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



In [1]:

    
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









    



/usr/local/lib/python3.5/site-packages/matplotlib/__init__.py:1035: UserWarning: Duplicate key in file "/Users/mercybenzaquen/.matplotlib/matplotlibrc", line #2
  (fname, cnt))

2. Read in the hanford.csv file



In [2]:

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

3. Calculate the basic descriptive statistics on the data



In [3]:

    
df.mean()









    Out[3]:





Exposure       4.617778
Mortality    157.344444
dtype: float64



In [4]:

    
df.median()









    Out[4]:





Exposure       3.41
Mortality    147.10
dtype: float64



In [5]:

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









    Out[5]:





Exposure      3.92
Mortality    47.80
dtype: float64



In [6]:

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









    Out[6]:





Exposure      12.29
Mortality    249.60
dtype: float64



In [8]:

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









    Out[8]:





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 [9]:

    
df.corr()









    Out[9]:






  
    
      
      Exposure
      Mortality
    
  
  
    
      Exposure
      1.000000
      0.926345
    
    
      Mortality
      0.926345
      1.000000



In [10]:

    
df



In [16]:

    
#fig, ax = plt.subplots()
ax= df.plot(kind='scatter', y='Exposure', x='Mortality', color='green', figsize= (7,5))
ax









    Out[16]:





<matplotlib.axes._subplots.AxesSubplot at 0x108975c50>

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

# y = ß0 + ß1x Here: y: is the variable that we want to predict ß0: is intercept of the regression line i.e. value of y when x is 0 ß1: is coefficient of x i.e. variation in y with change in value of x x: Variables that affects value of y i.e. already know variable whose effect we want to se on values of y



In [17]:

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



In [20]:

    
lm.params









    Out[20]:





Intercept    114.715631
Exposure       9.231456
dtype: float64



In [21]:

    
def mortality_rate_calculator(exposure): 
    return (114.715631 + (9.231456 * float(exposure)))



In [23]:

    
df['predicted_mortality_rate'] = df['Exposure'].apply(mortality_rate_calculator)
df









    Out[23]:






  
    
      
      County
      Exposure
      Mortality
      predicted_mortality_rate
    
  
  
    
      0
      Umatilla
      2.49
      147.1
      137.701956
    
    
      1
      Morrow
      2.57
      130.1
      138.440473
    
    
      2
      Gilliam
      3.41
      129.9
      146.194896
    
    
      3
      Sherman
      1.25
      113.5
      126.254951
    
    
      4
      Wasco
      1.62
      137.5
      129.670590
    
    
      5
      HoodRiver
      3.83
      162.3
      150.072107
    
    
      6
      Portland
      11.64
      207.5
      222.169779
    
    
      7
      Columbia
      6.41
      177.9
      173.889264
    
    
      8
      Clatsop
      8.34
      210.3
      191.705974

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



In [26]:

    
intercept, slope = lm.params



In [ ]:

    
#DONT KNOW WHAT HAPPENED HERE :S



In [31]:

    
df.plot(kind='scatter', y='Exposure', x='Mortality', color='green', figsize= (7,5))

plt.plot(df["Exposure"],slope *df["Exposure"]+ intercept,"-",color="red")









    Out[31]:





[<matplotlib.lines.Line2D at 0x1090a48d0>]

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



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