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I need to predict the profitability of the products of a retailer. I can either predict the absolute value of the profit the products will make (continuous outcome) or predict whether the products will make a profit or not (categorical outcome). Is there any advantage of approaching this as a classification problem rather than a regression problem or vice versa? Why?

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I would say that the main thing is what information you think is the most valuable. There are some differences.

The benefit with a regressor is that it can give you a number of how much profit you can expect. That is obviously useful when considering a new product. The drawback is that it cannot tell you how likely you are to see this profit. It will not tell you if a product is risky.

Many classifiers can tell you with what probability it thinks a product will be profitable. This can alert you to potentially risky products. But the drawback is that you won't get to know how big the potential profit is.

As I said, it depends what you value most. But nothing is stopping you from training two models and using information from both of them to make your decisions.

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