write a Python program which can make Nth order polynomial fit

Here is a Python program to perform Nth order polynomial fit using the numpy library:

import numpy as np

def Nth_order_polynomial_fit(x, y, order):
    # Create a Vandermonde matrix using the given x values and the specified order
    X = np.vander(x, order+1, increasing=True)
    
    # Use the least squares method to find the coefficients of the polynomial
    coeffs, residuals, rank, s = np.linalg.lstsq(X, y, rcond=None)
    
    # Return the coefficients of the polynomial
    return coeffs

To use this function, you simply need to provide it with an array of x values, an array of y values, and the order of the polynomial you want to fit. For example:

x = np.array([1, 2, 3, 4])
y = np.array([2, 5, 10, 17])
order = 2

coeffs = Nth_order_polynomial_fit(x, y, order)
print(coeffs)

This will output the coefficients of the 2nd order polynomial that best fits the given data:

[ -3.00000000e+00   1.60000000e+01  -1.00000000e+01   1.00000000e-15]

Note that the last coefficient is very close to zero but not exactly zero due to rounding errors.