In healthcare applications, predictive uncertainty has been used to assess predictive accuracy. In this paper, we demonstrate that predictive uncertainty estimated by the current methods does not highly correlate with prediction error by decomposing the latter into random and systematic errors, and showing that the former is equivalent to the variance of the random error. In addition, we observe that current methods unnecessarily compromise performance by modifying the model and training loss to estimate the target and uncertainty jointly. We show that estimating them separately without modifications improves performance. Following this, we propose a novel method that estimates the target labels and magnitude of the prediction error in two steps. We demonstrate this method on a large-scale MRI reconstruction task, and achieve significantly better results than the state-of-the-art uncertainty estimation methods.