Parametric Estimation for Multivariate Polynomial Regression

Say we have a dataset with 2 features and it cannot be fit using Linear Regression.

We may want to use Multivariate Polynomial Regression. The equation is given by:

$g(x_2,x_1|w_5,w_4,w_3,w_2,w_1,w_0) = w_5x_2^2+w_4x_1^2+w_3x_1x_2+w_2x_2+w_1x_1+w_0$

This is a degree 2 polynomial and we need to estimate $w_5,w_4,w_3,w_2,w_1,w_0$ that minimize the squared error.

Note: In some cases, this can be simplified to a Linear Regression (as shown in Simple Polynomial Regression) by simply adding appropriate features to the dataset.