The expected predicted error of a regression method splits into two parts: squared bias and variance

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BlackTom AI · Accepted Answer

When evaluating a regression method, it's important to consider how prediction errors are composed. 
Option 1: True. This statement attempts to describe the decomposition, but it is incomplete because it omits a third component that is always present in the standard bias-variance tradeoff. 
Option 2: False. In the classic bias-variance decomposition for squared error, the expected squared prediction error can be broken down into three parts: the squared bias (how far the average prediction is from the true value), the variance (how much predictions fluctuate around their mean), and the irreducible error (the inherent noise in the data that cannot be eliminated by any model). Since the irreducible error term is missing from the claim, the statement is not fully correct. 
Option 3: Another way to think about it is to remember that prediction error is not solely about model bias and variance; there is always some irreducible noise in the data-generating process that contributes to the overall error. This is why many textbooks present the full decomposition as E[(Y − f_hat(X))^2] = Bias^2 + Variance + Noise (often denoted as σ^2). 
Option 4: Additionally, the wording might cause confusion about what is being decomposed. If one interprets the phrase "expected predicted error" as the mean squared error of predictions, the presence of an irreducible error term becomes even more important, reinforcing why the two-term claim is incorrect. 
In summary, the incorrect aspect is the omission of the irreducible error term from the decomposition; the complete and accurate expression includes three components rather than two.

QBUS6810 (ND) Week 5 Quiz

The expected predicted error of a regression method splits into two parts: squared bias and variance

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