In [1]:

    

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


    

    




Populating the interactive namespace from numpy and matplotlib

In [2]:

    

import requests
URL = 'http://people.sc.fsu.edu/~jburkardt/datasets/regression/x03.txt'
response = requests.get(URL)
text = response.text


    

In [6]:

    

columns = ['Index', 'One', 'Age', 'Systolic Blood Pressure']


    

In [10]:

    

lines = [line.strip() for line in text.split('\n') if not line.strip().startswith('#')]
data = lines[6:-2]
data = np.array([row.split() for row in data], dtype=np.float)
data[:, 1] = data[:, 1].astype(np.int)


    

In [12]:

    

data_df = pd.DataFrame(data=data, columns=columns)
data_df = data_df.rename(columns={name: name.lower().replace(' ', '_') for name in data_df.keys()})


    

In [14]:

    

data_pressure = data_df[['age', 'systolic_blood_pressure']]


    

In [15]:

    

data_pressure.plot(kind='scatter', x='age', y='systolic_blood_pressure')


    

    
Out[15]:





<matplotlib.axes._subplots.AxesSubplot at 0x26c1b0aa400>






    

In [17]:

    

import statsmodels.formula.api as sm
result = sm.ols(formula='systolic_blood_pressure ~ age', data=data_df).fit()
result.summary()


    

    
Out[17]:





OLS Regression Results

  
Dep. Variable:
    
systolic_blood_pressure
 
  R-squared:         
 
   0.394


  
Model:
                      
OLS
           
  Adj. R-squared:    
 
   0.372


  
Method:
                
Least Squares
      
  F-statistic:       
 
   17.58


  
Date:
                
Thu, 30 Mar 2017
     
  Prob (F-statistic):
 
0.000265


  
Time:
                    
21:20:47
         
  Log-Likelihood:    
 
 -123.16


  
No. Observations:
         
    29
          
  AIC:               
 
   250.3


  
Df Residuals:
             
    27
          
  BIC:               
 
   253.1


  
Df Model:
                 
     1
          
                     
     
 
   


  
Covariance Type:
         
nonrobust
        
                     
     
 
   




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


  
Intercept
 
  100.0359
 
   10.391
 
    9.627
 
 0.000
 
   78.714   121.357


  
age
       
    0.9338
 
    0.223
 
    4.193
 
 0.000
 
    0.477     1.391




  
Omnibus:
       
44.232
 
  Durbin-Watson:     
 
   1.712


  
Prob(Omnibus):
 
 0.000
 
  Jarque-Bera (JB):  
 
 199.817


  
Skew:
          
 2.981
 
  Prob(JB):          
 
4.08e-44


  
Kurtosis:
      
14.394
 
  Cond. No.          
 
    149.

In [27]:

    

without_outliers = data_pressure.sort_values(by='systolic_blood_pressure', ascending=False).iloc[1:]


    

In [28]:

    

without_outliers.plot(kind='scatter', x='age', y='systolic_blood_pressure')


    

    
Out[28]:





<matplotlib.axes._subplots.AxesSubplot at 0x26c1c0a1c50>






    

In [29]:

    

result = sm.ols(formula='systolic_blood_pressure ~ age', data=without_outliers).fit()
result.summary()


    

    
Out[29]:





OLS Regression Results

  
Dep. Variable:
    
systolic_blood_pressure
 
  R-squared:         
 
   0.686


  
Model:
                      
OLS
           
  Adj. R-squared:    
 
   0.674


  
Method:
                
Least Squares
      
  F-statistic:       
 
   56.74


  
Date:
                
Thu, 30 Mar 2017
     
  Prob (F-statistic):
 
5.37e-08


  
Time:
                    
21:37:36
         
  Log-Likelihood:    
 
 -101.41


  
No. Observations:
         
    28
          
  AIC:               
 
   206.8


  
Df Residuals:
             
    26
          
  BIC:               
 
   209.5


  
Df Model:
                 
     1
          
                     
     
 
   


  
Covariance Type:
         
nonrobust
        
                     
     
 
   




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


  
Intercept
 
   98.8335
 
    5.571
 
   17.741
 
 0.000
 
   87.382   110.285


  
age
       
    0.8996
 
    0.119
 
    7.532
 
 0.000
 
    0.654     1.145




  
Omnibus:
       
 0.199
 
  Durbin-Watson:     
 
   1.478


  
Prob(Omnibus):
 
 0.905
 
  Jarque-Bera (JB):  
 
   0.094


  
Skew:
          
-0.122
 
  Prob(JB):          
 
   0.954


  
Kurtosis:
      
 2.852
 
  Cond. No.          
 
    146.

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