Consider m-th order polynomial regression. Which of the the following statements are true? [Select ALL that apply.]

Question

BlackTom AI · Accepted Answer

When evaluating m-th order polynomial regression, it's important to recognize how model complexity interacts with the data.
Option 1: The choice of m depends on the dataset. This is true because the appropriate polynomial degree balances bias and variance given the sample size, noise level, and underlying pattern in the data. A dataset with clear nonlinear structure or sufficient data points may benefit from a higher m, while noisy or small datasets may require a lower m to avoid overfitting.
Option 2: The m value does not affect generalisation performance of the model. This is incorrect. The degree m directly affects the model's capacity; a higher m increases flexibility and can reduce training error but often harms generalisation to unseen data due to overfitting, whereas a lower m can improve generalisation by imposing simpler structure.
Option 3: The smaller m is more likely to overfit the data. This is false. Smaller m restricts the model’s flexibility, which generally reduces overfitting risk but can lead to underfitting if the true relationship is nonlinear. Overfitting is typically associated with larger m, not smaller.
Option 4: The larger m is more likely to overfit the data. This is true. As m grows, the model can fit increasingly complex patterns, including noise, which tends to degrade generalisation on new data unless there is a compensating increase in data quality or regularisation.

Consider m-th order polynomial regression. Which of the the following statements are true? [Select ALL that apply.]多项选择题

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