meyers hw 12.ipynb

Kernel: SageMath 8.2

import pandas as pd

df = pd.Series({'Year': [1994,1995,1996,1997,1998,1999,2000,2001,2002,2003], "bbl/day*10^6": [67.052,68.008,69.803,72.024,73.400,72063,74.669,74.487,74.065,76.777]})

A = [1994,1995,1996,1997,1998,1999,2000,2001,2002,2003]
b = [67.052,68.008,69.803,72.024,73.400,72063,74.669,74.487,74.065,76.777]
show(df)

import numpy as np

c1, c2, c3, c4, c5, c6, c7, c8, c9, c10 = np.polyfit(A,b,9)
t = var('t')

f(t) = c10*t^9+c9*t^8+c8*t^7+c7*t^6+c6*t^5+c5*t^4+c4*t^3+c3*t^2+c2*t+c1
print "D-9 Esitmation for 2010: ", f(2010)
plot(c1*t^9+c2*t^8+c3*t^7+c4*t^6+c5*t^5+c6*t^4+c7*t^3+c8*t^2+c9*t+c10, (t,1990,2020))

/ext/sage/sage-8.2/local/lib/python2.7/site-packages/sage/repl/ipython_kernel/__main__.py:11: RankWarning: Polyfit may be poorly conditioned

D-9 Esitmation for 2010:  1.0185356829006386e+44

It appears that the D-9 polynomial is a bad fit because of the Runge phenomenon. A linear regression would be more appropriate.