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A receiver operating characteristic curve, or ROC curve, is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied.

Could it be used for a regression problem, e.g. housing price prediction? How about bias-variance?

I am trying to train a model that predict the length of cut for operation on patients. I worry about it is reasonable and enough to just using error rate. The indirect evaluation is the recovery of patients after operation.

Could someone please give a hint? Thanks in advance.

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    $\begingroup$ I think not, but it may depend on what you are asking from your regression. Can you say more about your aims? In any case, often the scale (or continuous) variable used in an ROC analysis will itself have been created as the output of a regression, e.g., as a probability saved via logistic regression. $\endgroup$
    – rolando2
    Mar 27 '20 at 11:04
  • $\begingroup$ @rolando2 Thanks for your reminder. I've updated my OP. $\endgroup$
    – WXJ96163
    Mar 27 '20 at 11:15
  • $\begingroup$ There's a related concept: the Gini coefficient $\endgroup$
    – Firebug
    Mar 27 '20 at 11:51
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In survival regression, a common metric is the "concordance index" that measures how well a regressor ranks pairs of samples. This concordance index is equivalent to the area under the ROC curve, see Why is ROC AUC equivalent to the probability that two randomly-selected samples are correctly ranked?

Note that the concordance index does not care about the absolute values of your predictions. The only thing that matters are the relative values compared to other samples in the dataset. A good concordance does therefore not mean that the regressor is also well calibrated.

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This is not possible without modifications, since the ROC curve by definition works with a binary classification problem by plotting true positive rate against false positive rate as you vary the classification threshold.

I suppose in theory, if you defined some threshold within which a model's answer could be deemed "correct," you could in theory do something like this, because after all, TPR, FPR, and a set of thresholds are the only prerequisites for a ROC curve plot. However, defining a good set of thresholds in an infinite space seems difficult, and there are far less contrived ways to evaluate the performance of regression.

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