In this paper, an approximate mathematical expression is proposed for the residual variance of Auto-Regressive (AR) estimation in the case where the AR estimation method is Least-Squares- Forward (LSF), using statistical arguments and approximations as well as Hilbert space concepts. This expression approximates the statistical behavior of the residual variance. While its validity is tested through simulations. This important formula can be employed to propose various AR Order selection methods. Such as the method proposed in this paper which is an iterative algorithm. The performance of this algorithm is compared with other existing Order selection methods using simulations. The results of which demonstrate that in spite of the information criteria, the overestimation probability of the proposed algorithm does not increase in short data record cases.