For which purpose is the root mean square error primarily used?

The root mean square error (RMSE) is primarily used to measure the differences between values predicted by a model and the actual values. This statistical metric is particularly useful because it provides a way to quantify how well a model is performing by taking the square root of the average of squared differences, making it sensitive to large errors.

The correct answer indicates that RMSE provides insight into how forecast values align with historical data, thus indicating the accuracy of the model's predictions in relation to actual outcomes. By analyzing the RMSE, one can understand how closely the forecasted values correlate with the actual dataset, giving a clear indication of the model's predictive capability.

In contrast, the other options focus on aspects that RMSE does not specifically address. While variance relates to how spread out the forecast values are, RMSE does not represent variance itself. The calculation of average errors could refer to a different measure, such as mean absolute error (MAE), which assesses average magnitude of errors without considering their direction. Percentage error rates typically involve a different calculation method and context, focusing on the scale of errors in relation to the actual values. Thus, while these alternatives are useful metrics in their right, they do not accurately reflect the primary purpose of RMSE.