第四章 多元线性回归

0导入&加载数据

一个完整的机器学习项目

import os
import tarfile
import urllib
import urllib.request

DOWNLOAD_ROOT = "https://raw.githubusercontent.com/ageron/handson-ml2/master/"
HOUSING_PATH = os.path.join("datasets", "housing") # 把目录和文件名合成一个路径
HOUSING_URL = DOWNLOAD_ROOT + "datasets/housing/housing.tgz"

def fetch_housing_data(housing_url=HOUSING_URL, housing_path=HOUSING_PATH):
    if not os.path.isdir(housing_path): # 判断路径是否为目录
        os.makedirs(housing_path) # 递归创建目录
    tgz_path = os.path.join(housing_path, "housing.tgz")
    urllib.request.urlretrieve(housing_url, tgz_path) # 将URL检索到磁盘上的临时位置
    housing_tgz = tarfile.open(tgz_path) # 打开
    housing_tgz.extractall(path=housing_path) # 解压
    housing_tgz.close() # 关闭

fetch_housing_data()

import pandas as pd

def load_housing_data(housing_path=HOUSING_PATH):
    csv_path = os.path.join(housing_path, "housing.csv")
    return pd.read_csv(csv_path) # 加载数据

housing = load_housing_data()
housing.head()

1 可视化

import seaborn as sns

sns.set() # 设置/重设美学参数
sns.pairplot(housing, height=2) # 散点图矩阵

2 相关分析

housing.corr() # 相关阵

R = housing.corr()
sns.heatmap(R)

3 回归建模

housing = housing.dropna() # 去除缺失值NaN

import statsmodels.api as sm

features = list(housing) # 提取列名
features.remove('median_house_value')
features.remove('ocean_proximity') # 非数值类型
labels = ['median_house_value'] 

X = sm.add_constant(housing[features]) # 特征(添加一列1)
y = housing['median_house_value'] # 标签

model = sm.OLS(y, X)
result = model.fit()

3.1 参数估计

result.params

print(result.summary())

多重共线性

3.2 残差图

import matplotlib.pyplot as plt

plt.plot(result.predict(), result.resid)

4 使用Sklean做回归

4.1 建模

from sklearn import linear_model
from sklearn.model_selection import train_test_split

# 随机产生训练集&测试集
trainSet, testSet = train_test_split(housing, test_size=0.2, random_state=2020)
# 回归建模
model = linear_model.LinearRegression()
model.fit(trainSet[features], trainSet[labels])

4.2 建模结果

model.coef_

model.intercept_

4.3 评估

均方误差

import numpy as np

np.mean((model.predict(testSet[features]) - testSet[labels])**2)

决定系数$R^2$

model.score(testSet[features], testSet[labels])

模型表现超级差

未完待续……