meyers hw 11.ipynb

Kernel: SageMath 8.2

import numpy as np
A = np.array([1960,1970,1990,2000])
show('Years = ', A)

b = np.array([[3039585530],[3707475887],[5281653820],[6079603571]])
show('Population = ', b)

linear = ((b[2]+b[1])/2)[0]
show ('Linear Estimate is: ', linear)

c1, c2, c3 = np.polyfit(A,b, 2)
show("Quadratic Estimation is: ",int(c3+c2*1980+c1*1980^2) )

linear/ (c3+c2*1980+c1*1980^2)

array([ 1.00484621])

c1, c2, c3, c4 = np.polyfit(A,b, 3)
show("Degree 3 Estimation is: ", int(c4+c3*1980+c2*1980^2+c1*1980^3) )

The Quadratic and 3-rd degree Polynomial estimations were equally as accurate and fit more closely to the measured value of 4.4e9

def interpret(x, y, degree):
    return np.polyfit(x,y,degree)
interpret(A,b,3)

array([[ -9.02815208e+03],
       [  5.38439890e+07],
       [ -1.06960683e+11],
       [  7.07767052e+13]])