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



In [2]:

    
import pandas as pd
%matplotlib inline



In [3]:

    
import matplotlib.pyplot as plt
import statsmodels.formula.api as smf

2. Read in the hanford.csv file



In [4]:

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



In [5]:

    
df.head()









    Out[5]:






  
    
      
      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



In [6]:

    
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 [7]:

    
df.corr()









    Out[7]:






  
    
      
      Exposure
      Mortality
    
  
  
    
      Exposure
      1.000000
      0.926345
    
    
      Mortality
      0.926345
      1.000000

There seems to be a highly positive correlation between both variables, as shown by the coefficient of correlation, which equals 0.92.



In [8]:

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









    Out[8]:





<matplotlib.axes._subplots.AxesSubplot at 0x10d570320>

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



In [9]:

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



In [17]:

    
lm.params









    Out[17]:





Intercept    114.715631
Exposure       9.231456
dtype: float64



In [18]:

    
intercept, slope = lm.params



In [19]:

    
def mortality_rate(exposure):
    for item in df['Exposure']:
        mortality = exposure * slope + intercept
    return mortality



In [20]:

    
mortality_rate(3)









    Out[20]:





142.4099996330761

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



In [13]:

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









    Out[13]:





[<matplotlib.lines.Line2D at 0x10d632940>]



In [14]:

    
det_corr = (df.corr())* (df.corr())



In [15]:

    
det_corr









    Out[15]:






  
    
      
      Exposure
      Mortality
    
  
  
    
      Exposure
      1.000000
      0.858115
    
    
      Mortality
      0.858115
      1.000000

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



In [16]:

    
mortality_rate(10)









    Out[16]:





207.03019352841989

	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

	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