Power efficiency is crucial for mobile devices, where software inefficiencies can rapidly drain battery life and reduce device longevity. To help developers diagnose inefficiency issues and optimize power use, this paper introduces a novel methodology for estimating power consumption at a hardware component level in mobile devices. Unlike existing approaches that rely on coarse-grained battery discharge measurements, our approach consists of modeling per-component power usage as an inverse problem, utilizing linear statistical models and system metrics to estimate the contributions of individual components. In this paper, we model the total power usage using system metrics, we evaluate the accuracy of per-component power estimations, and we investigate the impact of dataset size on the model's performance. Our empirical evaluation shows that linear models achieve high predictive accuracy, with R-squared values exceeding 0.90 for total power usage, and robust correlations are observed between predicted and ground-truth power consumption for key components such as the CPU and GPU. We also observe that the amount of measures required to build such a model is of the order of magnitude of the hundred rather than the thousand.