Isolate the irreducible noise from prediction error

Question

A model's expected squared error when predicting a new observation is 10. The model's estimation error (its squared bias plus variance combined) is 3.

Prediction error is $\text{estimation error} + \sigma^2$ , where $\sigma^2$ is the outcome's irreducible noise.

What is the irreducible noise $\sigma^2$ ?

Accepted Answer

The idea. Total prediction error is the model's estimation error plus the noise of the outcome itself. Subtract the estimation error to isolate the noise. Solve. \sigma^2 = 	ext{Prediction MSE} - 	ext{estimation error} = 10 - 3 = 7. So 7 of the 10 units of prediction error comes from the irreducible randomness of the outcome, and only 3 from the model. This split is diagnostic: since the noise (7) dwarfs the model error (3), there is little room to improve by building a better model. You have nearly hit the wall set by the noise, and effort is better spent elsewhere (for instance, finding n…

Isolate the irreducible noise from prediction error

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