Write a Python program which takes any data set (1, 1), (2, 92),... (N, YN) and computes the best fit polynomial P(x) = a + a₁ + a₂x² +...+akak, for any polynomial order K. I have provided codes that do this for K = 1 (linear best fit), K = 2 (quadratic best fit), and K = 4 (quartic best fit).
Write a Python program which takes any data set (1, 1), (2, 92),... (N, YN) and computes the best fit polynomial P(x) = a + a₁ + a₂x² +...+akak, for any polynomial order K. I have provided codes that do this for K = 1 (linear best fit), K = 2 (quadratic best fit), and K = 4 (quartic best fit).
Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Transcribed Image Text:Write a Python program which takes any data set
(1, 1), (2, y2),... (*N, YN)
and computes the best fit polynomial
P(x)= a + a₁ + a₂x² + ....
+akak,
for any polynomial order K. I have provided codes that do this for K = 1
(linear best fit), K = 2 (quadratic best fit), and K = 4 (quartic best fit).
You need to generalize this code to work for any K.
![import time
import math
import matplotlib.pyplot as plt
import numpy as np
#def f(x):
#
return 1.76 *x + 2.5
def f(x):
return 2*x**4 - 0.5*x**3 + 0.5*x**2 - x + 0.25
N = 7
a = -2
b = 2
step = (b-a)/N
X = np.linspace(a, b, N)
Y = np.zeros (N)
the_random_noise = np.random.random (N)
for n in range (0,N):
X[n]X[n] +
((-1) **n) *0.1*step*the_random_noise[n]
for n in range (0,N):
Y[n] = f(X[n]) +
((-1) **n) *0.5*the_random_noise[n]
#Try quartic best fit: K = 4 (5 equations in 5
unknowns a0, al, a2, a3, a4):
# N = 7 Data points
b0= 0
O O O O O
b1 = 0
b2 =
b3
b4
0
A1 = 0
A2 = 0
A3 = 0
A4 = 0
0
= 0
=
A5 = 0
A6 = 0
A7 = 0
A8 = 0
for i in range(0, N):
b0b0 + Y[i]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34c2a7c6-20d8-45e7-8c90-b1c224068cda%2F05283407-679d-40f4-9152-835048e9905c%2F1orwq8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:import time
import math
import matplotlib.pyplot as plt
import numpy as np
#def f(x):
#
return 1.76 *x + 2.5
def f(x):
return 2*x**4 - 0.5*x**3 + 0.5*x**2 - x + 0.25
N = 7
a = -2
b = 2
step = (b-a)/N
X = np.linspace(a, b, N)
Y = np.zeros (N)
the_random_noise = np.random.random (N)
for n in range (0,N):
X[n]X[n] +
((-1) **n) *0.1*step*the_random_noise[n]
for n in range (0,N):
Y[n] = f(X[n]) +
((-1) **n) *0.5*the_random_noise[n]
#Try quartic best fit: K = 4 (5 equations in 5
unknowns a0, al, a2, a3, a4):
# N = 7 Data points
b0= 0
O O O O O
b1 = 0
b2 =
b3
b4
0
A1 = 0
A2 = 0
A3 = 0
A4 = 0
0
= 0
=
A5 = 0
A6 = 0
A7 = 0
A8 = 0
for i in range(0, N):
b0b0 + Y[i]
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