Non-linear regression
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Flip to reveal answersHow do you choose which non-linear model to fit?
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All 8 Flashcards — Non-linear regression
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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.
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.
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.
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.
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.
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.
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).
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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Topic 4.13 hub
Non-linear regression (HL only)
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