Estimating the development effort of a software project in the early stages of the software life cycle is a significant task. Accurate estimates help project managers to overcome the problems regarding budget and time overruns. This paper proposes a new multiple linear regression analysis based effort estimation method, which has brought a different perspective to the software effort estimation methods and increased the success of software effort estimation processes. The proposed method is compared with standard Use Case Point (UCP) method, which is a well-known method in this area, and simple linear regression based effort estimation method developed by Nassif et al. In order to evaluate and compare the proposed method, the data of 10 software projects developed by four well-established software companies in Turkey were collected and datasets were created. When effort estimations obtained from datasets and actual efforts spent to complete the projects are compared with each other, it has been observed that the proposed method has higher effort estimation accuracy compared to the other methods.