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/x11.txt'
response = requests.get(URL)
text = response.text


    

In [3]:

    

columns = ['Index',
'Rent per arable acre',
'Milk cows per square mile',
'Difference between pasture and arable land',
'Rental price per grassy acre']
columns = [c.lower().replace(' ', '_') for c in columns]


    

In [7]:

    

lines = [line.strip() for line in text.split('\n') if not line.strip().startswith('#')]


    

In [14]:

    

data = lines[7:-2]
data = [row.split() for row in data]
data_df = pd.DataFrame(data=data, columns=columns).drop('index', axis=1).astype(np.float)


    

In [15]:

    

data_df.head()


    

    
Out[15]:






  

    

      

      
rent_per_arable_acre
      
milk_cows_per_square_mile
      
difference_between_pasture_and_arable_land
      
rental_price_per_grassy_acre
    
  
  

    

      
0
      
15.50
      
17.25
      
0.24
      
18.38
    
    

      
1
      
22.29
      
18.51
      
0.20
      
20.00
    
    

      
2
      
12.36
      
11.13
      
0.12
      
11.50
    
    

      
3
      
31.84
      
5.54
      
0.12
      
25.00
    
    

      
4
      
83.90
      
5.44
      
0.04
      
62.50
    
  

In [16]:

    

data_df.corr()


    

    
Out[16]:






  

    

      

      
rent_per_arable_acre
      
milk_cows_per_square_mile
      
difference_between_pasture_and_arable_land
      
rental_price_per_grassy_acre
    
  
  

    

      
rent_per_arable_acre
      
1.000000
      
0.045504
      
-0.497893
      
0.885082
    
    

      
milk_cows_per_square_mile
      
0.045504
      
1.000000
      
0.522598
      
0.303392
    
    

      
difference_between_pasture_and_arable_land
      
-0.497893
      
0.522598
      
1.000000
      
-0.330177
    
    

      
rental_price_per_grassy_acre
      
0.885082
      
0.303392
      
-0.330177
      
1.000000
    
  

In [18]:

    

data_df.plot(kind='scatter', x='rent_per_arable_acre', y='rental_price_per_grassy_acre')


    

    
Out[18]:





<matplotlib.axes._subplots.AxesSubplot at 0x21495796780>






    

In [19]:

    

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


    

    
Out[19]:





OLS Regression Results

  
Dep. Variable:
    
rental_price_per_grassy_acre
 
  R-squared:         
 
   0.783


  
Model:
                         
OLS
             
  Adj. R-squared:    
 
   0.780


  
Method:
                   
Least Squares
        
  F-statistic:       
 
   235.1


  
Date:
                   
Thu, 30 Mar 2017
       
  Prob (F-statistic):
 
2.86e-23


  
Time:
                       
22:35:51
           
  Log-Likelihood:    
 
 -252.88


  
No. Observations:
            
    67
            
  AIC:               
 
   509.8


  
Df Residuals:
                
    65
            
  BIC:               
 
   514.2


  
Df Model:
                    
     1
            
                     
     
 
   


  
Covariance Type:
            
nonrobust
          
                     
     
 
   




            
              
coef
     
std err
      
t
      
P>|t|
  
[0.025
    
0.975]
  


  
Intercept
            
    0.8915
 
    3.011
 
    0.296
 
 0.768
 
   -5.121
 
    6.904


  
rent_per_arable_acre
 
    0.9494
 
    0.062
 
   15.331
 
 0.000
 
    0.826
 
    1.073




  
Omnibus:
       
 3.592
 
  Durbin-Watson:     
 
   2.363


  
Prob(Omnibus):
 
 0.166
 
  Jarque-Bera (JB):  
 
   2.722


  
Skew:
          
 0.440
 
  Prob(JB):          
 
   0.256


  
Kurtosis:
      
 3.447
 
  Cond. No.          
 
    112.

In [20]:

    

import statsmodels.formula.api as sm
result = sm.ols(formula='rental_price_per_grassy_acre ~ rent_per_arable_acre + difference_between_pasture_and_arable_land', data=data_df).fit()
result.summary()


    

    
Out[20]:





OLS Regression Results

  
Dep. Variable:
    
rental_price_per_grassy_acre
 
  R-squared:         
 
   0.800


  
Model:
                         
OLS
             
  Adj. R-squared:    
 
   0.793


  
Method:
                   
Least Squares
        
  F-statistic:       
 
   127.7


  
Date:
                   
Thu, 30 Mar 2017
       
  Prob (F-statistic):
 
4.57e-23


  
Time:
                       
22:36:50
           
  Log-Likelihood:    
 
 -250.27


  
No. Observations:
            
    67
            
  AIC:               
 
   506.5


  
Df Residuals:
                
    64
            
  BIC:               
 
   513.2


  
Df Model:
                    
     2
            
                     
     
 
   


  
Covariance Type:
            
nonrobust
          
                     
     
 
   




                       
                         
coef
     
std err
      
t
      
P>|t|
  
[0.025
    
0.975]
  


  
Intercept
                                  
   -6.4823
 
    4.359
 
   -1.487
 
 0.142
 
  -15.191
 
    2.226


  
rent_per_arable_acre
                       
    1.0279
 
    0.069
 
   14.851
 
 0.000
 
    0.890
 
    1.166


  
difference_between_pasture_and_arable_land
 
   23.2037
 
   10.190
 
    2.277
 
 0.026
 
    2.846
 
   43.561




  
Omnibus:
       
 3.721
 
  Durbin-Watson:     
 
   2.307


  
Prob(Omnibus):
 
 0.156
 
  Jarque-Bera (JB):  
 
   2.834


  
Skew:
          
 0.413
 
  Prob(JB):          
 
   0.242


  
Kurtosis:
      
 3.577
 
  Cond. No.          
 
    412.

In [ ]: