An algorithm for estimating variance components (Method R) based on the linear regression coefficient (R) of recent (more accurate) on previous (less accurate) individual genetic predictions is presented. The previous prediction is obtained by analyzing a subsample of the whole data set. First raw moment of R equals 1 regardless of the distribution of observations and predictions. A condition such as the use of inappropriate variance components ratio (VC) can cause this regression to deviate from its expectation. If the computed R (Rc) is greater than 1, then VC ratio has been underestimated, and if Rc is less than 1, then VC ratio has been overestimated. Several iterations are performed, changing the VC ratio at each iteration, until Rc approximately equal to 1. When an Rc is obtained that is acceptably close to 1 (precision is reached), then the appropriate VC has been used. Method R does not require computation of the inverse of the coefficient matrix and has desirable properties of convergence, precision, and computing feasibility. Additional sampling variance in the estimate of VC is expected due to the requirement of taking a subsample of the entire data set to obtain the lower accuracy predictions. This sampling variance is shown to be small for simulated datasets of size n = 10,000 with no selection.