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



In [1]:

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

2. Read in the hanford.csv file



In [3]:

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



In [4]:

    
df.head()









    Out[4]:






  
    
      
      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

3. Calculate the basic descriptive statistics on the data

Central Tendency:

Mean



In [5]:

    
df.mean()









    Out[5]:





Exposure       4.617778
Mortality    157.344444
dtype: float64

Median



In [6]:

    
df.median()









    Out[6]:





Exposure       3.41
Mortality    147.10
dtype: float64

Mode



In [7]:

    
df.mode()









    Out[7]:






  
    
      
      County
      Exposure
      Mortality

Spread:

Range



In [9]:

    
max(df['Exposure']) - min(df['Exposure'])









    Out[9]:





10.390000000000001



In [10]:

    
max(df['Mortality']) - min(df['Mortality'])









    Out[10]:





96.800000000000011

Interquartile Range



In [11]:

    
df['Exposure'].quantile(q=0.75)  - df['Exposure'].quantile(q=0.25)









    Out[11]:





3.9199999999999999



In [12]:

    
df['Mortality'].quantile(q=0.75)  - df['Mortality'].quantile(q=0.25)









    Out[12]:





47.800000000000011

Standard Deviation



In [13]:

    
df.std()









    Out[13]:





Exposure      3.491192
Mortality    34.791346
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 [14]:

    
df.corr()









    Out[14]:






  
    
      
      Exposure
      Mortality
    
  
  
    
      Exposure
      1.000000
      0.926345
    
    
      Mortality
      0.926345
      1.000000



In [15]:

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









    Out[15]:





<matplotlib.axes._subplots.AxesSubplot at 0x10d60e550>

Yes.

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 = 'Mortality~Exposure', data = df).fit()



In [18]:

    
b, m = lm.params



In [21]:

    
def predicted_mortality_rate(exposure):
    y = m * exposure + b
    return y

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



In [20]:

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









    Out[20]:





[<matplotlib.lines.Line2D at 0x10d8dcc88>]

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



In [22]:

    
predicted_mortality_rate(10)









    Out[22]:





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