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



In [1]:

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

2. Read in the hanford.csv file



In [2]:

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









    Out[2]:






  
    
      
      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

County = Name of county
Exposure = Index of exposure
Mortality = Cancer mortality per 100,000 man-years

3. Calculate the basic descriptive statistics on the data



In [11]:

    
print('Mortality interquantile: ', df['Mortality'].quantile(0.75) - df['Mortality'].quantile(0.25))

print('Exposure interquantile: ', df['Exposure'].quantile(0.75) - df['Exposure'].quantile(0.25))


print('Mode:', df.mode)

df.describe()









    



Mortality interquantile:  47.8
Exposure interquantile:  3.92
Mode: <bound method DataFrame.mode of       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>






    Out[11]:






  
    
      
      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

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



In [4]:

    
print("The coefficient is {}. It seems worthy of investigation.".format(df.corr()['Exposure']['Mortality']))









    



The coefficient is 0.9263448207173691. It seems worthy of investigation.

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



In [5]:

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









    Out[5]:





Intercept    114.715631
Exposure       9.231456
dtype: float64

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



In [6]:

    
fig, ax = plt.subplots()
ax.plot(df['Exposure'], df['Mortality'], 'o', label="Data")
ax.plot(df['Exposure'], lm.fittedvalues, '-', color='red', label="Prediction")









    Out[6]:





[<matplotlib.lines.Line2D at 0x10fc6a828>]

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



In [7]:

    
intercept, slope = lm.params
result = slope*10 + intercept
print("The result is {}.".format(result))









    



The result is 207.0301935284199.

	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

	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