11.20

import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as plt

num_year = len(year)
one_years = np.ones(num_year)

xy, x, y, x2 = 0,0,0,0
A = np.vstack([year,one_years]).T
for i in range(num_year):
    x += year[i]
    x2 += year[i]**2
    y += percent [i]
    xy = percent[i]*year[i]

c1, c0 = np.linalg.lstsq(A, percent)[0]

plt.scatter(year, percent)
plt.plot(year, c1*year + c0)
plt.xlabel (" x axis")
plt.ylabel("y axis")
plt.title("graph ")


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11.21

import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as plt

A = np.array([1+0*year,year,year**2]).T

c0, c1, c2 = np.linalg.lstsq(A, percent)[0]

plt.scatter(year, percent)
plt.plot(year, c2*year**2 + c1*year + c0)
plt.xlabel (" x axis")
plt.ylabel("y axis")
plt.title("graph ")

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11.22

import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as pt

y_log = np.log(y)
coeffs = np.polyfit(x,y_log,1)
c1 = coeffs[0]
c0 =np.exp(coeffs[1])
pt.plot(xp, coeffs[0]*np.exp(coeffs[1]*xp))
pt.plot(x, y, "o")