Confusion with np.polyfit and unexpected coefficients in higher-degree polynomial fitting with NumPy 1.24.1
I'm maintaining legacy code that Quick question that's been bugging me - I'm wondering if anyone has experience with Hey everyone, I'm running into an issue that's driving me crazy... I've been banging my head against this for hours. I'm relatively new to this, so bear with me... I've been trying to fit a higher-degree polynomial to a set of data points using `np.polyfit`, but I'm getting coefficients that don't seem to represent the underlying trend of my data correctly. For instance, using a degree of 5 with my dataset produces coefficients that oscillate wildly, which I didn't expect. Here's the code I'm using: ```python import numpy as np import matplotlib.pyplot as plt # Sample data x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) y = np.array([2.1, 3.9, 6.5, 8.2, 10.0, 12.7, 14.5, 17.4, 20.1, 25.0]) # Fit a 5th degree polynomial degree = 5 coefficients = np.polyfit(x, y, degree) # Generate polynomial function from coefficients poly_func = np.poly1d(coefficients) # Predict values y_fit = poly_func(x) # Plotting the results plt.scatter(x, y, color='red', label='Data points') plt.plot(x, y_fit, label='5th Degree Polynomial Fit') plt.legend() plt.show() ``` The coefficients I get from `np.polyfit` are: ```python print(coefficients) ``` This outputs something like: ``` [-1.2, 7.4, -13.1, 10.0, -2.9, 0.1] ``` This just doesn’t seem to fit my data well at all, and the resulting polynomial looks like it has a lot of wiggles. I've already tried reducing the degree to 3, which gives better results, but I'm curious why the 5th degree polynomial behaves so poorly. Is it possible that my data isn’t suitable for such a high-degree polynomial, or am I missing something fundamental about how `np.polyfit` works? I've also checked the documentation but couldn't find a clear explanation on this behavior. Any insights would be greatly appreciated! My development environment is Windows. How would you solve this? For context: I'm using Python on Ubuntu. Has anyone else encountered this? Any ideas what could be causing this? This is happening in both development and production on Windows 10. Could someone point me to the right documentation? Is there a better approach?