The use of novel displays and interaction resources to support immersive data visualization and improve analytical reasoning is a research trend in the information visualization community. In this work, we evaluate the use of an HMD-based environment for the exploration of multidimensional data, represented in 3D scatterplots as a result of dimensionality reduction (DR). We present a new modeling for this problem, accounting for the two factors whose interplay determine the impact on the overall task performance: the difference in errors introduced by performing dimensionality reduction to 2D or 3D, and the difference in human perception errors under different visualization conditions. This two-step framework offers a simple approach to estimate the benefits of using an immersive 3D setup for a particular dataset. Here, the DR errors for a series of roll call voting datasets when using two or three dimensions are evaluated through an empirical task-based approach. The perception error and overall task performance, on the other hand, are assessed through a comparative user study with 30 participants. Results indicated that perception errors were low and similar in all approaches, resulting in overall performance benefits in both desktop and HMD-based 3D techniques. The immersive condition, however, was found to require less effort to find information and less navigation, besides providing much larger subjective perception of accuracy and engagement.