In this paper, we describe a fully automatic method using latent root regression based on the generalized sidelobe can-celer (GSC) parameterization of the minimum variance beam-former. The proposed method gives a theoretically optimal solution in mean-squared error (MSE) sense (minimized MSE solution) by choosing a linear combination of individual latent root regression predictors in the GSC formulation. The performance of the resulting beamformer is illustrated via numerical examples and compared with existing automatic diagonal loading techniques including HKB and the general linear combination (GLC) shrinkage-based method. The simulations show that the proposed method usually gives better performance than HKB, meanwhile, is more robust to errors on steering vectors than GLC when the sample sizes are high.