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



In [10]:

    
import pandas as pd
%matplotlib inline
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
import numpy as np

2. Read in the hanford.csv file



In [25]:

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

3. Calculate the basic descriptive statistics on the data



In [26]:

    
df



In [4]:

    
df.describe()



In [5]:

    
df.hist()









    Out[5]:





array([[<matplotlib.axes.AxesSubplot object at 0x1071de490>,
        <matplotlib.axes.AxesSubplot object at 0x107289850>]], dtype=object)

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



In [7]:

    
df.corr()









    Out[7]:






  
    
      
      Exposure
      Mortality
    
  
  
    
      Exposure
      1.000000
      0.926345
    
    
      Mortality
      0.926345
      1.000000



In [8]:

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









    Out[8]:





<matplotlib.axes.AxesSubplot at 0x108ff8190>

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



In [9]:

    
lm = LinearRegression()



In [11]:

    
data = np.asarray(df[['Mortality','Exposure']])
x = data[:,1:]
y = data[:,0]



In [12]:

    
lm.fit(x,y)









    Out[12]:





LinearRegression(copy_X=True, fit_intercept=True, normalize=False)



In [14]:

    
lm.score(x,y)









    Out[14]:





0.85811472686989465



In [19]:

    
m = lm.coef_[0]



In [20]:

    
b = lm.intercept_

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



In [21]:

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









    Out[21]:





[<matplotlib.lines.Line2D at 0x10918ba10>]

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



In [24]:

    
lm.predict(10)









    Out[24]:





array([ 207.03019353])



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

	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