Back to Topic 4.13 — Non-linear regression (HL only)
4.13.1Math AI HL8 flashcards

Non-linear regression

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Card 1 of 84.13.1
4.13.1
Question

How do you choose which non-linear model to fit?

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All 8 Flashcards — Non-linear regression

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Card 1concept

Question

How do you choose which non-linear model to fit?

Answer

Look at the SHAPE of the scatter and pick the family that matches (exponential = constant % change, power = scaling/flattening, quadratic = rise-then-fall, sinusoidal = repeating). Then compare R² between candidates.

Card 2concept

Question

What does the coefficient of determination R² tell you?

Answer

How much of the variation in the data the model explains. R² = 1 is a perfect fit; closer to 1 is better; near 0 is poor.

Card 3concept

Question

How do you decide which of two models fits better?

Answer

Fit both on the GDC and compare R² — the model with the higher R² (closer to 1) fits better. Also check the shape and context make sense.

Card 4formula

Question

What is a residual, and what is SSres?

Answer

A residual is data − model (y − ŷ) for one point. SSres = Σ(y − ŷ)² is the sum of squared residuals; regression minimises it, and a smaller SSres gives a higher R².

Card 5concept

Question

Why square the residuals instead of just adding them?

Answer

So positive and negative residuals don't cancel out, and larger misses are penalised more heavily.

Card 6formula

Question

Forms of the exponential model on the GDC?

Answer

y = k·aˣ (base form) or y = k·eʳˣ (natural form). a > 1 (or r > 0) = growth; 0 < a < 1 (or r < 0) = decay.

Card 7concept

Question

What is the difference between interpolation and extrapolation?

Answer

Interpolation = predicting inside the data range (safer). Extrapolation = predicting outside it (riskier — the model may not hold).

Card 8concept

Question

Does a high R² guarantee a prediction far outside the data is reliable?

Answer

No — R² only measures fit to the EXISTING data. Predictions far beyond the range (extrapolation) can be unreliable even when R² is near 1.

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