In the paper, the formerly introduced spherical multivariate tests are coupled with procedures for selecting the relevant variables. These procedures work in such a way that a non-relevant set of variables is chosen with the probability of significance \alfa, at most. Furthermore, a new method of the calculation of linear principal-component scores is presented, which is based only on the within-sample covariances and yields, nevertheless, a level-\alfa test in each case. This method enables us to determine novel multivariate confidence regions of the unknown mean vector. The statistical procedures are demonstrated by a neurological example.