Testing and regression testing tasks can become very complex and highly expensive. Currently, studies in the software industry that testing activities may absorb more than 50% of the project cost. Of this cost, 40% may correspond to the cost of regression testing which, if not taken into account from the beginning, leads to a cost increase large enough to jeopardize the success of the project. To address this issue, an approach named “TeqReq+” is proposed. The main objective of TeqReq + is to provide an early integration of the cost of regression testing into the initial estimates of the project effort. From this, a reduction of the difference between the initial effort estimate and the final cost of the project will take place, after the regression testing has already been carried out. Additionally, in order to record valuable information for the testing process, TeqReq + will also record information related to the testing status and to the person responsible for the testing tasks associated to a requirement. The proposed approach was validated in an industrial case study involving several real-world projects. The analysis of the information gathered was performed under a mixed approach and, in turn, the results were validated via double triangulation. The findings lead to confirm that TeqReq + had a positive impact not only at the time of budgeting the cost of regression testing but in reducing the deviations due to a bad estimation of the regression testing costs, while also providing several other improvements regarding the testing process.