鲍鱼数据案例（岭回归 、LASSO回归）

数据集探索性分析

import pandas as pd
import warnings
warnings.filterwarnings('ignore')
data=pd.read_csv(r"E:\大二下\机器学习实践\abalone_dataset.csv")
data.head()

	sex	length	diameter	height	whole weight	shucked weight	viscera weight	shell weight	rings
0	M	0.455	0.365	0.095	0.5140	0.2245	0.1010	0.150	15
1	M	0.350	0.265	0.090	0.2255	0.0995	0.0485	0.070	7
2	F	0.530	0.420	0.135	0.6770	0.2565	0.1415	0.210	9
3	M	0.440	0.365	0.125	0.5160	0.2155	0.1140	0.155	10
4	I	0.330	0.255	0.080	0.2050	0.0895	0.0395	0.055	7

#查看数据集中样本数量和特征数量
data.shape

(4177, 9)

#查看数据信息，检查是否有缺失值
data.info()

RangeIndex: 4177 entries, 0 to 4176
Data columns (total 9 columns):
sex               4177 non-null object
length            4177 non-null float64
diameter          4177 non-null float64
height            4177 non-null float64
whole weight      4177 non-null float64
shucked weight    4177 non-null float64
viscera weight    4177 non-null float64
shell weight      4177 non-null float64
rings             4177 non-null int64
dtypes: float64(7), int64(1), object(1)
memory usage: 293.8+ KB

data.describe()

	length	diameter	height	whole weight	shucked weight	viscera weight	shell weight	rings
count	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000	4177.000000
mean	0.523992	0.407881	0.139516	0.828742	0.359367	0.180594	0.238831	9.933684
std	0.120093	0.099240	0.041827	0.490389	0.221963	0.109614	0.139203	3.224169
min	0.075000	0.055000	0.000000	0.002000	0.001000	0.000500	0.001500	1.000000
25%	0.450000	0.350000	0.115000	0.441500	0.186000	0.093500	0.130000	8.000000
50%	0.545000	0.425000	0.140000	0.799500	0.336000	0.171000	0.234000	9.000000
75%	0.615000	0.480000	0.165000	1.153000	0.502000	0.253000	0.329000	11.000000
max	0.815000	0.650000	1.130000	2.825500	1.488000	0.760000	1.005000	29.000000

#观察sex列的取值的分布情况
import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline

sns.countplot(x = "sex",data=data)

data['sex'].value_counts()

M    1528
I    1342
F    1307
Name: sex, dtype: int64

i=1 #子图计数
plt.figure(figsize=(16,8))
for col in data.columns[1:]:
    plt.subplot(4,2,i)
    i = i + 1
    sns.distplot(data[col])
plt.tight_layout()

sns.pairplot(data,hue="sex")

corr_df = data.corr()
corr_df

	length	diameter	height	whole weight	shucked weight	viscera weight	shell weight	rings
length	1.000000	0.986812	0.827554	0.925261	0.897914	0.903018	0.897706	0.556720
diameter	0.986812	1.000000	0.833684	0.925452	0.893162	0.899724	0.905330	0.574660
height	0.827554	0.833684	1.000000	0.819221	0.774972	0.798319	0.817338	0.557467
whole weight	0.925261	0.925452	0.819221	1.000000	0.969405	0.966375	0.955355	0.540390
shucked weight	0.897914	0.893162	0.774972	0.969405	1.000000	0.931961	0.882617	0.420884
viscera weight	0.903018	0.899724	0.798319	0.966375	0.931961	1.000000	0.907656	0.503819
shell weight	0.897706	0.905330	0.817338	0.955355	0.882617	0.907656	1.000000	0.627574
rings	0.556720	0.574660	0.557467	0.540390	0.420884	0.503819	0.627574	1.000000

fig ,ax =plt.subplots(figsize=(12,12))
##绘制热力图
ax = sns.heatmap(corr_df,linewidths=.5,
                cmap="Greens",
                annot=True,
                xticklabels=corr_df.columns,
                yticklabels=corr_df.index)
ax.xaxis.set_label_position('top')
ax.xaxis.tick_top()

