Linear regression of nonlinear function

gantovnik

6 years ago

import os
import matplotlib.pyplot as plt
import numpy as np
import math
os.chdir('/home/vg/Downloads/projects/ex10')
os.getcwd()
plt.figure(figsize=(10,8)) 
N = 100
start = 0
end = 2
A = np.random.rand() + 0.5
B = np.random.rand()
x = np.linspace(start,end,N)
y = B*np.exp(A*x)
y = y + np.random.randn(N)/5
p = np.polyfit(x,np.log(y),1)
plt.plot(x,y,'o',label='Given data: A=%.2f. B=%.2f' % (A,np.exp(B)))
plt.plot(x,np.exp(np.polyval(p,x)),'-',label='Linear regression: A=%.2f. B=%.2f' % (p[0],np.exp(p[1])))
plt.legend(loc='best')
plt.grid()
plt.title('Linear regression, $y=Be^{Ax}$')
plt.savefig("example10.png", dpi=100)
plt.show()
plt.close()

<img class="  wp-image-69 aligncenter" src="https://gantovnik.com/bio-tips/wp-content/uploads/2018/12/example10.png" alt="example10" width="606" height="485" />

import os

import matplotlib.pyplot as plt

import numpy as np

import math

os.chdir('/home/vg/Downloads/projects/ex10')

os.getcwd()

plt.figure(figsize=(10,8))

N = 100

start = 0

end = 2

A = np.random.rand() + 0.5

B = np.random.rand()

x = np.linspace(start,end,N)

y = B*np.exp(A*x)

y = y + np.random.randn(N)/5

p = np.polyfit(x,np.log(y),1)

plt.plot(x,y,'o',label='Given data: A=%.2f. B=%.2f' % (A,np.exp(B)))

plt.plot(x,np.exp(np.polyval(p,x)),'-',label='Linear regression: A=%.2f. B=%.2f' % (p[0],np.exp(p[1])))

plt.legend(loc='best')

plt.grid()

plt.title('Linear regression, $y=Be^{Ax}$')

plt.savefig("example10.png", dpi=100)

plt.show()

plt.close()

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