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How do you choose which non-linear model to fit?
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All Flashcards in Topic 4.13
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4.13.18 cards
How do you choose which non-linear model to fit?
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.
What does the coefficient of determination R² tell you?
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.
How do you decide which of two models fits better?
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.
What is a residual, and what is SSres?
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.
Why square the residuals instead of just adding them?
So positive and negative residuals don't cancel out, and larger misses are penalised more heavily.
Forms of the exponential model on the GDC?
y = k·aˣ (base form) or y = k·eʳˣ (natural form). a > 1 (or r > 0) = growth; 0 < a < 1 (or r < 0) = decay.
What is the difference between interpolation and extrapolation?
Interpolation = predicting inside the data range (safer). Extrapolation = predicting outside it (riskier — the model may not hold).
Does a high R² guarantee a prediction far outside the data is reliable?
No — R² only measures fit to the EXISTING data. Predictions far beyond the range (extrapolation) can be unreliable even when R² is near 1.
Topic 4.13 study notes
Full notes & explanations for Non-linear regression (HL only)
Math AI exam skills
Paper structures, command terms & tips
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