1. Import the necessary packages to read in the data, plot, and create a linear regression model



In [14]:

    
import pandas as pd
%matplotlib inline
import matplotlib.pyplot as plt 
import statsmodels.formula.api as smf 
import numpy as np
import scipy as sp

2. Read in the hanford.csv file



In [3]:

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



In [4]:

    
df

3. Calculate the basic descriptive statistics on the data



In [5]:

    
df.describe()

4. Calculate the coefficient of correlation (r) and generate the scatter plot. Does there seem to be a correlation worthy of investigation?



In [6]:

    
df.corr()









    Out[6]:






  
    
      
      Exposure
      Mortality
    
  
  
    
      Exposure
      1.000000
      0.926345
    
    
      Mortality
      0.926345
      1.000000



In [9]:

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









    Out[9]:





<matplotlib.axes._subplots.AxesSubplot at 0x10dc3f780>



In [18]:

    
r =









    Out[18]:






  
    
      
      Exposure
      Mortality
    
  
  
    
      Exposure
      1.000000
      0.926345
    
    
      Mortality
      0.926345
      1.000000

5. Create a linear regression model based on the available data to predict the mortality rate given a level of exposure



In [16]:

    
lm = smf.ols(formula="Exposure-Mortality",data=df).fit()
intercept, slop, smf.ols









    



---------------------------------------------------------------------------
PatsyError                                Traceback (most recent call last)
<ipython-input-16-4a5209c96e84> in <module>()
----> 1 lm = smf.ols(formula="Exposure-Mortality",data=df).fit()
      2 intercept, slop, smf.ols

/Users/skkandrach/.virtualenvs/lede/lib/python3.5/site-packages/statsmodels/base/model.py in from_formula(cls, formula, data, subset, *args, **kwargs)
    145         (endog, exog), missing_idx = handle_formula_data(data, None, formula,
    146                                                          depth=eval_env,
--> 147                                                          missing=missing)
    148         kwargs.update({'missing_idx': missing_idx,
    149                        'missing': missing})

/Users/skkandrach/.virtualenvs/lede/lib/python3.5/site-packages/statsmodels/formula/formulatools.py in handle_formula_data(Y, X, formula, depth, missing)
     63         if data_util._is_using_pandas(Y, None):
     64             result = dmatrices(formula, Y, depth, return_type='dataframe',
---> 65                                NA_action=na_action)
     66         else:
     67             result = dmatrices(formula, Y, depth, return_type='dataframe',

/Users/skkandrach/.virtualenvs/lede/lib/python3.5/site-packages/patsy/highlevel.py in dmatrices(formula_like, data, eval_env, NA_action, return_type)
    310                                       NA_action, return_type)
    311     if lhs.shape[1] == 0:
--> 312         raise PatsyError("model is missing required outcome variables")
    313     return (lhs, rhs)

PatsyError: model is missing required outcome variables



In [11]:

    
lm.params









    



---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-11-62e627bdceb7> in <module>()
----> 1 lm.params

NameError: name 'lm' is not defined

6. Plot the linear regression line on the scatter plot of values. Calculate the r^2 (coefficient of determination)



In [ ]:

7. Predict the mortality rate (Cancer per 100,000 man years) given an index of exposure = 10



In [ ]:

    
def predict_mr(exposure):
    return intercept + float(expsure) * slope



In [ ]:

    
predict_mr(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
5	HoodRiver	3.83	162.3
6	Portland	11.64	207.5
7	Columbia	6.41	177.9
8	Clatsop	8.34	210.3

	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