线性回归 Statsmodels 模型预测波士顿房价

CRIM: 城镇人均犯罪率，百分比%
ZN: 住宅用地所占比例，百分比%
INDUS: 城镇中非住宅用地所占比例，百分比%
CHAS: CHAS 虚拟变量，用于回归分析
NOX: 环保指数
RM: 每栋住宅的房间数
AGE: 1940 年以前建成的自住单位的比例，百分比%
DIS: 距离 5 个波士顿的就业中心的加权距离
RAD: 距离高速公路的便利指数
TAX: 每一万美元的不动产税率,百分比%
PTRATIO: 城镇中的教师学生比例，百分比%
B: 关于黑人比例的一个参数
LSTAT: 地区中有多少房东属于低收入人群，百分比%
MEDV: 自住房屋房价中位数（也就是均价），单位 $1000 美元

from sklearn import datasets
data = datasets.load_boston()

data.DESCR # 查看数据集描述
data.feature_names # 查看特征变量名 
data.target # 查看目标变量数据
data.data # 查看自变量数据

Boston House Prices dataset
===========================

Notes
------
Data Set Characteristics:  

    :Number of Instances: 506 

    :Number of Attributes: 13 numeric/categorical predictive
    
    :Median Value (attribute 14) is usually the target

    :Attribute Information (in order):
        - CRIM     per capita crime rate by town
        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.
        - INDUS    proportion of non-retail business
 ...
---

['CRIM' 'ZN' 'INDUS' 'CHAS' 'NOX' 'RM' 'AGE' 'DIS' 'RAD' 'TAX' 'PTRATIO'
 'B' 'LSTAT']

---
...

# 将数据集转为 dataframe 格式 
import pandas as pd 
boston = pd.DataFrame(data.data,columns=data.feature_names)
boston['Price'] = data.data # 因变量也加入dataframe
boston.head()

"""
方法1 train_test_split
"""
from sklearn.model_selection import train_test_split
col_x = boston.columns[:-1]
train, test = train_test_split(boston, test_size=0.2, random_state=123)
print(train.shape)
print(test.shape)

# output：
(404, 14)
(102, 14)

"""
方法2 shuffle
"""
from sklearn.utils import shuffle 
x,y = shuffle(boston[col_x],boston['Price'],random_state=124)
offset = int(x.shape[0]*0.8)
x_train ,y_train= x[:offset],y[:offset]
x_test ,y_test= x[offset:],y[offset:]

boston.info()
# output：
RangeIndex: 506 entries, 0 to 505
Data columns (total 14 columns):
CRIM       506 non-null float64
ZN         506 non-null float64
INDUS      506 non-null float64
CHAS       506 non-null float64
NOX        506 non-null float64
RM         506 non-null float64
AGE        506 non-null float64
DIS        506 non-null float64
RAD        506 non-null float64
TAX        506 non-null float64
PTRATIO    506 non-null float64
B          506 non-null float64
LSTAT      506 non-null float64
Price      506 non-null float64
dtypes: float64(14)

boston.describe().round(2)
# output：

import matplotlib.pyplot as plt 
import seaborn as sns
import scipy.stats as stats 

sns.set(rc={'figure.figsize':(8,6),'font.sans-serif':['simhei','Arial']})  #设置字体，避免中文不显示
sns.distplot(train.Price,bins=20,
            fit = stats.norm, # 拟合标准正态分布
            kde_kws={'label':'核密度曲线'},
            fit_kws={'color':'red','label':'标准正态分布曲线'}
            )
plt.legend()

train.corrwith(train.Price).sort_values(ascending=False)
# output:
Price      1.000000
RM         0.716973
ZN         0.360129
B          0.327933
DIS        0.255739
CHAS       0.119402
AGE       -0.380633
CRIM      -0.386443
RAD       -0.392065
NOX       -0.436879
TAX       -0.493560
INDUS     -0.496211
PTRATIO   -0.506643
LSTAT     -0.746059
dtype: float64

import statsmodels.api as sm
sns.set(style='ticks',rc={'figure.figsize':(12,12)})

train_corr = train.corr()
sns.set(style='ticks',rc={'figure.figsize':(10,10)})
sns.heatmap(train_corr,cbar=True,annot=True,square=True,fmt='0.2f',annot_kws={'size':12})

from sklearn.feature_selection import SelectKBest,f_regression
X1 = train.iloc[:,:13]
selector = SelectKBest(f_regression,k=3) # k：筛选k个变量
selector.fit_transform(X1,train['Price'])
X1.columns[selector.get_support(indices=True)].tolist()
#output:
['RM', 'PTRATIO', 'LSTAT']