鲍鱼数据预处理

对sex特征进行OneHot编码，便于后续模型纳入哑变量

#只用pandas的get_dummies函数对sex特征做OneHot编码处理
sex_onehot = pd.get_dummies(data["sex"],prefix="sex")
data[sex_onehot.columns] = sex_onehot
data.head()

	sex	length	diameter	height	whole weight	shucked weight	viscera weight	shell weight	rings	sex_F	sex_I	sex_M
0	M	0.455	0.365	0.095	0.5140	0.2245	0.1010	0.150	15	0	0	1
1	M	0.350	0.265	0.090	0.2255	0.0995	0.0485	0.070	7	0	0	1
2	F	0.530	0.420	0.135	0.6770	0.2565	0.1415	0.210	9	1	0	0
3	M	0.440	0.365	0.125	0.5160	0.2155	0.1140	0.155	10	0	0	1
4	I	0.330	0.255	0.080	0.2050	0.0895	0.0395	0.055	7	0	1	0

data["ones"]=1
data.head()

	sex	length	diameter	height	whole weight	shucked weight	viscera weight	shell weight	rings	sex_F	sex_I	sex_M	ones
0	M	0.455	0.365	0.095	0.5140	0.2245	0.1010	0.150	15	0	0	1	1
1	M	0.350	0.265	0.090	0.2255	0.0995	0.0485	0.070	7	0	0	1	1
2	F	0.530	0.420	0.135	0.6770	0.2565	0.1415	0.210	9	1	0	0	1
3	M	0.440	0.365	0.125	0.5160	0.2155	0.1140	0.155	10	0	0	1	1
4	I	0.330	0.255	0.080	0.2050	0.0895	0.0395	0.055	7	0	1	0	1

data["age"]=data["rings"] + 1.5
data.head()

	sex	length	diameter	height	whole weight	shucked weight	viscera weight	shell weight	rings	sex_F	sex_I	sex_M	ones	age
0	M	0.455	0.365	0.095	0.5140	0.2245	0.1010	0.150	15	0	0	1	1	16.5
1	M	0.350	0.265	0.090	0.2255	0.0995	0.0485	0.070	7	0	0	1	1	8.5
2	F	0.530	0.420	0.135	0.6770	0.2565	0.1415	0.210	9	1	0	0	1	10.5
3	M	0.440	0.365	0.125	0.5160	0.2155	0.1140	0.155	10	0	0	1	1	11.5
4	I	0.330	0.255	0.080	0.2050	0.0895	0.0395	0.055	7	0	1	0	1	8.5

筛选特征

data.columns

Index(['sex', 'length', 'diameter', 'height', 'whole weight', 'shucked weight',
       'viscera weight', 'shell weight', 'rings', 'sex_F', 'sex_I', 'sex_M',
       'ones', 'age'],
      dtype='object')

y = data["age"] #因变量
features_with_ones = ["length", "diameter", "height", "whole weight", "shucked weight",
       "viscera weight", "shell weight", "sex_F", "sex_M","ones"]
features_without_ones = ["length", "diameter", "height", "whole weight", "shucked weight",
       "viscera weight", "shell weight", "sex_F", "sex_M"]
X=data[features_with_ones]

将鲍鱼数据集划分为训练集和测试集

#拆分训练集和测试集
from sklearn.model_selection import train_test_split

X_train,X_test,y_train,y_test = train_test_split(X,y,test_size=0.2,random_state=111)

