-y_train训练数据偏差值
plt.scatter(y_train_predict, y_train_predict-y_train, c='r',
            marker='s', edgecolor='white', label='训练数据')
# y_train_predict-y_train测试数据偏差值
plt.scatter(y_test_predict, y_test_predict-y_test, c='g',
            marker='o', edgecolor='white', label='测试数据')
plt.xlabel('预测值', fontproperties=font)
plt.ylabel('偏差值', fontproperties=font)
# 可视化y=0的一条直线即偏差为0的直线
plt.hlines(y=0, xmin=-10, xmax=50, color='k')
plt.xlim(-10, 50)
plt.legend(prop=font)
plt.show()

_8_0.png?x-oss-process=style/watermark)

5、均方偏差测试

from sklearn.metrics import mean_squared_error

# 训练集的均方偏差
train_mse = mean_squared_error(y_train,y_train_predict)
# 测试集的均方偏差
test_mse = mean_squared_error(y_test,y_test_predict)
print('训练集的均方偏差:{}'.format(train_mse))
print('测试集的均方偏差:{}'.format(test_mse))

训练集的均方偏差:23.049177061822277
测试集的均方偏差:19.901828312902534

训练集的均方偏差是19.4，而测试集的均方偏差是28.4，能够发现测试集的偏差更大了，也就是说训练集过拟合了。