Paper Run Regression

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 [13]:

    

import requests
URL = 'http://people.sc.fsu.edu/~jburkardt/datasets/regression/x04.txt'
response = requests.get(URL)
text = response.text


    

In [32]:

    

columns = ['Index', 'Print Runs', 'Page Numbers', 'Orders']


    

In [40]:

    

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[:, 0] = data[:, 0].astype(np.int)
data_df = pd.DataFrame(data, columns=columns)
data_df = data_df.rename(columns={name: name.lower().replace(' ', '_') for name in data_df.keys()})
data_df = data_df.drop('index', axis=1)


    

In [43]:

    

data_df.head()


    

    
Out[43]:






  

    

      

      
print_runs
      
page_numbers
      
orders
    
  
  

    

      
0
      
2800.0
      
22.0
      
437.0
    
    

      
1
      
2670.0
      
14.0
      
204.0
    
    

      
2
      
2800.0
      
37.0
      
725.0
    
    

      
3
      
2784.0
      
15.0
      
279.0
    
    

      
4
      
2800.0
      
38.0
      
474.0
    
  

In [42]:

    

data_df.corr()


    

    
Out[42]:






  

    

      

      
print_runs
      
page_numbers
      
orders
    
  
  

    

      
print_runs
      
1.000000
      
0.403569
      
0.555822
    
    

      
page_numbers
      
0.403569
      
1.000000
      
0.946250
    
    

      
orders
      
0.555822
      
0.946250
      
1.000000
    
  

In [44]:

    

data_df.plot(kind='scatter', x='page_numbers', y='orders')


    

    
Out[44]:





<matplotlib.axes._subplots.AxesSubplot at 0x12aa3e19b00>






    

In [46]:

    

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


    

    
Out[46]:





OLS Regression Results

  
Dep. Variable:
         
orders
      
  R-squared:         
 
   0.895


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.892


  
Method:
             
Least Squares
  
  F-statistic:       
 
   308.1


  
Date:
             
Thu, 30 Mar 2017
 
  Prob (F-statistic):
 
3.13e-19


  
Time:
                 
22:06:42
     
  Log-Likelihood:    
 
 -258.16


  
No. Observations:
      
    38
      
  AIC:               
 
   520.3


  
Df Residuals:
          
    36
      
  BIC:               
 
   523.6


  
Df Model:
              
     1
      
                     
     
 
   


  
Covariance Type:
      
nonrobust
    
                     
     
 
   




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


  
Intercept
    
  -76.0962
 
   59.571
 
   -1.277
 
 0.210
 
 -196.912
 
   44.719


  
page_numbers
 
   11.2620
 
    0.642
 
   17.554
 
 0.000
 
    9.961
 
   12.563




  
Omnibus:
       
 1.714
 
  Durbin-Watson:     
 
   1.196


  
Prob(Omnibus):
 
 0.424
 
  Jarque-Bera (JB):  
 
   1.630


  
Skew:
          
 0.450
 
  Prob(JB):          
 
   0.443


  
Kurtosis:
      
 2.529
 
  Cond. No.          
 
    154.

In [47]:

    

import statsmodels.formula.api as sm
result = sm.ols(formula='orders ~ page_numbers + print_runs', data=data_df).fit()
result.summary()


    

    
Out[47]:





OLS Regression Results

  
Dep. Variable:
         
orders
      
  R-squared:         
 
   0.932


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.928


  
Method:
             
Least Squares
  
  F-statistic:       
 
   238.1


  
Date:
             
Thu, 30 Mar 2017
 
  Prob (F-statistic):
 
4.18e-21


  
Time:
                 
22:07:41
     
  Log-Likelihood:    
 
 -250.11


  
No. Observations:
      
    38
      
  AIC:               
 
   506.2


  
Df Residuals:
          
    35
      
  BIC:               
 
   511.1


  
Df Model:
              
     2
      
                     
     
 
   


  
Covariance Type:
      
nonrobust
    
                     
     
 
   




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


  
Intercept
    
 -364.8455
 
   83.076
 
   -4.392
 
 0.000
 
 -533.499
 
 -196.192


  
page_numbers
 
   10.2639
 
    0.575
 
   17.840
 
 0.000
 
    9.096
 
   11.432


  
print_runs
   
    0.1833
 
    0.043
 
    4.298
 
 0.000
 
    0.097
 
    0.270




  
Omnibus:
       
 1.161
 
  Durbin-Watson:     
 
   1.514


  
Prob(Omnibus):
 
 0.560
 
  Jarque-Bera (JB):  
 
   0.547


  
Skew:
          
 0.279
 
  Prob(JB):          
 
   0.761


  
Kurtosis:
      
 3.188
 
  Cond. No.          
 
5.96e+03

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