Question 2: Kernel regression with a polynomial kernel is applied on …

Kernel regression with a polynomial kernel is applied on the following dataset with two features:

$X = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix}, \qquad y = [2, 1, 2]^T$

Weight vector can be written as $w = \phi(X)\alpha$, where $\phi$ is the transformation mapping corresponding to the kernel $k(x_i, x_j) = (1 + x_i^T x_j)^2$. The vector $\alpha$ is given by $(K)^{-1}y$, where $K$ is the kernel matrix.

Based on the above data, answer the given subquestions.