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
import matplotlib.pyplot as plt # package for doing plotting (necessary for adding the line)
import statsmodels.formula.api as smf # package we'll be using for linear regression

2. Read in the hanford.csv file



In [3]:

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

3. Calculate the basic descriptive statistics on the data



In [5]:

    
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 [6]:

    
df.corr()









    Out[6]:






  
    
      
      Exposure
      Mortality
    
  
  
    
      Exposure
      1.000000
      0.926345
    
    
      Mortality
      0.926345
      1.000000

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() #notice the formula regresses Y on X (Y~X)
intercept,slope=lm.params
lm.params









    Out[9]:





Intercept    114.715631
Exposure       9.231456
dtype: float64

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



In [10]:

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









    Out[10]:





[<matplotlib.lines.Line2D at 0x11281be80>]

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



In [11]:

    
#y=mx+b
mortality=intercept*10+114.715631



In [12]:

    
mortality









    Out[12]:





1261.8719392078594



In [ ]:

	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