In [1]:

    

%matplotlib inline
import numpy as np
import scipy.stats as stats
import pandas as pd
import matplotlib.pyplot as plt
import statsmodels.formula.api as smf
import seaborn as sns


    

In [2]:

    

b0 = 0.5
b1 = 0.1
# from 1 to 100 in 1000 increments
x = np.linspace(1, 100, 1000)
# select a random subset of x values
x = np.random.choice(x, 100, replace=True)
# generate noise from a normal distribution
noise1 = stats.norm.rvs(loc=0.0, scale=10.0, size=len(x))
noise2 = stats.norm.rvs(loc=0.0, scale=1.0, size=len(x))
y1 = b0 + b1*x + noise1
y2 = b0 + b1*x + noise2
df = pd.DataFrame({'x': x, 'y1': y1, 'y2': y2})


    

In [3]:

    

sns.jointplot('x', 'y1', data=df, kind='reg', xlim=(-5, 105), color="r", size=7)


    

    
Out[3]:





<seaborn.axisgrid.JointGrid at 0x10cd74e80>






    

In [4]:

    

model = smf.ols(formula='y1 ~ x', data=df).fit()
model.summary()


    

    
Out[4]:





OLS Regression Results

  
Dep. Variable:
           
y1
        
  R-squared:         
 
   0.044


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.034


  
Method:
             
Least Squares
  
  F-statistic:       
 
   4.497


  
Date:
             
Sat, 06 May 2017
 
  Prob (F-statistic):
  
0.0365
 


  
Time:
                 
10:41:13
     
  Log-Likelihood:    
 
 -371.18


  
No. Observations:
      
   100
      
  AIC:               
 
   746.4


  
Df Residuals:
          
    98
      
  BIC:               
 
   751.6


  
Df Model:
              
     1
      
                     
     
 
   


  
Covariance Type:
      
nonrobust
    
                     
     
 
   




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


  
Intercept
 
    2.3566
 
    2.050
 
    1.150
 
 0.253
 
   -1.712
 
    6.425


  
x
         
    0.0738
 
    0.035
 
    2.121
 
 0.036
 
    0.005
 
    0.143




  
Omnibus:
       
 4.639
 
  Durbin-Watson:     
 
   1.885


  
Prob(Omnibus):
 
 0.098
 
  Jarque-Bera (JB):  
 
   4.475


  
Skew:
          
-0.518
 
  Prob(JB):          
 
   0.107


  
Kurtosis:
      
 2.956
 
  Cond. No.          
 
    121.

In [5]:

    

sns.jointplot('x', 'y2', data=df, kind='reg', xlim=(-5, 105), size=7)


    

    
Out[5]:





<seaborn.axisgrid.JointGrid at 0x12036a4e0>






    

In [6]:

    

model = smf.ols(formula='y2 ~ x', data=df).fit()
model.summary()


    

    
Out[6]:





OLS Regression Results

  
Dep. Variable:
           
y2
        
  R-squared:         
 
   0.876


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.875


  
Method:
             
Least Squares
  
  F-statistic:       
 
   694.7


  
Date:
             
Sat, 06 May 2017
 
  Prob (F-statistic):
 
2.80e-46


  
Time:
                 
10:41:14
     
  Log-Likelihood:    
 
 -145.38


  
No. Observations:
      
   100
      
  AIC:               
 
   294.8


  
Df Residuals:
          
    98
      
  BIC:               
 
   300.0


  
Df Model:
              
     1
      
                     
     
 
   


  
Covariance Type:
      
nonrobust
    
                     
     
 
   




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


  
Intercept
 
    0.7513
 
    0.214
 
    3.505
 
 0.001
 
    0.326
 
    1.177


  
x
         
    0.0959
 
    0.004
 
   26.358
 
 0.000
 
    0.089
 
    0.103




  
Omnibus:
       
 1.578
 
  Durbin-Watson:     
 
   1.778


  
Prob(Omnibus):
 
 0.454
 
  Jarque-Bera (JB):  
 
   1.623


  
Skew:
          
 0.253
 
  Prob(JB):          
 
   0.444


  
Kurtosis:
      
 2.635
 
  Cond. No.          
 
    121.

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