X

	length	diameter	height	whole weight	shucked weight	viscera weight	shell weight	sex_F	sex_M	ones
0	0.455	0.365	0.095	0.5140	0.2245	0.1010	0.1500	0	1	1
1	0.350	0.265	0.090	0.2255	0.0995	0.0485	0.0700	0	1	1
2	0.530	0.420	0.135	0.6770	0.2565	0.1415	0.2100	1	0	1
3	0.440	0.365	0.125	0.5160	0.2155	0.1140	0.1550	0	1	1
4	0.330	0.255	0.080	0.2050	0.0895	0.0395	0.0550	0	0	1
5	0.425	0.300	0.095	0.3515	0.1410	0.0775	0.1200	0	0	1
6	0.530	0.415	0.150	0.7775	0.2370	0.1415	0.3300	1	0	1
7	0.545	0.425	0.125	0.7680	0.2940	0.1495	0.2600	1	0	1
8	0.475	0.370	0.125	0.5095	0.2165	0.1125	0.1650	0	1	1
9	0.550	0.440	0.150	0.8945	0.3145	0.1510	0.3200	1	0	1
10	0.525	0.380	0.140	0.6065	0.1940	0.1475	0.2100	1	0	1
11	0.430	0.350	0.110	0.4060	0.1675	0.0810	0.1350	0	1	1
12	0.490	0.380	0.135	0.5415	0.2175	0.0950	0.1900	0	1	1
13	0.535	0.405	0.145	0.6845	0.2725	0.1710	0.2050	1	0	1
14	0.470	0.355	0.100	0.4755	0.1675	0.0805	0.1850	1	0	1
15	0.500	0.400	0.130	0.6645	0.2580	0.1330	0.2400	0	1	1
16	0.355	0.280	0.085	0.2905	0.0950	0.0395	0.1150	0	0	1
17	0.440	0.340	0.100	0.4510	0.1880	0.0870	0.1300	1	0	1
18	0.365	0.295	0.080	0.2555	0.0970	0.0430	0.1000	0	1	1
19	0.450	0.320	0.100	0.3810	0.1705	0.0750	0.1150	0	1	1
20	0.355	0.280	0.095	0.2455	0.0955	0.0620	0.0750	0	1	1
21	0.380	0.275	0.100	0.2255	0.0800	0.0490	0.0850	0	0	1
22	0.565	0.440	0.155	0.9395	0.4275	0.2140	0.2700	1	0	1
23	0.550	0.415	0.135	0.7635	0.3180	0.2100	0.2000	1	0	1
24	0.615	0.480	0.165	1.1615	0.5130	0.3010	0.3050	1	0	1
25	0.560	0.440	0.140	0.9285	0.3825	0.1880	0.3000	1	0	1
26	0.580	0.450	0.185	0.9955	0.3945	0.2720	0.2850	1	0	1
27	0.590	0.445	0.140	0.9310	0.3560	0.2340	0.2800	0	1	1
28	0.605	0.475	0.180	0.9365	0.3940	0.2190	0.2950	0	1	1
29	0.575	0.425	0.140	0.8635	0.3930	0.2270	0.2000	0	1	1
...	...	...	...	...	...	...	...	...	...	...
4147	0.695	0.550	0.195	1.6645	0.7270	0.3600	0.4450	0	1	1
4148	0.770	0.605	0.175	2.0505	0.8005	0.5260	0.3550	0	1	1
4149	0.280	0.215	0.070	0.1240	0.0630	0.0215	0.0300	0	0	1
4150	0.330	0.230	0.080	0.1400	0.0565	0.0365	0.0460	0	0	1
4151	0.350	0.250	0.075	0.1695	0.0835	0.0355	0.0410	0	0	1
4152	0.370	0.280	0.090	0.2180	0.0995	0.0545	0.0615	0	0	1
4153	0.430	0.315	0.115	0.3840	0.1885	0.0715	0.1100	0	0	1
4154	0.435	0.330	0.095	0.3930	0.2190	0.0750	0.0885	0	0	1
4155	0.440	0.350	0.110	0.3805	0.1575	0.0895	0.1150	0	0	1
4156	0.475	0.370	0.110	0.4895	0.2185	0.1070	0.1460	0	1	1
4157	0.475	0.360	0.140	0.5135	0.2410	0.1045	0.1550	0	1	1
4158	0.480	0.355	0.110	0.4495	0.2010	0.0890	0.1400	0	0	1
4159	0.560	0.440	0.135	0.8025	0.3500	0.1615	0.2590	1	0	1
4160	0.585	0.475	0.165	1.0530	0.4580	0.2170	0.3000	1	0	1
4161	0.585	0.455	0.170	0.9945	0.4255	0.2630	0.2845	1	0	1
4162	0.385	0.255	0.100	0.3175	0.1370	0.0680	0.0920	0	1	1
4163	0.390	0.310	0.085	0.3440	0.1810	0.0695	0.0790	0	0	1
4164	0.390	0.290	0.100	0.2845	0.1255	0.0635	0.0810	0	0	1
4165	0.405	0.300	0.085	0.3035	0.1500	0.0505	0.0880	0	0	1
4166	0.475	0.365	0.115	0.4990	0.2320	0.0885	0.1560	0	0	1
4167	0.500	0.380	0.125	0.5770	0.2690	0.1265	0.1535	0	1	1
4168	0.515	0.400	0.125	0.6150	0.2865	0.1230	0.1765	1	0	1
4169	0.520	0.385	0.165	0.7910	0.3750	0.1800	0.1815	0	1	1
4170	0.550	0.430	0.130	0.8395	0.3155	0.1955	0.2405	0	1	1
4171	0.560	0.430	0.155	0.8675	0.4000	0.1720	0.2290	0	1	1
4172	0.565	0.450	0.165	0.8870	0.3700	0.2390	0.2490	1	0	1
4173	0.590	0.440	0.135	0.9660	0.4390	0.2145	0.2605	0	1	1
4174	0.600	0.475	0.205	1.1760	0.5255	0.2875	0.3080	0	1	1
4175	0.625	0.485	0.150	1.0945	0.5310	0.2610	0.2960	1	0	1
4176	0.710	0.555	0.195	1.9485	0.9455	0.3765	0.4950	0	1	1

