In [1]:

    

import pandas as pd
import matplotlib.pyplot as plt
pd.set_option('display.notebook_repr_html', False)
pd.set_option('display.max_columns', 20)
pd.set_option('display.max_rows', 25)

mpl.rc('figure', figsize=(10, 8))


    

In [2]:

    

data = pd.read_csv('./data/Advertising.csv', index_col=[0])
data.head()


    

    
Out[2]:





      TV  Radio  Newspaper  Sales
1  230.1   37.8       69.2   22.1
2   44.5   39.3       45.1   10.4
3   17.2   45.9       69.3    9.3
4  151.5   41.3       58.5   18.5
5  180.8   10.8       58.4   12.9

[5 rows x 4 columns]

In [3]:

    

fig, axes=plt.subplots(figsize=(15, 5), nrows=1, ncols=3)
axes[0].scatter(data['TV'], data['Sales'], c='r')
axes[0].set_title("TV")

axes[1].scatter(data['Radio'], data['Sales'], c='r')
axes[1].set_title("Radio")

axes[2].scatter(data['Newspaper'], data['Sales'], c='r')
axes[2].set_title("Newspaper")
fig.tight_layout()


    

In [4]:

    

import statsmodels.formula.api as sm


    

In [5]:

    

tv_model = sm.ols(formula='Sales ~ TV', data=data)
tv_fitted = tv_model.fit()

radio_model = sm.ols(formula='Sales ~ Radio', data=data)
radio_fitted = radio_model.fit()

np_model = sm.ols(formula='Sales ~ Newspaper', data=data)
np_fitted = np_model.fit()


    

In [6]:

    

fig, axes=plt.subplots(figsize=(15, 5), nrows=1, ncols=3)
axes[0].plot(data['TV'], data['Sales'], 'ro')
axes[0].plot(data['TV'], tv_fitted.fittedvalues, 'b')
axes[0].set_title('TV')

axes[1].plot(data['Radio'], data['Sales'], 'ro')
axes[1].plot(data['Radio'], radio_fitted.fittedvalues, 'b')
axes[1].set_title('Radio')

axes[2].plot(data['Newspaper'], data['Sales'], 'ro')
axes[2].plot(data['Newspaper'], np_fitted.fittedvalues, 'b')
axes[2].set_title('Newspaper')

fig.tight_layout()


    

In [7]:

    

tv_fitted.summary()


    

    
Out[7]:





OLS Regression Results

  
Dep. Variable:
          
Sales
      
  R-squared:         
 
   0.612


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.610


  
Method:
             
Least Squares
  
  F-statistic:       
 
   312.1


  
Date:
             
Sat, 15 Feb 2014
 
  Prob (F-statistic):
 
1.47e-42


  
Time:
                 
12:23:10
     
  Log-Likelihood:    
 
 -519.05


  
No. Observations:
      
   200
      
  AIC:               
 
   1042.


  
Df Residuals:
          
   198
      
  BIC:               
 
   1049.


  
Df Model:
              
     1
      
                     
     
 
   




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


  
Intercept
 
    7.0326
 
    0.458
 
   15.360
 
 0.000
 
    6.130     7.935


  
TV
        
    0.0475
 
    0.003
 
   17.668
 
 0.000
 
    0.042     0.053




  
Omnibus:
       
 0.531
 
  Durbin-Watson:     
 
   1.935


  
Prob(Omnibus):
 
 0.767
 
  Jarque-Bera (JB):  
 
   0.669


  
Skew:
          
-0.089
 
  Prob(JB):          
 
   0.716


  
Kurtosis:
      
 2.779
 
  Cond. No.          
 
    338.

In [8]:

    

radio_fitted.summary()


    

    
Out[8]:





OLS Regression Results

  
Dep. Variable:
          
Sales
      
  R-squared:         
 
   0.332


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.329


  
Method:
             
Least Squares
  
  F-statistic:       
 
   98.42


  
Date:
             
Sat, 15 Feb 2014
 
  Prob (F-statistic):
 
4.35e-19


  
Time:
                 
12:23:10
     
  Log-Likelihood:    
 
 -573.34


  
No. Observations:
      
   200
      
  AIC:               
 
   1151.


