Multivariate linear regression is a statistical method used to analyze multiple response variables at once. The model assumes that the relationship between the responses and predictors can be represented by a coefficient matrix. Estimating these coefficients can be done using least squares or maximum likelihood methods, which yield similar results to running separate regressions for each response variable. However, this approach does not take into account any relationships between the response variables. Estimating all coefficients accurately may require a large number of observations, which can be a practical challenge.