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Line fitting by order

The same points, fitted by polynomials of rising order. Watch R² climb — and watch where climbing stops meaning the fit got better and starts meaning it got bendier. Click the plot to add a point, click a point to drop it.

Order 1 is already the honest answer. Every order above it is the curve learning the noise.

0 0 2 2 4 4 6 6 8 8 10 10
14 points
Remove a point

0.9235

R²

0.603

RMS error

y = 4.864 + 3.377·u

where u = (x − 5.00) / 5.00 — fitting in a centred, scaled x is what stops order 9 from dissolving into rounding error.

What it is doing

  • Ordinary least squares — it minimises the sum of squared vertical distances, so one far-off point pulls harder than several near ones. Drop an outlier onto the plot and watch it drag the curve.
  • R² never falls when the order rises. That is arithmetic, not evidence: every higher order contains the lower one as a special case, so it can always do at least as well on the points it was shown.
  • The interesting number is the one you cannot see here — the error on points the fit was not given. That is what stops rising, and usually well before the last order on the slider.