Inconsistent results when using np.polyfit on large datasets with high-degree polynomials in NumPy 1.25
I've tried everything I can think of but I've tried everything I can think of but I'm experiencing some unexpected behavior when using `np.polyfit` on large datasets with high-degree polynomials. When fitting a polynomial of degree 10 to my dataset (which consists of 10,000 points), the coefficients returned sometimes lead to very high errors during prediction. I've tried using `np.polyval` to compute the fitted values and compare them against the original data, but the results seem heavily influenced by outliers, and I'm not sure if the fit is reasonable. Here’s a code snippet of what I’m doing: ```python import numpy as np import matplotlib.pyplot as plt # Generate some synthetic data with noise np.random.seed(0) x = np.linspace(0, 10, 10000) y = 0.5 * x**10 - 30 * x**5 + np.random.normal(0, 10, x.size) # Fit a polynomial of degree 10 coeffs = np.polyfit(x, y, 10) # Predict using the fitted polynomial fitted_y = np.polyval(coeffs, x) # Plot the original data and the fitted polynomial plt.scatter(x, y, s=1, color='blue', label='Data') plt.plot(x, fitted_y, color='red', label='Fitted polynomial') plt.legend() plt.show() ``` While the plot looks decent at first glance, the residuals are quite large, and sometimes the fit seems to oscillate dramatically, which I suspect is a result of the high degree. I tried using lower degrees, and while that improves the residuals, it doesn't capture the underlying data well. Is there a best practice for dealing with high-degree polynomial fits in NumPy, especially on larger datasets like this? Am I missing something in my approach, or is there a configuration I should consider to improve the fitting accuracy? The project is a web app built with Python. Thanks, I really appreciate it! I'm coming from a different tech stack and learning Python. What's the correct way to implement this?