Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I knew that, ROC curve are use to assess the performance of classifiers. But is it possible to generate ROC curve for the regression model? If yes, How?

share|improve this question
An ROC curve shows the TPR as a function of FPR. Neither of these measures exists in the context of regression, so there is no such thing as ROC curves for regression. – Marc Claesen Mar 5 '14 at 16:46
Linking a related question:… – Alexey Grigorev Apr 14 '15 at 8:35

I haven't enough reputation to make a comment to Matt's comment, that's why I add something via an "answer". Maybe I am wrong, but you can use regression as a classifier, like a logit/probit model, if you have a binary outcome (y variable). Than your "knob", as Matt called it, would be the threshold at which value you choose to see your y* (your continuous prediction of e.g. a linear regression) to be y = 1. Than you can use this threshold for a ROC.

Edit: I agree to the (*) edit of Matt's answer.

Example: There is a continuous variable x and a binary variable y. What you can do is a normal regression of y on x. Then you calculate the predictions of your model dependent on x for each individual, calling these predictions y*. Than you look for a threshold c which does something like $y_{prediction} = \left\{\begin{matrix} 1\text{ if y*} > c \\ 0\text{ else} \end{matrix}\right.$

Than you can use this c for a ROC analysis. (Sorry for my bad formatting, it is my first post here)

share|improve this answer
Unless I am missing something, this is basically shoe-horning a classification problem into a regression problem and then evaluating it using classification metrics. – Marc Claesen Mar 5 '14 at 17:46
Agreed; maybe I should make my footnote a little more general. In fact, I think some of the early credit modeling stuff worked like this--linear regression with the output "clamped" to within a certain range, followed by a decision rule. – Matt Krause Mar 5 '14 at 17:47
At least, to my own answer I can do a comment :) @MarcClaesen: I don't say it is the best way to do it. But in our Econometrics class we still had it under "you can do it, with the advantage of using a familiar tool to a new subject; now let's move on to more elaborated stuff for this problem -> logit/probit" – user2075339 Mar 5 '14 at 17:57
By the way, you should have enough reputation to comment everywhere now. Welcome to Cross Validated! – Matt Krause Mar 5 '14 at 20:39

You can't, really.

A (binary) classification task has a small set of possible outcomes: you either correctly detect/reject something or you don't. The ROC curve measures the trade-off between these (specifically, between the false positive rate and the true positive rate). In this setting, there's no notion of "close-but-not-quite-right", but there is often a "knob" you can turn to increase your true positive rate (at the expense of more false positives too), or vice versa.

Regression typically(*) makes continuous predictions. With so many possible outcomes, it's vanishingly unlikely that the model will make an exact prediction (imagine predicting Amazon's annual sales down to the penny--it's not going to happen). There also isn't a TP/FP trade-off.

Instead, people measure a regression model's performance using a loss function, which describes how good/bad a certain amount of error is. For example, a common loss function is the mean-squared error: $\frac{1}{N}\sum_{i=1}^{i=N} (\textrm{obs}_i - \textrm{pred}_i)^2$. This penalizes large errors a lot, but tolerates smaller errors more.

* In some cases, regression can be converted into a classification problem by adding a decision rule. For example, logistic regression, despite the name, is often used as classifier. The "bare" logistic regression output is the probability that an example (i.e., a feature vector) belongs to the positive class: $P(\textrm{class=+} | \textrm{ data})$.

However, you could use a decision rule to assign that example to a class. The obvious decision rule is to assign it to the more likely class: the positive one if the probability is at least a half, and the negative one otherwise. By varying this decision rule (e.g., an example is in the positive class if $P(\textrm{class}=+) > \{0.25, 0.5, 0.75, \textrm{etc}\}$, you can turn the TP/FP knob and generate an ROC curve.

All that said, for most regression tasks, where you're predicting something continuous, ROC analysis is an odd choice.

share|improve this answer
Logistic regression is only a classification technique in conjunction with some rule that a predicted probability > $x|x \in [0,1]$ is assigned to one outcome or another. On its own, the logistic regression model is inference on the latent variable Pr(class membership=1). – General Abrial Mar 5 '14 at 17:25
That's a fair point. Interestingly, you could something similar about Naive Bayes (or many other maximum likelihood classifier). How do you feel about the edited version? – Matt Krause Mar 5 '14 at 17:58
I agree with the edit overall. However, I'm not sure what you mean by "you could assign an example to the more likely class if you wanted to perform a classification task instead." What example? Why assign it to a class? I think if you delete that text, it's a great addition to your answer. – General Abrial Mar 5 '14 at 18:18
I'm not sure where I picked this up, but I tend to call one "row" of the data matrix an example. For example, the Fisher's Iris data set has 3 classes (the species of flower), 50 examples per class, and each example has 4 attributes (the length/width of the petal and sepal). – Matt Krause Mar 5 '14 at 18:26
(+1) After the rewrite, I understood -- It makes sense to me now. Regardless, good answer. – General Abrial Mar 5 '14 at 18:29

This is too late to answer the original question, but it's something I've been interested in and while searching for a method of implementing ROC curves for regression I came across the following paper which may be of some use to others wondering the same thing

Hernández-Orallo, José. "ROC curves for regression."

Pattern Recognition 46.12 (2013): 3395-3411.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.