No. A larger does not automatically mean that a model is more appropriate or valid. Model selection must also consider residuals, the model’s shape, its complexity, the data’s domain, and the real-world context.
In AHL 4.13 Non-linear regression, the coefficient of determination measures the proportion of variation in the dependent variable accounted for by the chosen model. For example, means that the model accounts for approximately of the variation in the response variable.
However, measures fit to the observed data, not whether the model is sensible. Suppose a cubic model has , while an exponential model has . The cubic fits the recorded points slightly more closely, but it may behave unrealistically outside the observed interval. If the context describes population growth, the exponential model may be more meaningful.
| Factor | What to check |
|---|---|
| Residuals | Residuals should be small and randomly distributed. A visible pattern suggests that the model misses part of the relationship. |
| Model complexity | A flexible model with more parameters may fit accidental variation, producing overfitting. |
| Context | The model’s shape and parameters must have realistic meanings. |
| Domain | A model may fit within the data range but give impossible values when extrapolated. |
| Overall fit | Compare the graph, residuals, , and, where provided, the sum of squared residuals . |
A common misconception is that “the model with the highest is always best.” The correct conclusion is that the highest identifies the closest numerical fit among the tested models, but not necessarily the most valid model.
Exam technique: This is HL-only content under AHL 4.13 and may appear on any GDC-active HL paper. When asked to justify a model choice, quote relevant values but also discuss residual patterns, contextual suitability, the data range, and the danger of extrapolation.