What does the ROC curve represent in model evaluation?

The ROC (Receiver Operating Characteristic) curve is a graphical representation used in model evaluation, particularly for binary classification tasks. It illustrates the trade-off between sensitivity (true positive rate) and specificity (false positive rate) at various threshold settings.

When assessing the ROC curve, the true positive rate is plotted on the y-axis, which reflects the proportion of actual positive cases that are correctly identified by the model. Conversely, the false positive rate is plotted on the x-axis, indicating the proportion of actual negative cases that are incorrectly classified as positive.

The ROC curve effectively showcases how adjusting the classification threshold impacts the true positive and false positive rates. A model with a good ROC curve will demonstrate high sensitivity while maintaining low false positive rates, highlighting its potential effectiveness in distinguishing between the two classes.

Other options refer to different aspects of model evaluation. The correlation between predicted and actual values pertains to regression models and not specifically to the ROC curve's purpose. The distribution of errors in predictions focuses on evaluating prediction errors rather than classification thresholds. Finally, the accuracy of the model over time doesn't align with what the ROC curve captures, as it doesn't provide time-series insights but rather emphasizes the performance trade-offs at varying thresholds.