Which of the following evaluation metrics is used to evaluate a model while modelling a continuous output variable? AUC-ROC Accuracy Logloss Mean-Squared-Error

The evaluation metric used to evaluate a model while modelling a continuous output variable is Mean-Squared-Error.

Here's why:

1. AUC-ROC: This is used for classification problems, not for continuous output variables. It measures the area under the receiver operating characteristic curve.

2. Accuracy: This is also used for classification problems. It measures the proportion of correct predictions over total predictions.

3. Logloss: This is a loss function used in (multinomial) logistic regression and extensions of it such as neural networks, defined as the negative log-likelihood of the true labels given a probabilistic classifier’s predictions. Again, it's not used for continuous output variables.

4. Mean-Squared-Error: This is used for regression problems, which involve predicting a continuous output variable. It measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value.