Estimation is still a challenging process for planning and managing software projects. Often, estimates are being done on experiential or analogous basis or using effort estimation models. Mostly, these approaches take software size (e.g., Lines of Code, Function Points, Object points) and other cost factors as the main inputs to estimation. This study focuses on functional size based effort estimation for Web application development and investigates the significance of the functional sizes of each of the COSMIC Base Functional Component (BFC) types in explaining the variation in the development effort. A case study was conducted collecting data on 25 Web projects from a software organization. The results show that the size of only one of the BFC Types can explain the variation in the effort nearly as good as the total functional size.