The curve that remembered too much

Does the curve explain the pattern or remember the noise?

Make your own investigation

Choose a degree using validation data, lock the choice, then evaluate a fresh seeded test set.

Fit a polynomial by regularised least squares on training rows. Compare validation errors; final tests use a fresh seeded quadratic fixture.

Case cards

Cut these cards apart. Use the original example first, then let a partner supply a changed case. Keep sealed/final cards with the teacher until the learner commits a rule.

Case 1

x: -2

y: 4

Split: train

My prediction and reason:

Case 2

x: -1

y: 1.2

Split: train

My prediction and reason:

Case 3

x: 0

y: -0.2

Split: train

My prediction and reason:

Case 4

x: 1

y: 1.1

Split: train

My prediction and reason:

Case 5

x: 2

y: 4

Split: train

My prediction and reason:

Case 6

x: -1.5

y: 2.25

Split: validation

My prediction and reason:

Case 7

x: 1.5

y: 2.25

Split: validation

My prediction and reason:

What this cannot establish

A synthetic quadratic favours particular hypotheses. Do not tune repeatedly on final tests.