This is more of a numerical methods question. Hopefully, this is the right stackexchange board to post this question.
I am wondering if anyone is aware of the order of accuracy of using least squares to compute gradients, numerically, using the Linear basis:
$\phi = \begin{bmatrix} 1 & x & y & z \end{bmatrix}$
and
Quadratic basis: $\phi = \begin{bmatrix} 1 & x & y & z & xy & xz & yz & x^2 & y^2 & z^2 \end{bmatrix}$
With other schemes such as finite difference, I can just plug in taylor series approximations, and look at the truncation error to determine the theoretical order of accuracy, but I am not sure how to go about doing this with least squares.