The choice of a loss function is a critical part of machine learning. This paper evaluated two different loss functions commonly used in regression-task dimensional speech emotion recognition, an error-based and a correlation-based loss functions. We found that using a correlation-based loss function with a concordance correlation coefficient (CCC) loss resulted in better performance than an error-based loss function with mean squared error (MSE) loss and mean absolute error (MAE), in terms of the averaged CCC score. The results are consistent with two input feature sets and two datasets. The scatter plots of test prediction by those two loss functions also confirmed the results measured by CCC scores.