模型评价：回归模型的常用评价指标

1) 样本误差：衡量模型在一个样本上的预测准确性

样本误差 = 样本预测值 - 样本实际值

2) 最常用的评价指标：均误差方(MSE)

指标解释：所有样本的样本误差的平方的均值

指标解读：均误差方越接近0，模型越准确

3) 较为好解释的评价指标：平均绝对误差(MAE)

指标解释：所有样本的样本误差的绝对值的均值

指标解读：平均绝对误差的单位与因变量单位一致，越接近0，模型越准确

4)平均绝对误差的衍生指标：平均绝对比例误差(MAPE)

指标解释：所有样本的样本误差的绝对值占实际值的比值

指标解读：指标越接近与0，模型越准确

5)模型解释度：R squared R方 r2

指标解释：应变量的方差能被自变量解释的程度

指标解读：指标越接近1，则代表自变量对于应变量的解释度越高

使用sklearn查看回归模型的各项指标

1) 加载数据

import pandas as pd

import matplotlib.pyplot as plt

import os

os.chdir(r'C:\Users\86177\Desktop')

# 样例数据读取

df = pd.read_excel('realestate_sample_preprocessed.xlsx')

# 根据共线性矩阵，保留与房价相关性最高的日间人口，将夜间人口和20-39岁夜间人口进行比例处理

def age_percent(row):

if row['nightpop'] == 0:

return 0

else:

return row['night20-39']/row['nightpop']

df['per_a20_39'] = df.apply(age_percent,axis=1)

df = df.drop(columns=['nightpop','night20-39'])

# 数据集基本情况查看

print(df.shape)

print(df.dtypes)

print(df.isnull().sum())

–> 输出的结果为：(这里直接加载数据并对共线性数据进行处理)

(898, 9)

id int64

complete_year int64

average_price float64

area float64

daypop float64

sub_kde float64

bus_kde float64

kind_kde float64

per_a20_39 float64

dtype: object

id 0

complete_year 0

average_price 0

area 0

daypop 0

sub_kde 0

bus_kde 0

kind_kde 0

per_a20_39 0

dtype: int64

2) 划分数据集

x = df[['complete_year','area', 'daypop', 'sub_kde',

'bus_kde', 'kind_kde','per_a20_39']]

y = df['average_price']

print(x.shape)

print(y.shape)

–> 输出的结果为：(创建模型前需要将数据集划分好，查看数据维度)

(898, 7)

(898,)

3) 建立回归模型

之前提到的Pipeline模型工作流就可以直接使用了，将要执行的工作流程全部封装在Pipeline中，具体的有：

数据标准化

StandardScaler()

，

数据纠偏

PowerTransformer()

，

变量拓展

PolynomialFeatures(degree=3)

，样本值为1000，特征有7个，这里选择

degree=3

，

线性回归中选择了

lasso

回归，里面的

LassoCV(alphas=(list(np.arange(8, 10) * 10)

，可以实现自动训练出最优的

alpha

值带入模型中

import numpy as np

from sklearn.linear_model import LinearRegression, LassoCV

from sklearn.model_selection import KFold

from sklearn.preprocessing import StandardScaler, PowerTransformer

from sklearn.preprocessing import PolynomialFeatures

from sklearn.pipeline import Pipeline

# 构建模型工作流

pipe_lm = Pipeline([

('sc',StandardScaler()),

('power_trans',PowerTransformer()),

('polynom_trans',PolynomialFeatures(degree=3)),

('lasso_regr', LassoCV(alphas=(

list(np.arange(8, 10) * 10)

),

cv=KFold(n_splits=3, shuffle=True),

n_jobs=-1))

])

print(pipe_lm)

–> 输出的结果为：

Pipeline(memory=None,

steps=[('sc',

StandardScaler(copy=True, with_mean=True, with_std=True)),

('power_trans',

PowerTransformer(copy=True, method='yeo-johnson',

standardize=True)),

('polynom_trans',

PolynomialFeatures(degree=3, include_bias=True,

interaction_only=False, order='C')),

('lasso_regr',

LassoCV(alphas=[80, 90], copy_X=True,

cv=KFold(n_splits=3, random_state=None, shuffle=True),

eps=0.001, fit_intercept=True, max_iter=1000,

n_alphas=100, n_jobs=-1, normalize=False,

positive=False, precompute='auto', random_state=None,

selection='cyclic', tol=0.0001, verbose=False))],

verbose=False)

4) 查看模型表现

import warnings

from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score

warnings.filterwarnings('ignore')

pipe_lm.fit(x,y)

y_predict = pipe_lm.predict(x)

print(f'mean squared error is: {mean_squared_error(y,y_predict)}')

print(f'mean absolute error is: {mean_absolute_error(y,y_predict)}')

print(f'R Squared is: {r2_score(y,y_predict)}')

# 计算MAPE

check = df[['average_price']]

check['y_predict'] = pipe_lm.predict(x)

check['abs_err'] = abs(check['y_predict']-check['average_price'] )

check['ape'] = check['abs_err']/check['average_price']

ape = check['ape'].mean()

print(f'mean absolute percent error is: {ape}')

–> 输出的结果为：(MAPE需要手动单独计算，没有模块可以使用)

mean squared error is: 27731808.3971612

mean absolute error is: 3764.8763555076

R Squared is: 0.671538868244777

mean absolute percent error is: 0.16143438261828635

最后可以看一下

check

数据

average_pricey_predictabs_errape

033464.00040132.9811806668.9811800.199288

138766.00034522.8543224243.1456780.109455

233852.00032718.5080301133.4919700.033484

339868.00039242.949615625.0503850.015678

442858.00039242.9496153615.0503850.084349

...............

89340113.00039559.520171553.4798290.013798

89441806.00048224.3538206418.3538200.153527

89551895.37537610.72715214284.6478480.275259

89634546.00044010.8965349464.8965340.273980

89733595.00032194.0551271400.9448730.041701

898 rows × 4 columns