Specificity, validity, and reliability, not to mention time and money, all underscore the importance of multivariate statistics. This area of statistics is of vital importance to business, government, and social science.

The authors of this paper investigate the effect of finite-order weights on the tractability of linear multivariate problems. After an introduction, which presents the theory of, and research in, linear multivariate models, the authors continue with the problem formulation. Theorems and proofs follow. In the main results section, the authors explain, in depth, tractability results. A major part of the paper discusses lower bounds. The concluding section details multivariate integration. The reference section, though not exhaustive, is much more than cursory. The serious statistical theoretician will find this paper interesting and valuable, as well as profitable.