The Feature That Correlation Cannot See

A dataset consists of exactly these five $(x, y)$ pairs, each appearing once:

$x: \; -2, \; -1, \; 0, \; 1, \; 2 \qquad\qquad y = x^2$

so the paired $y$ values are $4, \; 1, \; 0, \; 1, \; 4$.

A feature-screening filter ranks candidate features purely by the magnitude of the Pearson correlation $|r|$ with the target, and drops the ones at the bottom.

Compute $r$ for this feature, and decide what the filter does with it.