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



In [1]:

    
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
import statsmodels.formula.api as smf

2. Read in the hanford.csv file



In [3]:

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

3. Calculate the basic descriptive statistics on the data



In [4]:

    
df.describe()



In [7]:

    
iqr = df.quantile(q=0.75) - df.quantile(q=0.25)
iqr









    Out[7]:





Exposure      3.92
Mortality    47.80
dtype: float64



In [9]:

    
ual = df.quantile(q=0.75) + (iqr * 1.5)
ual









    Out[9]:





Exposure      12.29
Mortality    249.60
dtype: float64



In [10]:

    
lal = df.quantile(q=0.25) - (iqr * 1.5)
lal









    Out[10]:





Exposure     -3.39
Mortality    58.40
dtype: float64

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

Yes, it seems very much so that there's a correlation worth to be investigated

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



In [21]:

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









    Out[21]:





Intercept    114.715631
Exposure       9.231456
dtype: float64



In [22]:

    
intercept, slope = lm.params



In [17]:

    
exposure_input = input("Type in an exposre you'd like to know the mortality for:")
if exposure_input:
    prediction = (float(lm.params['Exposure']) * float(exposure_input)) + (float(lm.params['Intercept']))
    print(prediction)









    



Type in an exposre you'd like to know the mortality for:4
151.6414559038395

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



In [24]:

    
fig, ax = plt.subplots(figsize=(7,7))
plt.style.use('ggplot')

ax = df.plot(ax = ax, kind= 'scatter', x = 'Exposure', y = 'Mortality')
plt.plot(df['Exposure'],slope*df['Exposure']+intercept, color="red", linewidth=2)









    Out[24]:





[<matplotlib.lines.Line2D at 0x1140b0cf8>]



In [25]:

    
r = df.corr()['Exposure']['Mortality']
r









    Out[25]:





0.92634482071736912



In [27]:

    
coefficient_determination = r **2
coefficient_determination









    Out[27]:





0.85811472686989476

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



In [30]:

    
prediction = (float(lm.params['Exposure']) * 10 + (float(lm.params['Intercept'])))
print(prediction)









    



207.03019352841983



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