4177 rows × 10 columns

实现线性回归和岭回归

使用numpy实现线性回归

import numpy as np

def linear_regression(X,y):
    w = np.zeros_like(X.shape[1])
    if np.linalg.det(X.T.dot(X)) != 0:
        w = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)
    return w

#使用上述实现的线性回归模型在鲍鱼训练集上训练模型
w1 = linear_regression(X_train,y_train)

w1 = pd.DataFrame(data = w1,index=X.columns,columns =["numpy_w"])
w1.round(decimals=2)

	numpy_w
length	-1.12
diameter	10.00
height	20.74
whole weight	9.61
shucked weight	-20.05
viscera weight	-12.07
shell weight	6.55
sex_F	0.88
sex_M	0.87
ones	4.32

使用sklearn实现线性回归

from sklearn.linear_model import LinearRegression 
lr = LinearRegression()
lr.fit(X_train[features_without_ones],y_train)
print(lr.coef_)

[ -1.118146    10.00094599  20.73712616   9.61484657 -20.05079291
 -12.06849193   6.54529076   0.87855188   0.87283083]

w1

	numpy_w
length	-1.118146
diameter	10.000946
height	20.737126
whole weight	9.614847
shucked weight	-20.050793
viscera weight	-12.068492
shell weight	6.545291
sex_F	0.878552
sex_M	0.872831
ones	4.324477

w_lr=[]
w_lr.extend(lr.coef_)
w_lr.append(lr.intercept_)
w1["lr_sklearn_w"]=w_lr
w1.round(decimals=2)

	numpy_w	lr_sklearn_w
length	-1.12	-1.12
diameter	10.00	10.00
height	20.74	20.74
whole weight	9.61	9.61
shucked weight	-20.05	-20.05
viscera weight	-12.07	-12.07
shell weight	6.55	6.55
sex_F	0.88	0.88
sex_M	0.87	0.87
ones	4.32	4.32

