Question: Explain how one training error value, such as 12%, can lead to two very different conclusions about a model’s bias depending on the estimated best achievable error rate.

Sample answer: A training error of 12% by itself does not tell us whether bias is high or low. We have to compare it with the estimated best achievable error to determine the avoidable gap. If the best achievable error is about 1%, then a 12% training error leaves an 11-point gap, which means the model still has a lot of room to improve and bias-reducing changes are likely to help. If the best achievable error is about 11%, then a 12% training error is already very close to the best possible level, leaving only a 1-point gap and little room for further bias reduction.

Key points:

• Training error alone is not enough to judge bias.
• A low best achievable error can make a 12% training error look far from ideal.
• A high best achievable error can make the same 12% training error look nearly optimal.
• The size of the gap determines whether bias-reduction work is likely to help.

Rubric: Answers must explain that bias diagnosis depends on the gap between training error and the estimated best achievable error. They must contrast a case with a very low best achievable error, where the gap is large and improvement is likely, with a case where the best achievable error is close to 12%, where little improvement remains.