Regression and Prediction

In [1]:

    

import pandas as pd
import numpy as np
import seaborn as sns
import statsmodels.formula.api as sm
from scipy import stats
stats.chisqprob = lambda chisq, df: stats.chi2.sf(chisq, df)


    

In [2]:

    

tips = pd.read_csv('input/tips.csv')
tips['tip_percent'] = (tips['tip'] / tips['total_bill'] * 100)
tips['tip_above_avg'] = np.where(tips['tip_percent'] >= tips['tip_percent'].mean(), 1, 0)
tips.replace({'Yes': 1, 'No': 0}, inplace=True)


    

In [3]:

    

# Describe what we want using R-style formulas
formula = 'tip_percent ~ total_bill + party_size + C(ordered_alc_bev) + C(gender) + C(day) + C(time)'
model = sm.ols(formula, data=tips)    # Describe model
results = model.fit()                 # Fit model       
results.summary()                     # Summarize model


    

    
Out[3]:





OLS Regression Results

  
Dep. Variable:
       
tip_percent
   
  R-squared:         
 
   0.334


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.312


  
Method:
             
Least Squares
  
  F-statistic:       
 
   14.76


  
Date:
             
Mon, 16 Apr 2018
 
  Prob (F-statistic):
 
1.89e-17


  
Time:
                 
23:47:54
     
  Log-Likelihood:    
 
 -916.52


  
No. Observations:
      
   244
      
  AIC:               
 
   1851.


  
Df Residuals:
          
   235
      
  BIC:               
 
   1883.


  
Df Model:
              
     8
      
                     
     
 
   


  
Covariance Type:
      
nonrobust
    
                     
     
 
   




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


  
Intercept
               
   42.5140
 
    3.720
 
   11.429
 
 0.000
 
   35.186
 
   49.842


  
C(ordered_alc_bev)[T.1]
 
    1.7912
 
    1.473
 
    1.216
 
 0.225
 
   -1.110
 
    4.692


  
C(gender)[T.Male]
       
    0.3495
 
    1.461
 
    0.239
 
 0.811
 
   -2.528
 
    3.227


  
C(day)[T.Sat]
           
   -8.5745
 
    3.188
 
   -2.689
 
 0.008
 
  -14.856
 
   -2.293


  
C(day)[T.Sun]
           
   -7.9049
 
    3.286
 
   -2.406
 
 0.017
 
  -14.378
 
   -1.432


  
C(day)[T.Thur]
          
   -4.7105
 
    4.048
 
   -1.164
 
 0.246
 
  -12.686
 
    3.265


  
C(time)[T.Lunch]
        
   -2.1070
 
    4.569
 
   -0.461
 
 0.645
 
  -11.108
 
    6.895


  
total_bill
              
   -0.6502
 
    0.097
 
   -6.674
 
 0.000
 
   -0.842
 
   -0.458


  
party_size
              
   -1.5466
 
    0.916
 
   -1.689
 
 0.093
 
   -3.351
 
    0.257




  
Omnibus:
       
172.635
 
  Durbin-Watson:     
 
   2.119


  
Prob(Omnibus):
 
 0.000
  
  Jarque-Bera (JB):  
 
2382.625


  
Skew:
          
 2.613
  
  Prob(JB):          
 
    0.00


  
Kurtosis:
      
17.389
  
  Cond. No.          
 
    206.

In [4]:

    

columns = ['total_bill', 'gender', 'ordered_alc_bev', 'day', 'time', 'party_size']
data = [[15.52, 'Female', 0, 'Sun', 'Lunch', 1]]

df = pd.DataFrame(data, columns=columns)

predictions = results.predict(df).tolist()  # Convert to simple list
predictions


    

    
Out[4]:





[20.8648081851993]

In [5]:

    

columns = ['total_bill', 'party_size', 'ordered_alc_bev']
training_columns = tips[columns].columns
logit = sm.Logit(tips['tip_above_avg'], tips[training_columns])  # Describe model
results = logit.fit()                                            # Fit model  
results.summary()                                                # Summarize model


    

    




Optimization terminated successfully.
         Current function value: 0.576896
         Iterations 6






    
Out[5]:





Logit Regression Results

  
Dep. Variable:
   
tip_above_avg
  
  No. Observations:  
  
   244
  


  
Model:
               
Logit
      
  Df Residuals:      
  
   241
  


  
Method:
               
MLE
       
  Df Model:          
  
     2
  


  
Date:
          
Mon, 16 Apr 2018
 
  Pseudo R-squ.:     
  
0.1457
  


  
Time:
              
23:47:54
     
  Log-Likelihood:    
 
 -140.76
 


  
converged:
           
True
       
  LL-Null:           
 
 -164.77
 


  
 
                      
 
        
  LLR p-value:       
 
3.763e-11




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


  
total_bill
      
   -0.1123
 
    0.025
 
   -4.524
 
 0.000
 
   -0.161
 
   -0.064


  
party_size
      
    0.3599
 
    0.172
 
    2.095
 
 0.036
 
    0.023
 
    0.697


  
ordered_alc_bev
 
    1.1323
 
    0.280
 
    4.039
 
 0.000
 
    0.583
 
    1.682

In [6]:

    

data = [[10.52, 4, 0]]
df = pd.DataFrame(data, columns=columns)
predictions = results.predict(df).tolist()  # Convert to simple list

predictions


    

    
Out[6]:





[0.5640802818887375]

In [7]:

    

from requests import get, post
request_data = [
	{"total_bill": 22.50, "party_size": 3, "ordered_alc_bev": 1, "gender": "Female", "day": "Sat", "time": "Dinner"},
	{"total_bill": 18.62, "party_size": 3, "ordered_alc_bev": 1, "gender": "Female", "day": "Sat", "time": "Dinner"},
	{"total_bill": 17.14, "party_size": 3, "ordered_alc_bev": 0, "gender": "Female", "day": "Sat", "time": "Dinner"},
]
post('http://localhost:5000/', json=request_data).json()


    

    
Out[7]:





{'total_bill': 58.26,
 'predicted_tip': 8.08,
 'tip_percentage': 0.14,
 'tip_above_average': 'No'}

In [ ]: