In [23]:

    

import math
import matplotlib.pyplot as plt
import random


    

In [45]:

    

x=random.sample(range(10000),300)


    

In [46]:

    

y=[math.sqrt(xx)+random.randint(0,100) for xx in x]


    

In [47]:

    

plt.scatter(x,y)


    

    
Out[47]:





<matplotlib.collections.PathCollection at 0x7faf00fa6c18>

In [48]:

    

plt.show()


    

In [49]:

    

import numpy as np
import pandas as pd
from numpy.linalg import inv
from numpy import dot


    

In [54]:

    

Xb=pd.DataFrame()
Xb['data']=x
Xb['constant']=np.ones(300)


    

In [55]:

    

np.dot(np.linalg.inv(np.dot(Xb.T,Xb)),np.dot(Xb.T,y))


    

    
Out[55]:





array([  8.66251066e-03,   7.45185183e+01])

In [56]:

    

import statsmodels.api as sm


    

In [65]:

    

dx=pd.Series(x)
dy=pd.Series(y)
dx=sm.add_constant(dx)


    

In [66]:

    

linear_regression=sm.OLS(dy,dx)


    

In [67]:

    

model_fitted=linear_regression.fit()


    

In [68]:

    

model_fitted.summary()


    

    
Out[68]:





OLS Regression Results

  
Dep. Variable:
            
y
        
  R-squared:         
 
   0.369


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.366


  
Method:
             
Least Squares
  
  F-statistic:       
 
   173.9


  
Date:
             
Tue, 07 Mar 2017
 
  Prob (F-statistic):
 
1.36e-31


  
Time:
                 
16:22:59
     
  Log-Likelihood:    
 
 -1455.7


  
No. Observations:
      
   300
      
  AIC:               
 
   2915.


  
Df Residuals:
          
   298
      
  BIC:               
 
   2923.


  
Df Model:
              
     1
      
                     
     
 
   


  
Covariance Type:
      
nonrobust
    
                     
     
 
   




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


  
const
 
   74.5185
 
    3.795
 
   19.636
 
 0.000
 
   67.050    81.987


  
None
  
    0.0087
 
    0.001
 
   13.187
 
 0.000
 
    0.007     0.010




  
Omnibus:
       
172.203
 
  Durbin-Watson:     
 
   2.095


  
Prob(Omnibus):
 
 0.000
  
  Jarque-Bera (JB):  
 
  18.846


  
Skew:
          
-0.107
  
  Prob(JB):          
 
8.08e-05


  
Kurtosis:
      
 1.791
  
  Cond. No.          
 
1.22e+04

In [69]:

    

xp=20
Xp=np.array([1,xp])
print(model_fitted.predict(Xp))


    

    




[ 74.6917685]

In [71]:

    

np.dot(Xp,np.array([7.45185183e+01,8.66251066e-03]))


    

    
Out[71]:





74.691768513200003

In [ ]: