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SUMMARY: This paper studies the effect of noise correlation in some models of multi-output regression. It argues that a method that does not benefit from the correlation, such as Ordinary Least Squares (OLS), may perform much worse than a method that does, such as Maximum Likelihood Estimation (MLE). For certain linear models (Pooled model and Seemingly Unrelated Regression), which are studied in the paper, the MLE estimator requires the joint optimization of the covariance and regression weights. This is a non-convex problem. Alternative Minimization (AltMin) algorithm is an approach to solve the problem by iteratively optimizing the covariance and the weights.