In [4]:

    

import pandas as pd
%matplotlib inline
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
import numpy as np


    

In [5]:

    

df = pd.read_csv("data/hanford.csv")


    

In [6]:

    

df


    

    
Out[6]:






  

    

      

      
County
      
Exposure
      
Mortality
    
  
  

    

      
0
      
Umatilla
      
2.49
      
147.1
    
    

      
1
      
Morrow
      
2.57
      
130.1
    
    

      
2
      
Gilliam
      
3.41
      
129.9
    
    

      
3
      
Sherman
      
1.25
      
113.5
    
    

      
4
      
Wasco
      
1.62
      
137.5
    
    

      
5
      
HoodRiver
      
3.83
      
162.3
    
    

      
6
      
Portland
      
11.64
      
207.5
    
    

      
7
      
Columbia
      
6.41
      
177.9
    
    

      
8
      
Clatsop
      
8.34
      
210.3
    
  

In [4]:

    

df.describe()


    

    
Out[4]:






  

    

      

      
Exposure
      
Mortality
    
  
  

    

      
count
      
9.000000
      
9.000000
    
    

      
mean
      
4.617778
      
157.344444
    
    

      
std
      
3.491192
      
34.791346
    
    

      
min
      
1.250000
      
113.500000
    
    

      
25%
      
2.490000
      
130.100000
    
    

      
50%
      
3.410000
      
147.100000
    
    

      
75%
      
6.410000
      
177.900000
    
    

      
max
      
11.640000
      
210.300000
    
  

In [5]:

    

df.hist()


    

    
Out[5]:





array([[<matplotlib.axes.AxesSubplot object at 0x1071de490>,
        <matplotlib.axes.AxesSubplot object at 0x107289850>]], dtype=object)






    

In [7]:

    

df.corr()


    

    
Out[7]:






  

    

      

      
Exposure
      
Mortality
    
  
  

    

      
Exposure
      
1.000000
      
0.926345
    
    

      
Mortality
      
0.926345
      
1.000000
    
  

In [8]:

    

df.plot(kind='scatter',x='Exposure',y='Mortality')


    

    
Out[8]:





<matplotlib.axes.AxesSubplot at 0x108ff8190>






    

In [19]:

    

lm = LinearRegression()


    

In [20]:

    

data = np.asarray(df[['Mortality','Exposure']])
x = data[:,1:]
y = data[:,0]


    

In [21]:

    

lm.fit(x,y)


    

    
Out[21]:





LinearRegression(copy_X=True, fit_intercept=True, normalize=False)

In [22]:

    

lm.score(x,y)


    

    
Out[22]:





0.85811472686989465

In [25]:

    

m = lm.coef_[0]
m


    

    
Out[25]:





9.2314562707633918

In [26]:

    

b = lm.intercept_
b


    

    
Out[26]:





114.71563082078595

In [21]:

    

df.plot(kind='scatter',x='Exposure',y='Mortality')
plt.plot(df['Exposure'],m*df['Exposure']+b,'-')


    

    
Out[21]:





[<matplotlib.lines.Line2D at 0x10918ba10>]






    

In [24]:

    

lm.predict(10)


    

    
Out[24]:





array([ 207.03019353])

In [1]:

    

import statsmodels.formula.api as smf


    

In [27]:

    

lm = smf.ols(formula='Mortality~Exposure',data=df).fit()


    

In [28]:

    

lm.params


    

    
Out[28]:





Intercept    114.715631
Exposure       9.231456
dtype: float64

In [29]:

    

intercept, slope = lm.params


    

In [33]:

    

df.plot(kind='scatter',x='Exposure',y='Mortality')
plt.plot(df['Exposure'],slope*df['Exposure']+intercept,'-')


    

    
Out[33]:





[<matplotlib.lines.Line2D at 0x1093571d0>]






    

In [34]:

    

plt.xkcd()
df.plot(kind='scatter',x='Exposure',y='Mortality')
plt.plot(df['Exposure'],slope*df['Exposure']+intercept,'-')


    

    
Out[34]:





[<matplotlib.lines.Line2D at 0x109524d50>]






    

In [30]:

    

lm.summary()


    

    
Out[30]:





OLS Regression Results

  
Dep. Variable:
        
Mortality
    
  R-squared:         
 
   0.858


  
Model:
                   
OLS
       
  Adj. R-squared:    
 
   0.838


  
Method:
             
Least Squares
  
  F-statistic:       
 
   42.34


  
Date:
             
Wed, 29 Jul 2015
 
  Prob (F-statistic):
 
0.000332


  
Time:
                 
21:35:49
     
  Log-Likelihood:    
 
 -35.397


  
No. Observations:
      
     9
      
  AIC:               
 
   74.79


  
Df Residuals:
          
     7
      
  BIC:               
 
   75.19


  
Df Model:
              
     1
      
                     
     
 
   




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


  
Intercept
 
  114.7156
 
    8.046
 
   14.258
 
 0.000
 
   95.691   133.741


  
Exposure
  
    9.2315
 
    1.419
 
    6.507
 
 0.000
 
    5.877    12.586




  
Omnibus:
       
 2.914
 
  Durbin-Watson:     
 
   1.542


  
Prob(Omnibus):
 
 0.233
 
  Jarque-Bera (JB):  
 
   0.915


  
Skew:
          
-0.030
 
  Prob(JB):          
 
   0.633


  
Kurtosis:
      
 1.439
 
  Cond. No.          
 
    9.97

In [31]:

    

lm.mse_model


    

    
Out[31]:





8309.5558645662404

In [32]:

    

lm.pvalues


    

    
Out[32]:





Intercept    0.000002
Exposure     0.000332
dtype: float64

In [ ]: