Add up the three sources of forecast error

Question

A demand-forecasting model's estimated response has bias 1 and variance 3. Actual demand also fluctuates around its true mean with irreducible variance $\sigma^2 = 5$ .

The expected squared error of predicting a new observation is $\text{bias}^2 + \text{variance} + \sigma^2$ .

What is the expected squared prediction error?

Accepted Answer

The idea. A prediction of a new outcome carries two kinds of error: how far your model's estimate sits from the true average (bias and variance), plus the inherent randomness of the outcome you are trying to hit (the noise). Add the three parts. 	ext{Prediction MSE} = 	ext{bias}^2 + 	ext{variance} + \sigma^2 = 1^2 + 3 + 5 = 1 + 3 + 5 = 9. Each source contributes: bias 1, model variance 3, outcome noise 5. Here no single term dominates, so improving the forecast would require both a better model (to shrink the bias and variance) and, unavoidably, accepting the noise floor of 5 that cannot b…

Add up the three sources of forecast error

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