Which model has the lowest expected test error?

Question

You are choosing a forecasting model. The expected squared error of a prediction splits into three parts: $\text{squared bias} + \text{variance} + \text{irreducible noise}$ . The noise is 4 for every model. The models are:

Model A: squared bias 9, variance 1
Model B: squared bias 1, variance 6
Model C: squared bias 0, variance 12

Which model has the lowest expected test error, and what is it?

Accepted Answer

The idea. Test error is not just about fitting the data. A prediction misses for three reasons: the model is too rigid to capture the truth (bias), the model wobbles from sample to sample (variance), and the world itself is random (irreducible noise). These add up, and the noise floor is unavoidable no matter which model you pick. Add the pieces (noise 4 throughout): - Model A: 9 + 1 + 4 = 14 (too simple, high bias) - Model B: 1 + 6 + 4 = 11 (balanced) - Model C: 0 + 12 + 4 = 16 (too flexible, high variance) The winner. Model B, with test error 11. Model A is underfit: it is rigid and steady …

Which model has the lowest expected test error?

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