# 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.