  
Df Residuals:
          
   198
      
  BIC:               
 
   1157.


  
Df Model:
              
     1
      
                     
     
 
   




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


  
Intercept
 
    9.3116
 
    0.563
 
   16.542
 
 0.000
 
    8.202    10.422


  
Radio
     
    0.2025
 
    0.020
 
    9.921
 
 0.000
 
    0.162     0.243




  
Omnibus:
       
19.358
 
  Durbin-Watson:     
 
   1.946


  
Prob(Omnibus):
 
 0.000
 
  Jarque-Bera (JB):  
 
  21.910


  
Skew:
          
-0.764
 
  Prob(JB):          
 
1.75e-05


  
Kurtosis:
      
 3.544
 
  Cond. No.          
 
    51.4

In [9]:

    

np_fitted.summary()


    

    
Out[9]:





OLS Regression Results

  
Dep. Variable:
          
Sales
      
  R-squared:         
 
   0.052


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.047


  
Method:
             
Least Squares
  
  F-statistic:       
 
   10.89


  
Date:
             
Sat, 15 Feb 2014
 
  Prob (F-statistic):
  
0.00115


  
Time:
                 
12:23:10
     
  Log-Likelihood:    
 
 -608.34


  
No. Observations:
      
   200
      
  AIC:               
 
   1221.


  
Df Residuals:
          
   198
      
  BIC:               
 
   1227.


  
Df Model:
              
     1
      
                     
     
 
   




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


  
Intercept
 
   12.3514
 
    0.621
 
   19.876
 
 0.000
 
   11.126    13.577


  
Newspaper
 
    0.0547
 
    0.017
 
    3.300
 
 0.001
 
    0.022     0.087




  
Omnibus:
       
 6.231
 
  Durbin-Watson:     
 
   1.983


  
Prob(Omnibus):
 
 0.044
 
  Jarque-Bera (JB):  
 
   5.483


  
Skew:
          
 0.330
 
  Prob(JB):          
 
  0.0645


  
Kurtosis:
      
 2.527
 
  Cond. No.          
 
    64.7

In [10]:

    

all_model = sm.ols(formula='Sales ~ TV + Radio + Newspaper', data=data)
all_fitted = all_model.fit()
all_fitted.summary()


    

    
Out[10]:





OLS Regression Results

  
Dep. Variable:
          
Sales
      
  R-squared:         
 
   0.897


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.896


  
Method:
             
Least Squares
  
  F-statistic:       
 
   570.3


  
Date:
             
Sat, 15 Feb 2014
 
  Prob (F-statistic):
 
1.58e-96


  
Time:
                 
12:23:13
     
  Log-Likelihood:    
 
 -386.18


  
No. Observations:
      
   200
      
  AIC:               
 
   780.4


  
Df Residuals:
          
   196
      
  BIC:               
 
   793.6


  
Df Model:
              
     3
      
                     
     
 
   




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


  
Intercept
 
    2.9389
 
    0.312
 
    9.422
 
 0.000
 
    2.324     3.554


  
TV
        
    0.0458
 
    0.001
 
   32.809
 
 0.000
 
    0.043     0.049


  
Radio
     
    0.1885
 
    0.009
 
   21.893
 
 0.000
 
    0.172     0.206


  
Newspaper
 
   -0.0010
 
    0.006
 
   -0.177
 
 0.860
 
   -0.013     0.011




  
Omnibus:
       
60.414
 
  Durbin-Watson:     
 
   2.084


  
Prob(Omnibus):
 
 0.000
 
  Jarque-Bera (JB):  
 
 151.241


  
Skew:
          
-1.327
 
  Prob(JB):          
 
1.44e-33


  
Kurtosis:
      
 6.332
 
  Cond. No.          
 
    454.

In [11]:

    

data.corr()


    

    
Out[11]:





                 TV     Radio  Newspaper     Sales
TV         1.000000  0.054809   0.056648  0.782224
Radio      0.054809  1.000000   0.354104  0.576223
Newspaper  0.056648  0.354104   1.000000  0.228299
Sales      0.782224  0.576223   0.228299  1.000000

[4 rows x 4 columns]