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



In [20]:

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

2. Read in the hanford.csv file



In [21]:

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

3. Calculate the basic descriptive statistics on the data



In [22]:

    
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 [23]:

    
df.corr()









    Out[23]:






  
    
      
      Exposure
      Mortality
    
  
  
    
      Exposure
      1.000000
      0.926345
    
    
      Mortality
      0.926345
      1.000000

r = 0.926345



In [24]:

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









    Out[24]:





Intercept    114.715631
Exposure       9.231456
dtype: float64



In [25]:

    
intercept, slope = lm.params



In [26]:

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









    Out[26]:





<matplotlib.axes._subplots.AxesSubplot at 0x10c047eb8>

Yes, there does seem to be a correlation 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 [31]:

    
exposure = int(input('What is the exposure level? '))
mortality = slope * exposure + intercept
print('If the exposure is ' + str(exposure) + ' the mortality rate is probably around ' + str(round(mortality, 2)))









    



What is the exposure level? 4
If the exposure is 4 the mortality rate is probably around 151.64

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



In [28]:

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

plt.title('Correlation between exposure and mortality rate')
plt.xlabel('Exposure')
plt.ylabel('Mortality Rate')









    Out[28]:





<matplotlib.text.Text at 0x110abc470>



In [ ]:

    
0.926345 ** 2

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



In [30]:

    
exposure = 10
mortality = slope * exposure + intercept
print('If the exposure is ' + str(exposure) + ' the mortality rate is probably around ' + str(round(mortality, 2)))









    



If the exposure is 10 the mortality rate is probably around 207.03

	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