The correct answer is D. Mean-Squared-Error (MSE).
MSE is a measure of the average squared difference between the predicted values and the actual values. It is a good metric to use when the output variable is continuous, as it penalizes both over- and under-predictions.
AUC-ROC is an area under the receiver operating characteristic curve. It is a measure of the model’s ability to distinguish between positive and negative examples. It is a good metric to use when the output variable is binary, as it takes into account the model’s ability to make correct predictions for both positive and negative examples.
Accuracy is the percentage of examples that the model correctly predicts. It is a simple metric to understand, but it can be misleading when the output variable is imbalanced. For example, if a model is predicting whether a patient has cancer, and the prevalence of cancer is 1%, then a model that always predicts that the patient does not have cancer will have an accuracy of 99%. However, this model would not be very useful.
Logloss is a measure of the cross-entropy between the predicted and actual values. It is a good metric to use when the output variable is categorical, as it takes into account the model’s ability to make correct predictions for all possible categories.
In conclusion, MSE is the best metric to use to evaluate a model while modeling a continuous output variable.