Logistic Regression

In [3]:

    

%pylab inline
pylab.style.use('ggplot')
import pandas as pd
import numpy as np


    

    




Populating the interactive namespace from numpy and matplotlib

In [4]:

    

import requests
url = 'http://www.ats.ucla.edu/stat/data/binary.csv'
response = requests.get(url)
response.status_code


    

    
Out[4]:





200

In [6]:

    

from io import StringIO
data = pd.read_csv(StringIO(response.text))


    

In [7]:

    

data.head()


    

    
Out[7]:






  

    

      

      
admit
      
gre
      
gpa
      
rank
    
  
  

    

      
0
      
0
      
380
      
3.61
      
3
    
    

      
1
      
1
      
660
      
3.67
      
3
    
    

      
2
      
1
      
800
      
4.00
      
1
    
    

      
3
      
1
      
640
      
3.19
      
4
    
    

      
4
      
0
      
520
      
2.93
      
4
    
  

In [15]:

    

data.admit.groupby(data.admit).count()


    

    
Out[15]:





admit
0    273
1    127
Name: admit, dtype: int64

In [34]:

    

data['admit'].groupby(data['rank']).value_counts()


    

    
Out[34]:





rank  admit
1     1        33
      0        28
2     0        97
      1        54
3     0        93
      1        28
4     0        55
      1        12
Name: admit, dtype: int64

In [16]:

    

data.drop('rank', axis=1).corr()


    

    
Out[16]:






  

    

      

      
admit
      
gre
      
gpa
    
  
  

    

      
admit
      
1.000000
      
0.184434
      
0.178212
    
    

      
gre
      
0.184434
      
1.000000
      
0.384266
    
    

      
gpa
      
0.178212
      
0.384266
      
1.000000
    
  

In [17]:

    

data.plot(kind='scatter', x='admit', y='gre')


    

    
Out[17]:





<matplotlib.axes._subplots.AxesSubplot at 0x1e9203e0cf8>






    

In [18]:

    

data.plot(kind='scatter', x='admit', y='gpa')


    

    
Out[18]:





<matplotlib.axes._subplots.AxesSubplot at 0x1e920460080>






    

In [55]:

    

import statsmodels.formula.api as sm

model = sm.logit(formula='admit ~ gpa + C(rank)', data=data)
result = model.fit()
result.summary()


    

    




Optimization terminated successfully.
         Current function value: 0.578594
         Iterations 6






    
Out[55]:





Logit Regression Results

  
Dep. Variable:
       
admit
      
  No. Observations:  
  
   400
  


  
Model:
               
Logit
      
  Df Residuals:      
  
   395
  


  
Method:
               
MLE
       
  Df Model:          
  
     4
  


  
Date:
          
Mon, 03 Apr 2017
 
  Pseudo R-squ.:     
  
0.07421
 


  
Time:
              
21:37:30
     
  Log-Likelihood:    
 
 -231.44
 


  
converged:
           
True
       
  LL-Null:           
 
 -249.99
 


  
 
                      
 
        
  LLR p-value:       
 
1.717e-07




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


  
Intercept
    
   -3.4636
 
    1.100
 
   -3.148
 
 0.002
 
   -5.620    -1.307


  
C(rank)[T.2]
 
   -0.6810
 
    0.314
 
   -2.168
 
 0.030
 
   -1.297    -0.065


  
C(rank)[T.3]
 
   -1.3919
 
    0.342
 
   -4.071
 
 0.000
 
   -2.062    -0.722


  
C(rank)[T.4]
 
   -1.5943
 
    0.415
 
   -3.840
 
 0.000
 
   -2.408    -0.780


  
gpa
          
    1.0521
 
    0.310
 
    3.392
 
 0.001
 
    0.444     1.660

In [58]:

    

from statsmodels.api import add_constant
predicted_probs = result.predict(data.drop('admit', axis=1))
predicted_ranks = np.where(predicted_probs > 0.5, 1, 0)

from sklearn.metrics import confusion_matrix

conf_matrix = confusion_matrix(y_true=data['admit'], y_pred=predicted_ranks)
print(conf_matrix)
conf_df = pd.DataFrame(data=conf_matrix, columns=['rejected', 'accepted'], index=['rejected', 'accepted'])

import seaborn as sns
sns.heatmap(conf_df, annot=True)
pylab.xlabel('true label')
pylab.ylabel('predicted label')


    

    




[[256  17]
 [ 93  34]]






    
Out[58]:





<matplotlib.text.Text at 0x1e923c53e48>






    

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