This article will explore and analyse how to design the capillary distribution network of an Overnight Parcel Logistics Company (hereby referred to as OPLC). The OPLC needs to design a capillary distribution network that is capable of collecting all the merchandise that their clients wish to deliver, and, at the same time, have the capacity to distribute all shipments to their destination. To reach this goal, the designers have to decide the type of vehicles (van, lorry or trailer) and the quantity of each type of vehicle the capillary distribution network needs to cover the area around each hub efficiently. This number of vehicles has to satisfy the delivery/collection quality requirements with the minimum cost to guarantee the maximum profit for the OPLC. This research will demonstrate that regression analysis is a valid technique to help an OPLC in the decision making related to the distribution costs of the capillary network. The way the costs of each distribution areas are obtained for the design of the capillary network is by regression models. Most models related to logistics companies have been based on deterministic techniques so far.