Brain aging, and more specifically the difference between the chronological and the biological age of a person, may be a promising biomarker for identifying neurodegenerative diseases. For this purpose accurate prediction is important but the localisation of the areas that play a significant role in the prediction is also crucial, in order to gain clinicians trust and reassurance about the performance of a prediction model. Most interpretability methods are focused on classification tasks and cannot be directly transferred to regression tasks. In this study, we focus on the task of brain age regression from 3D brain Magnetic Resonance (MR) images using a Convolutional Neural Network, termed prediction model. We interpret its predictions by extracting importance maps, which discover the parts of the brain that are the most important for brain age. In order to do so, we assume that voxels that are not useful for the regression are resilient to noise addition. We implement a noise model which aims to add as much noise as possible to the input without harming the performance of the prediction model. We average the importance maps of the subjects and end up with a population-based importance map, which displays the regions of the brain that are influential for the task. We test our method on 13,750 3D brain MR images from the UK Biobank, and our findings are consistent with the existing neuropathology literature, highlighting that the hippocampus and the ventricles are the most relevant regions for brain aging.