The paper explores design-based inference under variable probability sampling in which the inclusion probabilities, pi, are proportional to the auxiliary (design) variable x. It denotes this design as pi px, for inclusion probability proportional to x. Two pi px designs were investigated. In fixed configuration variable probability systematic (fcvps) sampling, the population is sampled in its natural or fixed ordering. If the population is sorted on x prior to sampling, the notation fcvps:x will be used. If the population ordering is randomly permuted prior to sampling, the design is randomized variable probability systematic, denoted rvps. The randomized design is often used as a model of the fixed configuration design for the purpose of variance estimation. To complete the assessment, it compares the behavior of these strategies to the performance of regression estimators under the same designs using the same variable, x. Lastly, these regression estimators are examined under simple random sampling (srs) and simple systematic sampling (sss).