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



In [26]:

    
import pandas as pd
import pandas as pd
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
%matplotlib inline

2. Read in the hanford.csv file



In [3]:

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

County: Name of county

Exposuere: Inde of exposure

Mortality: Cancer mortality per 100000 man-years



In [5]:

    
df

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 [14]:

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









    



           Exposure  Mortality
Exposure   1.000000   0.926345
Mortality  0.926345   1.000000






    Out[14]:





<matplotlib.axes._subplots.AxesSubplot at 0x7fc47a145fd0>

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
intercept, height = lm.params

# Function using the built math. 
def simplest_predictor(exposure, height, intercept):
    height = float(height)
    intercept = float(intercept)
    exposure = float(exposure)
    return height*exposure+intercept



In [22]:

    
# Input the data
exposure = input("Please enter the exposure: ")
print("The mortality rate for your exposure lies at", simplest_predictor(exposure,height,intercept), ".")









    



Please enter the exposure: 5
The mortality rate for your exposure lies at 160.8729121746029 .

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



In [24]:

    
df.plot(kind="scatter",x="Exposure",y="Mortality")
plt.plot(df["Exposure"],height*df["Exposure"]+intercept,"-",color="darkgrey") #we create the best fit line from the values in the fit model









    Out[24]:





[<matplotlib.lines.Line2D at 0x7fc47a018b38>]

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



In [ ]:

    
def predictiong_mortality_rate(exposure):
    return intercept + float()

	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