beyond Linearity

In [1]:

    

import pandas as pd
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
import statsmodels.api as sm
from sklearn.linear_model import LinearRegression,LogisticRegression
from sklearn.feature_selection import SelectKBest,f_regression
from sklearn.metrics import mean_squared_error
%matplotlib inline


    

In [2]:

    

# 读取数据
wage_df = pd.read_csv('data/Wage.csv')
wage_df.head()


    

    
Out[2]:






  

    

      

      
year
      
age
      
sex
      
maritl
      
race
      
education
      
region
      
jobclass
      
health
      
health_ins
      
logwage
      
wage
    
  
  

    

      
0
      
2006
      
18
      
1. Male
      
1. Never Married
      
1. White
      
1. < HS Grad
      
2. Middle Atlantic
      
1. Industrial
      
1. <=Good
      
2. No
      
4.318063
      
75.043154
    
    

      
1
      
2004
      
24
      
1. Male
      
1. Never Married
      
1. White
      
4. College Grad
      
2. Middle Atlantic
      
2. Information
      
2. >=Very Good
      
2. No
      
4.255273
      
70.476020
    
    

      
2
      
2003
      
45
      
1. Male
      
2. Married
      
1. White
      
3. Some College
      
2. Middle Atlantic
      
1. Industrial
      
1. <=Good
      
1. Yes
      
4.875061
      
130.982177
    
    

      
3
      
2003
      
43
      
1. Male
      
2. Married
      
3. Asian
      
4. College Grad
      
2. Middle Atlantic
      
2. Information
      
2. >=Very Good
      
1. Yes
      
5.041393
      
154.685293
    
    

      
4
      
2005
      
50
      
1. Male
      
4. Divorced
      
1. White
      
2. HS Grad
      
2. Middle Atlantic
      
2. Information
      
1. <=Good
      
1. Yes
      
4.318063
      
75.043154
    
  

In [4]:

    

from sklearn.preprocessing import PolynomialFeatures


    

In [21]:

    

X = wage_df[['age']].values
y = wage_df['wage']
#将特征换为多项式
poly = PolynomialFeatures(degree=4)
X_degree4 = poly.fit_transform(X)


    

In [23]:

    

ols = sm.OLS(y,X_degree4).fit()
ols.summary()


    

    
Out[23]:





OLS Regression Results

  
Dep. Variable:
          
wage
       
  R-squared:         
 
   0.086
 


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.085
 


  
Method:
             
Least Squares
  
  F-statistic:       
 
   70.69
 


  
Date:
             
Tue, 15 Sep 2015
 
  Prob (F-statistic):
 
2.77e-57
 


  
Time:
                 
15:17:59
     
  Log-Likelihood:    
 
 -15315.
 


  
No. Observations:
      
  3000
      
  AIC:               
 
3.064e+04


  
Df Residuals:
          
  2995
      
  BIC:               
 
3.067e+04


  
Df Model:
              
     4
      
                     
     
 
    


  
Covariance Type:
      
nonrobust
    
                     
     
 
    




    
       
coef
     
std err
      
t
      
P>|t|
 
[95.0% Conf. Int.]
 


  
const
 
 -184.1542
 
   60.040
 
   -3.067
 
 0.002
 
 -301.879   -66.430


  
x1
    
   21.2455
 
    5.887
 
    3.609
 
 0.000
 
    9.703    32.788


  
x2
    
   -0.5639
 
    0.206
 
   -2.736
 
 0.006
 
   -0.968    -0.160


  
x3
    
    0.0068
 
    0.003
 
    2.221
 
 0.026
 
    0.001     0.013


  
x4
    
-3.204e-05
 
 1.64e-05
 
   -1.952
 
 0.051
 
-6.42e-05  1.45e-07




  
Omnibus:
       
1097.594
 
  Durbin-Watson:     
 
   1.960


  
Prob(Omnibus):
  
 0.000
  
  Jarque-Bera (JB):  
 
4965.521


  
Skew:
           
 1.722
  
  Prob(JB):          
 
    0.00


  
Kurtosis:
       
 8.279
  
  Cond. No.          
 
5.67e+08

In [41]:

    

#图形显示拟合的形状
fig,ax = plt.subplots()
ax.scatter(x = X,y=y)
ax.set_xlabel('age')
ax.set_ylabel('wage')
xs = range(int(np.min(X[:,0])),int(np.max(X[:,0])))
xs_degree4 = [poly.fit_transform(x) for x in xs]
ys = [ols.predict(x)[0] for x in xs_degree4]
ax.plot(xs,ys,'r',linewidth=2.5)


    

    
Out[41]:





[<matplotlib.lines.Line2D at 0xdf4f470>]






    

In [49]:

    

from scipy.interpolate import LSQUnivariateSpline


    

In [52]:

    

x = wage_df['age'].values
y = wage_df['wage'].values
x = [i for (i,j) in sorted(zip(x,y))]
y = [j for (i,j) in sorted(zip(x,y))]
t=[20,40,60]
sql = LSQUnivariateSpline(x,y,t)


    

In [53]:

    

fig,ax = plt.subplots()
ax.scatter(x,y)
ax.set_xlabel('age')
ax.set_ylabel('wage')

xs = np.linspace(x[0],x[-1])
ax.plot(xs,sql(xs),'g-',lw=3,)


    

    
Out[53]:





[<matplotlib.lines.Line2D at 0xacefe10>]






    

In [ ]: