Linear regression for Catheter Length

In [1]:

    

%pylab inline
pylab.style.use('ggplot')
import numpy as np
import pandas as pd


    

    




Populating the interactive namespace from numpy and matplotlib

In [2]:

    

import requests
URL = 'http://people.sc.fsu.edu/~jburkardt/datasets/regression/x02.txt'
response = requests.get(URL)
text = response.text


    

In [8]:

    

lines = [line.strip() for line in text.split('\n') if not line.strip().startswith('#')]


    

In [9]:

    

lines[:10]


    

    
Out[9]:





['4 columns',
 '12 rows',
 'Index',
 'Patient Height (inches)',
 'Patient Weight (pounds)',
 'Catheter Length (centimeters)',
 '1  42.8  40.0  37',
 '2  63.5  93.5  50',
 '3  37.5  35.5  34',
 '4  39.5  30.0  36']

In [10]:

    

columns = ['Index', 'Patient Height', 'Patient Weight', 'Catheter Length']


    

In [16]:

    

data = lines[6:-2]


    

In [34]:

    

data_a = np.array([row.split() for row in data])
data_a = data_a.astype(np.float)
data_a[:, 1] = data_a[:, 1].astype(np.int)


    

In [42]:

    

data_df = pd.DataFrame(data=data_a, columns=columns).set_index('Index')
data_df = data_df.rename(columns={name: name.lower().replace(' ', '_') for name in data_df.keys()})


    

In [43]:

    

data_df.head(4)


    

    
Out[43]:






  

    

      

      
patient_height
      
patient_weight
      
catheter_length
    
    

      
Index
      

      

      

    
  
  

    

      
1.0
      
42.0
      
40.0
      
37.0
    
    

      
2.0
      
63.0
      
93.5
      
50.0
    
    

      
3.0
      
37.0
      
35.5
      
34.0
    
    

      
4.0
      
39.0
      
30.0
      
36.0
    
  

In [48]:

    

data_df.corr()


    

    
Out[48]:






  

    

      

      
patient_height
      
patient_weight
      
catheter_length
    
  
  

    

      
patient_height
      
1.000000
      
0.960965
      
0.895279
    
    

      
patient_weight
      
0.960965
      
1.000000
      
0.904510
    
    

      
catheter_length
      
0.895279
      
0.904510
      
1.000000
    
  

In [53]:

    

data_df[['patient_height', 'patient_weight']].corrwith(data_df['catheter_length'])


    

    
Out[53]:





patient_height    0.895279
patient_weight    0.904510
dtype: float64

In [54]:

    

data_df.plot(kind='scatter', x='patient_weight', y='catheter_length')


    

    
Out[54]:





<matplotlib.axes._subplots.AxesSubplot at 0x1ae288af048>






    

In [56]:

    

data_df.plot(kind='scatter', x='patient_height', y='catheter_length')


    

    
Out[56]:





<matplotlib.axes._subplots.AxesSubplot at 0x1ae28e26a20>






    

In [57]:

    

import statsmodels.formula.api as sm

result = sm.ols(formula='catheter_length ~ patient_weight', data=data_df).fit()
result.summary()


    

    




d:\anaconda3\lib\site-packages\scipy\stats\stats.py:1327: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=12
  "anyway, n=%i" % int(n))






    
Out[57]:





OLS Regression Results

  
Dep. Variable:
     
catheter_length
 
  R-squared:         
 
   0.818


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.800


  
Method:
             
Least Squares
  
  F-statistic:       
 
   44.99


  
Date:
             
Thu, 30 Mar 2017
 
  Prob (F-statistic):
 
5.32e-05


  
Time:
                 
21:02:36
     
  Log-Likelihood:    
 
 -31.495


  
No. Observations:
      
    12
      
  AIC:               
 
   66.99


  
Df Residuals:
          
    10
      
  BIC:               
 
   67.96


  
Df Model:
              
     1
      
                     
     
 
   


  
Covariance Type:
      
nonrobust
    
                     
     
 
   




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


  
Intercept
      
   25.3441
 
    1.928
 
   13.143
 
 0.000
 
   21.047    29.641


  
patient_weight
 
    0.2839
 
    0.042
 
    6.707
 
 0.000
 
    0.190     0.378




  
Omnibus:
       
 2.813
 
  Durbin-Watson:     
 
   1.937


  
Prob(Omnibus):
 
 0.245
 
  Jarque-Bera (JB):  
 
   0.591


  
Skew:
          
-0.325
 
  Prob(JB):          
 
   0.744


  
Kurtosis:
      
 3.872
 
  Cond. No.          
 
    83.2

In [58]:

    

result = sm.ols(formula='catheter_length ~ patient_height', data=data_df).fit()
result.summary()


    

    




d:\anaconda3\lib\site-packages\scipy\stats\stats.py:1327: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=12
  "anyway, n=%i" % int(n))






    
Out[58]:





OLS Regression Results

  
Dep. Variable:
     
catheter_length
 
  R-squared:         
 
   0.802


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.782


  
Method:
             
Least Squares
  
  F-statistic:       
 
   40.38


  
Date:
             
Thu, 30 Mar 2017
 
  Prob (F-statistic):
 
8.30e-05


  
Time:
                 
21:03:32
     
  Log-Likelihood:    
 
 -32.020


  
No. Observations:
      
    12
      
  AIC:               
 
   68.04


  
Df Residuals:
          
    10
      
  BIC:               
 
   69.01


  
Df Model:
              
     1
      
                     
     
 
   


  
Covariance Type:
      
nonrobust
    
                     
     
 
   




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


  
Intercept
      
   11.6997
 
    4.005
 
    2.921
 
 0.015
 
    2.776    20.623


  
patient_height
 
    0.6117
 
    0.096
 
    6.355
 
 0.000
 
    0.397     0.826




  
Omnibus:
       
 0.469
 
  Durbin-Watson:     
 
   1.825


  
Prob(Omnibus):
 
 0.791
 
  Jarque-Bera (JB):  
 
   0.124


  
Skew:
          
-0.225
 
  Prob(JB):          
 
   0.940


  
Kurtosis:
      
 2.789
 
  Cond. No.          
 
    151.

In [59]:

    

result = sm.ols(formula='catheter_length ~ patient_height + patient_weight', data=data_df).fit()
result.summary()


    

    




d:\anaconda3\lib\site-packages\scipy\stats\stats.py:1327: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=12
  "anyway, n=%i" % int(n))






    
Out[59]:





OLS Regression Results

  
Dep. Variable:
     
catheter_length
 
  R-squared:         
 
   0.827


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.789


  
Method:
             
Least Squares
  
  F-statistic:       
 
   21.51


  
Date:
             
Thu, 30 Mar 2017
 
  Prob (F-statistic):
 
0.000372


  
Time:
                 
21:06:31
     
  Log-Likelihood:    
 
 -31.195


  
No. Observations:
      
    12
      
  AIC:               
 
   68.39


  
Df Residuals:
          
     9
      
  BIC:               
 
   69.84


  
Df Model:
              
     2
      
                     
     
 
   


  
Covariance Type:
      
nonrobust
    
                     
     
 
   




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


  
Intercept
      
   19.9512
 
    8.177
 
    2.440
 
 0.037
 
    1.454    38.448


  
patient_height
 
    0.2327
 
    0.342
 
    0.680
 
 0.514
 
   -0.542     1.007


  
patient_weight
 
    0.1811
 
    0.157
 
    1.152
 
 0.279
 
   -0.175     0.537




  
Omnibus:
       
 0.784
 
  Durbin-Watson:     
 
   1.864


  
Prob(Omnibus):
 
 0.676
 
  Jarque-Bera (JB):  
 
   0.006


  
Skew:
          
-0.020
 
  Prob(JB):          
 
   0.997


  
Kurtosis:
      
 3.100
 
  Cond. No.          
 
    459.

In [61]:

    

data_df.plot(kind='scatter', x='patient_height', y='patient_weight')


    

    
Out[61]:





<matplotlib.axes._subplots.AxesSubplot at 0x1ae29c155c0>






    

In [ ]: