Exercise 02.1

Create a function that receives two inputs a and b, and returns the product of the a decimal of pi and the b decimal of pi.

i.e, 
pi = 3.14159
if a = 2 and b = 4
result = 4 * 5
result = 20

Caveats:

a and b are between 1 and 15
decimals positions 1 and 2 are 1 and 4, respectively. (remember that python start indexing in 0)



In [ ]:

    
from math import pi
def mult_dec_pi(a, b):
    
    # Add the solution here
    
    result = ''
    return result



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mult_dec_pi(a=2, b=4)
# 20.0



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mult_dec_pi(a=5, b=10)
# 45.0



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mult_dec_pi(a=14, b=1)
# 9.0



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mult_dec_pi(a=6, b=8)
# 10.0



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# Bonus
mult_dec_pi(a=16, b=4)
# 'Error'

Exercise 02.2

Using the given dataset. Estimate a linear regression between Employed and GNP.

$$Employed = b_0 + b_1 * GNP $$$$\hat b = (X^TX)^{-1}X^TY$$$$Y = Employed$$$$X = [1 \quad GNP]$$



In [1]:

    
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
# Import data
raw_data = """
Year,Employed,GNP
1947,60.323,234.289
1948,61.122,259.426
1949,60.171,258.054
1950,61.187,284.599
1951,63.221,328.975
1952,63.639,346.999
1953,64.989,365.385
1954,63.761,363.112
1955,66.019,397.469
1956,67.857,419.18
1957,68.169,442.769
1958,66.513,444.546
1959,68.655,482.704
1960,69.564,502.601
1961,69.331,518.173
1962,70.551,554.894"""

data = []
for line in raw_data.splitlines()[2:]:
    words = line.split(',')
    data.append(words)
data = np.array(data, dtype=np.float)
n_obs = data.shape[0]
plt.plot(data[:, 2], data[:, 1], 'bo')
plt.xlabel("GNP")
plt.ylabel("Employed")









    Out[1]:





<matplotlib.text.Text at 0x7fa5f2357a20>



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