The Rate Signature, Not the Silhouette

You'll learnto match a data set to the right function family by its rate signature, not its shape.

A model is a claim about how a quantity changes, not a curve that happens to pass near some dots. Every family leaves a fingerprint in the differences: linear holds them constant, quadratic holds the next layer constant, a trade-off holds a product constant. Over a short window the silhouettes are indistinguishable, so the picture is the one witness you must not call.

8 STEPS · 6 QUICK CHECKS · Δ SIGNATURES · SPACING RULE · ASSUMPTIONS · v2

the differences are the fingerprint; the shape is a costume

Before you start

What you're looking at

Three short data situations sharing the same inputs: one adds a fixed amount, one multiplies by a fixed factor, one keeps a product constant.

The question

Which function family matches this data?

Watch for

What stays constant — a difference, a factor, or a product — rather than what the dots happen to look like.

Step 1 / 8