In [8]:

    

import pandas as pd
import matplotlib.pyplot as plt
#DISPLAY MOTPLOTLIB INLINE WITH THE NOTEBOOK AS OPPOSED TO POP UP WINDOW
%matplotlib inline
import statsmodels.formula.api as smf # package we'll be using for linear regression


    

    




/Users/Monica/.virtualenvs/dataanalysis/lib/python3.5/site-packages/matplotlib/__init__.py:1035: UserWarning: Duplicate key in file "/Users/Monica/.matplotlib/matplotlibrc", line #2
  (fname, cnt))

In [9]:

    

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


    

In [10]:

    

df.head()


    

    
Out[10]:






  

    

      

      
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
    
  

In [11]:

    

df.corr()


    

    
Out[11]:






  

    

      

      
Exposure
      
Mortality
    
  
  

    

      
Exposure
      
1.000000
      
0.926345
    
    

      
Mortality
      
0.926345
      
1.000000
    
  

In [12]:

    

lm = smf.ols(formula="Mortality~Exposure",data=df).fit() #notice the formula regresses Y on X (Y~X)


    

In [13]:

    

lm.params


    

    
Out[13]:





Intercept    114.715631
Exposure       9.231456
dtype: float64

In [14]:

    

lm.summary() # R sQUARED IS 0.858 WHICH should be investigated!


    

    




/Users/Monica/.virtualenvs/dataanalysis/lib/python3.5/site-packages/scipy/stats/stats.py:1535: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=9
  "anyway, n=%i" % int(n))






    
Out[14]:





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:
             
Thu, 28 Jul 2016
 
  Prob (F-statistic):
 
0.000332


  
Time:
                 
10:29:52
     
  Log-Likelihood:    
 
 -35.397


  
No. Observations:
      
     9
      
  AIC:               
 
   74.79


  
Df Residuals:
          
     7
      
  BIC:               
 
   75.19


  
Df Model:
              
     1
      
                     
     
 
   


  
Covariance Type:
      
nonrobust
    
                     
     
 
   




      
         
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 [15]:

    

intercept, slope = lm.params


    

In [16]:

    

ax = df.plot(kind='scatter', x='Exposure', y='Mortality', alpha=0.5)
ax.set_title('Camcer Mortality Rates Based on Exposure')
ax.set_xlabel('Index of Exposure')
ax.set_ylabel('Cancer Mortality per 100,000 man-years')


    

    
Out[16]:





<matplotlib.text.Text at 0x107890c50>






    

In [17]:

    

df.plot(kind="scatter",x="Exposure",y="Mortality")
plt.plot(df["Exposure"],slope*df["Exposure"]+intercept,"-",color="red") #we create the best fit line from the values in the fit model


    

    
Out[17]:





[<matplotlib.lines.Line2D at 0x1079f7c88>]






    

In [18]:

    

R_squared = 0.858


    

In [19]:

    

index_ex = 10
plt.plot(index_ex,slope*index_ex+intercept,"-",color="red") #we create the best fit line from the values in the fit model


    

    
Out[19]:





[<matplotlib.lines.Line2D at 0x107b009e8>]






    

In [20]:

    

# y = mx + b
intercept = 114.7156


    

In [21]:

    

slope * 10 + 114.7156


    

    
Out[21]:





207.03016270763393

In [22]:

    

def predicting_mortality_rate(exposure):
    return slope * exposure + intercept


    

In [23]:

    

predicting_mortality_rate(10)


    

    
Out[23]:





207.03019352841989

In [ ]: