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



In [6]:

    
import pandas as pd
import matplotlib.pyplot as plt
import statsmodels.formula.api as smf
%matplotlib inline
plt.style.use('fivethirtyeight')

2. Read in the hanford.csv file



In [14]:

    
df = pd.read_csv("~/Documents/LEDE/algorithms/class6/data/hanford.csv")



In [17]:

    
df

3. Calculate the basic descriptive statistics on the data



In [15]:

    
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 [22]:

    
r = df.corr()
r**2









    Out[22]:






  
    
      
      Exposure
      Mortality
    
  
  
    
      Exposure
      1.000000
      0.858115
    
    
      Mortality
      0.858115
      1.000000



In [16]:

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









    Out[16]:





<matplotlib.axes._subplots.AxesSubplot at 0x10b5605c0>

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



In [23]:

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



In [24]:

    
lm.params









    Out[24]:





Intercept    114.715631
Exposure       9.231456
dtype: float64



In [25]:

    
intercept, slope = lm.params

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



In [26]:

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









    Out[26]:





[<matplotlib.lines.Line2D at 0x10b618358>]

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



In [27]:

    
def mortality_predictor(exposure):
    return slope*float(exposure)+intercept



In [29]:

    
mortality_predictor(10)









    Out[29]:





207.03019352841989



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