The causes of major archaeological transitions during the Upper Palaeolithic, such as the Aurignacian-Gravettian transition, remain poorly understood. In an effort to distinguish between demic and cultural diffusionary explanations for such transitions, analyses of radiocarbon and spatial data are sometimes employed. Here, we attempt to replicate a recent spatiotemporal study of the first appearance of Gravettian assemblages in Europe using linear regression analyses of radiocarbon dates and least-costpath measurements of the distances between sites. We find that there are problems with the corpus of 2 radiocarbon dates used and assemble two more appropriate sets of dates. We also find problems with the least-cost-path calculations and repeat these using a more appropriate method. We then repeat the regression analyses and use these as a case study to explore some of the problems with using linear regression analyses of radiocarbon and distance data for hypothesis testing where the total number of sites is very low. We conclude that this method is not capable of distinguishing the geographical origin of Gravettian traditions. We also find that this method frequently obtains false positive results, and that binning of sites may have a significant effect on the ease of obtaining positive results. Finally, we find that there is a negligible difference between the results of linear regression analyses obtained using least-cost-path measurements and those obtained using simple Euclidean distances, suggesting that the former adds little analytical value here despite its computational complexity.