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



In [1]:

    
import pandas as pd
%matplotlib inline
import matplotlib.pyplot as plt
import statsmodels.formula.api as smf

2. Read in the hanford.csv file



In [4]:

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



In [5]:

    
df

3. Calculate the basic descriptive statistics on the data



In [6]:

    
df['Exposure'].mean()









    Out[6]:





4.6177777777777784



In [7]:

    
df['Exposure'].describe()









    Out[7]:





count     9.000000
mean      4.617778
std       3.491192
min       1.250000
25%       2.490000
50%       3.410000
75%       6.410000
max      11.640000
Name: Exposure, dtype: float64

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



In [9]:

    
df.corr()









    Out[9]:






  
    
      
      Exposure
      Mortality
    
  
  
    
      Exposure
      1.000000
      0.926345
    
    
      Mortality
      0.926345
      1.000000



In [8]:

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









    Out[8]:





<matplotlib.axes._subplots.AxesSubplot at 0x10e652cf8>

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



In [10]:

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









    Out[10]:





Intercept    114.715631
Exposure       9.231456
dtype: float64



In [11]:

    
intercept, Exposure = lm.params
Mortality = Exposure*10+intercept



In [12]:

    
Mortality









    Out[12]:





199.93541569980266

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 [13]:

    
intercept, Exposure = lm.params
Mortality = Exposure*10+intercept



In [14]:

    
Mortality









    Out[14]:





207.03019352841983



In [ ]:

	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