#做正则化时不包含b lambda I不是真正的系数

使用Numpy实现岭回归

def ridge_regression(X,y,ridge_lambda):
    penalty_matrix = np.eye(X.shape[1])
    penalty_matrix[X.shape[1]-1][X.shape[1]-1] = 0
    w = np.linalg.inv(X.T.dot(X) + ridge_lambda * penalty_matrix).dot(X.T).dot(y)
    return w

在鲍鱼训练集上使用ridge_regression函数训练岭回归模型，正则化系数设置为1

w2 = ridge_regression(X_train,y_train,1.0)
print(w2)

[  2.30976528   6.72038628  10.23298909   7.05879189 -17.16249532
  -7.2343118    9.3936994    0.96869974   0.9422174    4.80583032]

w1["numpy_ridge_w"] = w2
w1.round(decimals=2)

	numpy_w	lr_sklearn_w	numpy_ridge_w
length	-1.12	-1.12	2.31
diameter	10.00	10.00	6.72
height	20.74	20.74	10.23
whole weight	9.61	9.61	7.06
shucked weight	-20.05	-20.05	-17.16
viscera weight	-12.07	-12.07	-7.23
shell weight	6.55	6.55	9.39
sex_F	0.88	0.88	0.97
sex_M	0.87	0.87	0.94
ones	4.32	4.32	4.81

利用sklearn实现岭回归

与sklearn中岭回归对比，同样正则化叙述设置为1

from sklearn.linear_model import Ridge
ridge = Ridge(alpha=1.0)
ridge.fit(X_train[features_without_ones],y_train)
w_ridge = []
w_ridge.extend(ridge.coef_)
w_ridge.append(ridge.intercept_)
w1["ridge_sklearn_w"] = w_ridge
w1.round(decimals=2)

	numpy_w	lr_sklearn_w	numpy_ridge_w	ridge_sklearn_w
length	-1.12	-1.12	2.31	2.31
diameter	10.00	10.00	6.72	6.72
height	20.74	20.74	10.23	10.23
whole weight	9.61	9.61	7.06	7.06
shucked weight	-20.05	-20.05	-17.16	-17.16
viscera weight	-12.07	-12.07	-7.23	-7.23
shell weight	6.55	6.55	9.39	9.39
sex_F	0.88	0.88	0.97	0.97
sex_M	0.87	0.87	0.94	0.94
ones	4.32	4.32	4.81	4.81

岭迹分析

alphas = np.logspace(-10,10,20)
coef = pd.DataFrame()
for alpha in alphas:
    ridge_clf = Ridge(alpha=alpha)
    ridge_clf.fit(X_train[features_without_ones],y_train)
    df = pd.DataFrame([ridge_clf.coef_],columns=X_train[features_without_ones].columns)
    df['alpha']=alpha
    coef =coef.append(df,ignore_index=True)
coef.round(decimals=2)

	length	diameter	height	whole weight	shucked weight	viscera weight	shell weight	sex_F	sex_M	alpha
0	-1.12	10.00	20.74	9.61	-20.05	-12.07	6.55	0.88	0.87	0.000000e+00
1	-1.12	10.00	20.74	9.61	-20.05	-12.07	6.55	0.88	0.87	0.000000e+00
2	-1.12	10.00	20.74	9.61	-20.05	-12.07	6.55	0.88	0.87	0.000000e+00
3	-1.12	10.00	20.74	9.61	-20.05	-12.07	6.55	0.88	0.87	0.000000e+00
4	-1.12	10.00	20.74	9.61	-20.05	-12.07	6.55	0.88	0.87	0.000000e+00
5	-1.12	10.00	20.74	9.61	-20.05	-12.07	6.55	0.88	0.87	0.000000e+00
6	-1.12	10.00	20.73	9.61	-20.05	-12.07	6.55	0.88	0.87	0.000000e+00
7	-1.10	9.98	20.68	9.60	-20.04	-12.05	6.56	0.88	0.87	0.000000e+00
8	-0.88	9.79	20.13	9.50	-19.94	-11.86	6.71	0.88	0.88	3.000000e-02
9	0.73	8.33	15.60	8.55	-18.97	-10.05	7.98	0.92	0.90	3.000000e-01
10	3.20	5.02	5.40	5.11	-13.71	-3.67	9.61	1.07	1.00	3.360000e+00
11	1.66	1.76	1.12	2.53	-3.54	-0.09	3.67	1.33	1.11	3.793000e+01
12	0.51	0.47	0.22	1.63	0.18	0.30	0.79	0.89	0.69	4.281300e+02
13	0.12	0.10	0.04	0.46	0.15	0.09	0.16	0.21	0.16	4.832930e+03
14	0.01	0.01	0.00	0.05	0.02	0.01	0.02	0.02	0.02	5.455595e+04
15	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	6.158482e+05
16	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	6.951928e+06
17	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	7.847600e+07
18	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	8.858668e+08
19	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	1.000000e+10

plt.rcParams['figure.dpi'] = 300#分辨率
plt.figure(figsize=(9,6))
coef['alpha']=coef['alpha']

for feature in X_train.columns[:-1]:
    plt.plot('alpha',feature,data=coef)
ax = plt.gca()
ax.set_xscale('log')
plt.legend(loc='upper right')
plt.xlabel(r'$\alpha$',fontsize=15)
plt.ylabel('系数',fontsize=15)

Text(0, 0.5, '系数')



Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U+2212], substituting with a dummy symbol.

使用LASSO构建鲍鱼年龄预测模型

from sklearn.linear_model import Lasso
lasso = Lasso(alpha=0.01)
lasso.fit(X_train[features_without_ones],y_train)
print(lasso.coef_)
print(lasso.intercept_)

[  0.           6.37435514   0.           4.46703234 -13.44947667
  -0.          11.85934842   0.98908791   0.93313403]
6.500338023591298

LASSO的正则化路径

coef = pd.DataFrame()
for alpha in np.linspace(0.0001,0.2,20):
    lasso_clf = Lasso(alpha=alpha)
    lasso_clf.fit(X_train[features_without_ones],y_train)
    df = pd.DataFrame([lasso_clf.coef_],columns=X_train[features_without_ones].columns)
    df['alpha']=alpha
    coef = coef.append(df,ignore_index=True)
coef.head()
#绘图
plt.figure(figsize=(9,6),dpi=600)
for feature in X_train.columns[:-1]:
    plt.plot('alpha',feature,data=coef)
plt.legend(loc='upper right')
plt.xlabel(r'$\alpha$',fontsize=15)
plt.ylabel('系数',fontsize=15)
plt.show()

coef

	length	diameter	height	whole weight	shucked weight	viscera weight	shell weight	sex_F	sex_M	alpha
0	-0.568043	9.39275	20.390041	9.542038	-19.995972	-11.900326	6.635352	0.881496	0.875132	0.000100
1	0.000000	6.02573	0.000000	4.375754	-13.127223	-0.000000	11.897189	0.995137	0.934129	0.010621
2	0.384927	0.00000	0.000000	2.797815	-7.702209	-0.000000	12.478541	1.093479	0.948281	0.021142
3	0.000000	0.00000	0.000000	0.884778	-2.749504	0.000000	11.705974	1.098990	0.897673	0.031663
4	0.000000	0.00000	0.000000	0.322742	-0.000000	0.000000	9.225919	1.072991	0.834021	0.042184
5	0.000000	0.00000	0.000000	1.555502	-0.000000	0.000000	4.610425	1.013824	0.757891	0.052705
6	0.000000	0.00000	0.000000	2.786784	-0.000000	0.000000	0.000000	0.954710	0.681821	0.063226
7	0.000000	0.00000	0.000000	2.797514	-0.000000	0.000000	0.000000	0.848412	0.581613	0.073747
8	0.000000	0.00000	0.000000	2.807843	-0.000000	0.000000	0.000000	0.742529	0.481711	0.084268
9	0.000000	0.00000	0.000000	2.818184	-0.000000	0.000000	0.000000	0.636632	0.381799	0.094789
10	0.000000	0.00000	0.000000	2.828630	-0.000000	0.000000	0.000000	0.530615	0.281801	0.105311
11	0.000000	0.00000	0.000000	2.838944	-0.000000	0.000000	0.000000	0.424750	0.181912	0.115832
12	0.000000	0.00000	0.000000	2.849325	-0.000000	0.000000	0.000000	0.318807	0.081967	0.126353
13	0.000000	0.00000	0.000000	2.851851	-0.000000	0.000000	0.000000	0.225024	0.000000	0.136874
14	0.000000	0.00000	0.000000	2.819079	-0.000000	0.000000	0.000000	0.186157	0.000000	0.147395
15	0.000000	0.00000	0.000000	2.786307	-0.000000	0.000000	0.000000	0.147290	0.000000	0.157916
16	0.000000	0.00000	0.000000	2.753535	0.000000	0.000000	0.000000	0.108422	0.000000	0.168437
17	0.000000	0.00000	0.000000	2.720762	0.000000	0.000000	0.000000	0.069555	0.000000	0.178958
18	0.000000	0.00000	0.000000	2.687990	0.000000	0.000000	0.000000	0.030688	0.000000	0.189479
19	0.000000	0.00000	0.000000	2.652940	0.000000	0.000000	0.000000	0.000000	0.000000	0.200000

from sklearn.metrics import mean_squared_error
from sklearn.metrics import mean_absolute_error
from sklearn.metrics import r2_score

#MAE
y_test_pred_lr = lr.predict(X_test.iloc[:,:-1])
print(round(mean_absolute_error(y_test,y_test_pred_lr),4))

1.6016

y_test_pred_ridge = ridge.predict(X_test[features_without_ones])
print(round(mean_absolute_error(y_test,y_test_pred_ridge),4))

1.5984

y_test_pred_lasso = lasso.predict(X_test[features_without_ones])
print(round(mean_absolute_error(y_test,y_test_pred_lasso),4))

1.6402

#MSE
y_test_pred_lr = lr.predict(X_test.iloc[:,:-1])
print(round(mean_squared_error(y_test,y_test_pred_lr),4))

5.3009

y_test_pred_ridge = ridge.predict(X_test[features_without_ones])
print(round(mean_squared_error(y_test,y_test_pred_ridge),4))

4.959

y_test_pred_lasso = lasso.predict(X_test[features_without_ones])
print(round(mean_squared_error(y_test,y_test_pred_lasso),4))

5.1

#R2系数
print(round(r2_score(y_test,y_test_pred_lr),4))
print(round(r2_score(y_test,y_test_pred_ridge),4))
print(round(r2_score(y_test,y_test_pred_lasso),4))

0.5257
0.5563
0.5437

残差图

plt.figure(figsize=(9,6),dpi=600)
y_train_pred_ridge = ridge.predict(X_train[features_without_ones])
plt.scatter(y_train_pred_ridge,y_train_pred_ridge - y_train,c="g",alpha=0.6)
plt.scatter(y_test_pred_ridge,y_test_pred_ridge - y_test,c="r",alpha=0.6)
plt.hlines(y=0,xmin=0,xmax=30,color="b",alpha=0.6)
plt.ylabel("Residuals")
plt.xlabel("Predict")

Text(0.5, 0, 'Predict')