You have 10 data points: hours-of-load on the x-axis, response-time on the y. The true underlying relationship is a smooth gentle curve — roughly cubic — but each measurement carries random noise (network jitter, GC pauses), so the points scatter around that hidden curve.
You fit polynomials of increasing degree — the capacity dial from last lesson, now with numbers on it:
- Degree 1 (a straight line, 2 parameters): too stiff for a curve. It misses real bend.
- Degree 3 (4 parameters): the same shape as the truth, as it happens.
- Degree 9 (10 parameters): with 10 parameters and 10 points, the fitted curve can — and will — pass through every point exactly.
Training error behaves the boring, predictable way: it can only go down as degree rises (a bigger family contains the smaller one, so its best member is at least as good). By degree 9 it hits zero — last lesson’s memorizer, reborn as algebra.
The question is what happens to test error — the error on fresh points from the same noisy process — as the degree climbs 1 → 3 → 9.
Before answering, picture what the degree-9 curve must do to thread all 10 scattered points: the wild swings between them, the vertical takeoffs past the data’s edges. It fit the points. What did it fit, exactly? The points were signal plus noise — and the noise in the next batch will be freshly rolled.