👀 Views: 458 💬 Answers: 1 📅 Created: 2025-06-23

numpy data-fitting polynomial-regression Python

I'm testing a new approach and I've been working on this all day and I'm working on a personal project and I'm trying to fit a polynomial to a noisy dataset using `np.polyfit`. However, the coefficients returned seem to be off, especially when I increase the degree of the polynomial. For example, when fitting a second-degree polynomial to my data, I expected the coefficients to reflect the underlying quadratic trend, but they are significantly distorted by the noise in the data. Here’s a simplified version of my code: ```python import numpy as np import matplotlib.pyplot as plt # Generating synthetic data np.random.seed(0) x = np.linspace(0, 10, 50) y = 0.5 * x**2 + np.random.normal(0, 5, x.size) # Noisy quadratic data # Fitting a second-degree polynomial coeffs = np.polyfit(x, y, 2) print('Coefficients:', coeffs) # Expecting something close to [0.5, 0, 0] but got [1.2, -0.3, 5.5] # Plotting plt.scatter(x, y, label='Data') plt.plot(x, np.polyval(coeffs, x), color='red', label='Fitted polynomial') plt.legend() plt.show() ``` I’ve tried several things, such as increasing the sample size and adjusting the noise level, but the coefficients remain inconsistent. Additionally, when I lower the degree to 1, the linear fit seems to converge correctly, yet when I switch back to degree 2, the results are still off. Is there a way to improve the fitting process or handle the noise better? Any insights on best practices for polynomial fitting in NumPy would be greatly appreciated! This is part of a larger application I'm building. Has anyone else encountered this? The stack includes Python and several other technologies. I'd love to hear your thoughts on this.