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Not sure if the title is confusing or not. Here is an example:

Let's say we build a regression model to predict the housing price. However, instead of caring about the prediction accuracy where MAE, MSE and some other metrics can help to define, I mainly care about the following scenario:

Given two houses A and B, does this regression model can actually tell whether the actual price of A is greater/equal/less than the one of B. Basically, I want to use the model to make directional guidance. In this scenario, which metric should I use?

Thanks.

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If the prediction is greater/equal/less, then it is no longer framed as a regression problem. Regression predicts a continuously-valued outcome.

Greater/equal/less are ordinally-valued categories. Thus categorical evaluation metrics would be more useful, such as accuracy, recall, and precision.

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