Diffusion imaging techniques are commonly used to study water diffusivity and white matter tracts in the brain. High angular resolution acquisitions yield high-quality fibre orientation distributions (FODs), but their longer acquisition time makes them impractical in the most clinical settings. Single-shell low angular resolution protocols are a more feasible alternative, though less informative to reconstruct FODs for complex white matter tracts. To address that gap, recent studies have focused on enhancing FODs from single-shell low angular resolution data. Nonetheless, uncertainty remains a critical concern due to the complex nature of white matter tracts and the impact of FOD enhancement on downstream tasks such as tractography and human connectome mapping. Current uncertainty estimation methods show promise in classification and segmentation (classification at the pixel or voxel level) tasks. However, medical image analysis often involves regression tasks, such as super resolution and denoising, where uncertainty estimation is equally important but in general less studied. This study formulates FOD enhancement from single-shell low angular resolution data as a multivariate regression problem and estimates the uncertainty of the predictions using convolutional neural networks (CNNs) from a statistical basis. Our results show that the proposed FOD uncertainty correlates with FOD-level errors, providing insights into prediction reliability. This is the first work to uncover the link between improving the coefficients of a model for water diffusivity (FOD) and its true effect on fibre estimation, thereby advancing the reliability of deep learning-driven enhancement for diffusion imaging.