Equation with summation - regression plotting - pgfplots

I am trying to 3D plot the below equation in tikz.

I have basic premise setup like this, with sample set as datatable.

\documentclass{article}\usepackage{pgfplots}\pgfplotsset{compat=1.15}\begin{document}% sample points\pgfplotstableread{X Y Z m2.2 14 0 02.7 23 0 03 13 0 03.55 22 0 04 15 0 04.5 20 0 04.75 28 0 05.5 23 0 0}\datatablet% Trying to recreate gnuplot here% https://en.wikipedia.org/wiki/Partial_derivative\begin{tikzpicture}\begin{axis}[    grid=both,    ztick={0,4,...,10},    zmin = 0, zmax = 10,    point meta min=0,     point meta max=10,    colormap/cool,    view={30}{30}  %tune here to change viewing angle    ]    \addplot3[surf,shader=faceted, domain=-2:2] {(x - y)^2};    \end{axis}\end{tikzpicture}\end{document}

What is confusing me is, the summation part on RHS. How do I compute that? For each x and y value, I need to take table entry one after one, compute, sum up and then proceed for plotting. I could not think of a simple for loop scenario to do this. Kindly help.

Below is the expected image (this was drawn using python):

Here is a simple document on how I constructed it in python if it could be hlepful (especially for that looping and summation part)