shadowbox

Interactive explainers for the statistical methods that reduce data. The figures here are working instruments rather than pictures of finished results. Drag a line, drag the points under it, flip a switch, and every number on the figure recomputes.

Each method is taught twice. First on simulated data, where the right answer is known and drawn on the screen, so you can watch whether the method recovers it. Then on simulated fetal biometry, generated from published growth centiles rather than taken from patients, where no answer is drawn in and the method is all you've got.

Reading the figures

Anything you can drag turns the cursor into a hand. Toggles are labeled with what they turn on. Where a figure has a true answer hidden inside it, revealing that answer is itself a toggle, so you can commit to a guess before you look.

The lessons

1 · Least squares - what fitting a line actually costs you
2 · Covariance - the shape hiding inside a 2×2 matrix
3 · PCA - finding the directions data really spreads along
4 · k-means - why you get exactly as many groups as you asked for

The name

Every method here flattens. Least squares drops each observation onto a line. Covariance compresses a whole cloud into a single ellipse. PCA picks which direction to flatten from. k-means replaces each point with the number of the group it landed in. A projection is a shadow, and no shadow keeps everything.