Big data offers the potential to calculate timely estimates of the socioeconomic development of a region. Mobile telephone activity provides an enormous wealth of information that can be utilized alongside household surveys. Estimates of poverty and wealth rely on the calculation of features from call detail records (CDRs), however, mobile network operators are reluctant to provide access to CDRs due to commercial and privacy concerns. As a compromise, this study shows that a sparse CDR dataset combined with other publicly available datasets based on satellite imagery can yield competitive results. In particular, a model is built using two CDR-based features, mobile ownership per capita and call volume per phone, combined with normalized satellite nightlight data and population density, to estimate the multi-dimensional poverty index (MPI) at the sector level in Rwanda. This model accurately estimates the MPI for sectors in Rwanda that contain mobile phone cell towers (cross-validated correlation of 0.88).