Write a Python program which takes any data set (x1, y₁), (2, y2),... (*N, YN) and computes the best fit polynomial P(x)= ao+ar+a₂²+...+ akak, for any polynomial order K. I have provided codes that do this for K=1
Write a Python program which takes any data set (x1, y₁), (2, y2),... (*N, YN) and computes the best fit polynomial P(x)= ao+ar+a₂²+...+ akak, for any polynomial order K. I have provided codes that do this for K=1
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
Related questions
Question
Please use best fit on python and show codes
![```python
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 1.76*x*x + 2.5
N = 25
a = -5
b = 8
step = (b-a)/N
the_x_values = np.linspace(a, b, N)
the_y_values = np.zeros(N)
the_random_noise = np.random.random(N)
for n in range(0, N):
the_x_values[n] = the_x_values[n] + ((-1)**n)*0.1*step*the_random_noise[n]
for n in range(0, N):
the_y_values[n] = f(the_x_values[n]) + ((-1)**n)*0.25*the_random_noise[n]
a11 = 0
a12 = 0
b1 = 0
b2 = 0
for n in range(N):
a11 = a11 + the_x_values[n]**2
a12 = a12 + the_x_values[n]
b1 = b1 + the_x_values[n]*the_y_values[n]
b2 = b2 + the_y_values[n]
A = np.array([[a11, a12], [a12, N]])
b = np.array([b1, b2])
tic = time.time()
mb = np.linalg.solve(A, b)
toc = time.time()
```
### Explanation:
This code is used to approximate the parameters of a linear function through a least squares fitting. Here's a detailed breakdown:
1. **Imports:**
- `time`, `math`: Basic libraries for time measurement and mathematical operations.
- `matplotlib.pyplot as plt`: For plotting graphs (though not used in the code).
- `numpy as np`: A powerful numerical computing library.
2. **Function Definition:**
- `f(x)`: Defines a linear function \( f(x) = 1.76x + 2.5 \).
- A quadratic function variant is commented out.
3. **Initialization:**
- \( N = 25 \): Number of data points.
- \( a = -5, b = 8 \): Defines the range for x-values.
- `step`: The increment between x-values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34c2a7c6-20d8-45e7-8c90-b1c224068cda%2Ff3649969-7b38-46d7-8377-0652d0f70946%2Fahktgm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:```python
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 1.76*x*x + 2.5
N = 25
a = -5
b = 8
step = (b-a)/N
the_x_values = np.linspace(a, b, N)
the_y_values = np.zeros(N)
the_random_noise = np.random.random(N)
for n in range(0, N):
the_x_values[n] = the_x_values[n] + ((-1)**n)*0.1*step*the_random_noise[n]
for n in range(0, N):
the_y_values[n] = f(the_x_values[n]) + ((-1)**n)*0.25*the_random_noise[n]
a11 = 0
a12 = 0
b1 = 0
b2 = 0
for n in range(N):
a11 = a11 + the_x_values[n]**2
a12 = a12 + the_x_values[n]
b1 = b1 + the_x_values[n]*the_y_values[n]
b2 = b2 + the_y_values[n]
A = np.array([[a11, a12], [a12, N]])
b = np.array([b1, b2])
tic = time.time()
mb = np.linalg.solve(A, b)
toc = time.time()
```
### Explanation:
This code is used to approximate the parameters of a linear function through a least squares fitting. Here's a detailed breakdown:
1. **Imports:**
- `time`, `math`: Basic libraries for time measurement and mathematical operations.
- `matplotlib.pyplot as plt`: For plotting graphs (though not used in the code).
- `numpy as np`: A powerful numerical computing library.
2. **Function Definition:**
- `f(x)`: Defines a linear function \( f(x) = 1.76x + 2.5 \).
- A quadratic function variant is commented out.
3. **Initialization:**
- \( N = 25 \): Number of data points.
- \( a = -5, b = 8 \): Defines the range for x-values.
- `step`: The increment between x-values.
![**Title: Creating a Python Program for Best Fit Polynomial**
In this educational guide, you will learn how to write a Python program that can handle any given dataset:
\[
(x_1, y_1), (x_2, y_2), \ldots, (x_N, y_N)
\]
The program is designed to compute the best fit polynomial:
\[
P(x) = a_0 + a_1x + a_2x^2 + \ldots + a_Kx^K
\]
for any polynomial order \( K \). Sample code provided covers the case where \( K = 1 \).
**Explanation of Concepts:**
- **Dataset:** A collection of points \((x_i, y_i)\) representing your data.
- **Best Fit Polynomial:** A polynomial function that approximates the trend of the data points.
- **Polynomial Order \( K \):** Determines the degree of the polynomial, dictating its curvature and the number of coefficients \((a_0, a_1, \ldots, a_K)\).
By following this guide, you will gain a foundational understanding of creating algorithms for polynomial regression in Python, enabling your dataset analysis and prediction capabilities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34c2a7c6-20d8-45e7-8c90-b1c224068cda%2Ff3649969-7b38-46d7-8377-0652d0f70946%2F72f0gw3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Creating a Python Program for Best Fit Polynomial**
In this educational guide, you will learn how to write a Python program that can handle any given dataset:
\[
(x_1, y_1), (x_2, y_2), \ldots, (x_N, y_N)
\]
The program is designed to compute the best fit polynomial:
\[
P(x) = a_0 + a_1x + a_2x^2 + \ldots + a_Kx^K
\]
for any polynomial order \( K \). Sample code provided covers the case where \( K = 1 \).
**Explanation of Concepts:**
- **Dataset:** A collection of points \((x_i, y_i)\) representing your data.
- **Best Fit Polynomial:** A polynomial function that approximates the trend of the data points.
- **Polynomial Order \( K \):** Determines the degree of the polynomial, dictating its curvature and the number of coefficients \((a_0, a_1, \ldots, a_K)\).
By following this guide, you will gain a foundational understanding of creating algorithms for polynomial regression in Python, enabling your dataset analysis and prediction capabilities.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY