#polynomial-regression

Inputs are uniform on the square $[-1, 1]^2$ and $y \sim \mathcal{N}(x_1^3 x_2^5 - 10x_1x_2 + 7x_1^2 + 5x_2 - 3,\; 1)$. Least-squares models with all polynomial features up to order 1, 2, 8 and 10 are each trained on $n = 20$ points. Which one typically has the lowest test error?