In [1]:

    

# imports
import pandas as pd
import matplotlib.pyplot as plt

# this allows plots to appear directly in the notebook
%matplotlib inline


    

In [4]:

    

data = pd.read_csv('data/wine.csv')
data.head()


    

    
Out[4]:






  

    

      

      
Year
      
Price
      
WinterRain
      
AGST
      
HarvestRain
      
Age
      
FrancePop
    
  
  

    

      
0
      
1952
      
7.4950
      
600
      
17.1167
      
160
      
31
      
43183.569
    
    

      
1
      
1953
      
8.0393
      
690
      
16.7333
      
80
      
30
      
43495.030
    
    

      
2
      
1955
      
7.6858
      
502
      
17.1500
      
130
      
28
      
44217.857
    
    

      
3
      
1957
      
6.9845
      
420
      
16.1333
      
110
      
26
      
45152.252
    
    

      
4
      
1958
      
6.7772
      
582
      
16.4167
      
187
      
25
      
45653.805
    
  

In [5]:

    

# print the shape of the DataFrame
data.shape


    

    
Out[5]:





(25, 7)

In [7]:

    

# visualize the relationship between the features and the response using scatterplots
fig, axs = plt.subplots(1, 3, sharey=True)
data.plot(kind='scatter', x='Year', y='Price', ax=axs[0], figsize=(16, 8))
data.plot(kind='scatter', x='WinterRain', y='Price', ax=axs[1])
data.plot(kind='scatter', x='AGST', y='Price', ax=axs[2])


    

    
Out[7]:





<matplotlib.axes._subplots.AxesSubplot at 0x10d89c8d0>






    

In [8]:

    

fig, axs = plt.subplots(1, 3, sharey=True)
data.plot(kind='scatter', x='HarvestRain', y='Price', ax=axs[0], figsize=(16, 8))
data.plot(kind='scatter', x='Age', y='Price', ax=axs[1])
data.plot(kind='scatter', x='FrancePop', y='Price', ax=axs[2])


    

    
Out[8]:





<matplotlib.axes._subplots.AxesSubplot at 0x10d833b00>






    

In [14]:

    

# this is the standard import if you're using "formula notation" (similar to R)
import statsmodels.formula.api as smf

# create a fitted model in one line
lm = smf.ols(formula='Price ~ Year + WinterRain + AGST + HarvestRain + Age + FrancePop', 
             data=data).fit()

# print the coefficients
lm.params


    

    
Out[14]:





Intercept      6.580350e-08
Year          -2.271301e-04
WinterRain     1.042507e-03
AGST           6.012239e-01
HarvestRain   -3.958125e-03
Age            3.576184e-04
FrancePop     -4.952730e-05
dtype: float64

In [15]:

    

lm.rsquared


    

    
Out[15]:





0.82935922232990378

In [16]:

    

lm.summary()


    

    
Out[16]:





OLS Regression Results

  
Dep. Variable:
          
Price
      
  R-squared:         
 
   0.829


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.784


  
Method:
             
Least Squares
  
  F-statistic:       
 
   18.47


  
Date:
             
Sat, 11 Jun 2016
 
  Prob (F-statistic):
 
1.04e-06


  
Time:
                 
10:25:26
     
  Log-Likelihood:    
 
 -2.1043


  
No. Observations:
      
    25
      
  AIC:               
 
   16.21


  
Df Residuals:
          
    19
      
  BIC:               
 
   23.52


  
Df Model:
              
     5
      
                     
     
 
   


  
Covariance Type:
      
nonrobust
    
                     
     
 
   




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


  
Intercept
   
  6.58e-08
 
 3.48e-05
 
    0.002
 
 0.999
 
-7.28e-05  7.29e-05


  
Year
        
   -0.0002
 
    0.005
 
   -0.044
 
 0.965
 
   -0.011     0.011


  
WinterRain
  
    0.0010
 
    0.001
 
    1.963
 
 0.064
 
-6.89e-05     0.002


  
AGST
        
    0.6012
 
    0.103
 
    5.836
 
 0.000
 
    0.386     0.817


  
HarvestRain
 
   -0.0040
 
    0.001
 
   -4.523
 
 0.000
 
   -0.006    -0.002


  
Age
         
    0.0004
 
    0.074
 
    0.005
 
 0.996
 
   -0.155     0.155


  
FrancePop
   
-4.953e-05
 
    0.000
 
   -0.297
 
 0.770
 
   -0.000     0.000




  
Omnibus:
       
 1.769
 
  Durbin-Watson:     
 
   2.792


  
Prob(Omnibus):
 
 0.413
 
  Jarque-Bera (JB):  
 
   1.026


  
Skew:
          
-0.005
 
  Prob(JB):          
 
   0.599


  
Kurtosis:
      
 2.008
 
  Cond. No.          
 
3.23e+22

In [19]:

    

# Create model using a smaller amount of significant variables
lm = smf.ols(formula='Price ~ AGST + HarvestRain + WinterRain + Age', 
             data=data).fit()


    

In [20]:

    

lm.rsquared


    

    
Out[20]:





0.82856621934242813

In [28]:

    

ypred = lm.predict(data)
ypred


    

    
Out[28]:





array([ 7.71515356,  7.87293687,  7.67732765,  7.00335549,  7.01993151,
        7.53932616,  6.75766829,  8.363191  ,  7.51318707,  6.63028304,
        7.56029312,  5.91863325,  7.55530516,  7.10919438,  6.26214399,
        6.60372738,  7.31679442,  7.18587836,  5.88022723,  7.0882792 ,
        6.56948742,  6.9897216 ,  6.9233729 ,  6.71339661,  6.91178436])

In [24]:

    

wine_test = pd.read_csv('data/wine_test.csv')


    

In [27]:

    

lm.predict(wine_test)


    

    
Out[27]:





array([ 6.76892463,  6.6849104 ])

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