Representational Similarity Analysis is a popular framework to flexibly represent the statistical dependencies between multi-voxel patterns on the one hand, and sensory or cognitive stimuli on the other hand. It has been used in an inferen-tial framework, whereby significance is given by a permutation test on the samples. In this paper , we outline an issue with this statistical procedure: namely that the so-called pattern similarity used can be influenced by various effects, such as noise variance, which can lead to inflated type I error rates. What we propose is to rely instead on proper linear models.