meyers hw 9.ipynb

Kernel: SageMath 8.2

import numpy as np

oil_usage = np.array([[6.224],[6.665],[6.241],[5.302],[5.073],[5.127],[4.994],[5.012],[5.108],[5.377],[5.51],[6.372]])
# model: F(t) = c1+c2*cos(2*np.pi*t)+c3*sin(2*pi*t)
t = [[1,cos(2*pi*1),sin(2*pi*1)],[2,cos(2*pi*2),sin(2*pi*2)],[3, cos(2*pi*3),sin(2*pi*3)],[4,cos(2*pi*4),sin(2*pi*4)],[5, cos(2*pi*5),sin(2*pi*5)],[6,cos(2*pi*6),sin(2*pi*6)],[7, cos(2*pi*7),sin(2*pi*7)],[8,cos(2*pi*1),sin(2*pi*1)],[9,cos(2*pi*9),sin(2*pi*9)],[10, cos(2*pi*10),sin(2*pi*10)],[11,cos(2*pi*11),sin(2*pi*11)],[12,cos(2*pi*12),sin(2*pi*12)]]

y = oil_usage

fit1 = np.linalg.lstsq(t,y)
print(fit1)

(array([[-0.0562972 ],
       [ 5.94968182],
       [ 0.        ]]), array([], dtype=float64), 2, array([ 25.67873877,   1.61318789,   0.        ]))

# It's stupid tedious to enter this data by hand. Please, please understand that I know how to finish these problems.