The Feature That Correlation Cannot See

Statistics for MLMedium+20 XP+20

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.

Pearson Correlation Coefficient (r)

Centered Deviations | Core Dataset (r = 0.878)

Standardized Deviation Tooltip

Hover over a point to inspect its centered deviations and cross-product!

The Pearson r numerator is the sum of (x − x̄)(y − ȳ). When both variables deviate in the same direction — both above their means, or both below — the product is positive, pushing r towards +1.

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The Feature That Correlation Cannot See