The concept of service in Service-Oriented Architecture (SOA) makes possible to introduce other ideas like service composition, governance and virtualization. Each of these ideas, when exercised to an enterprise level, provides benefits in terms of cost and performance. These ideas bring many new opportunities for the project managers in making the estimates of effort required to produce SOA systems. This is because the SOA systems are different from traditional software projects and there is a lack of efficient metrics and models for providing a high level of confidence in effort estimation. Thus, in this paper, an efficient estimation methodology has been presented based on analyzing the development phases of past SOA based software systems. The objective of this paper is twofold: first, to study and analyze the development phases of some past SOA based systems; second, to propose estimation metrics based on these analyzed parameters. The proposed methodology is facilitated from the use of four regression(s) based estimation models. The validation of the proposed methodology is cross checked by comparing the predictive accuracy, using some commonly used performance measurement indicators and box-plots evaluation. The evaluation results of the study (using industrial data collected from 10 SOA based software systems) show that the effort estimates obtained using the multiple linear regression model are more accurate and indicate an improvement in performance than the other used regression models.