I know that multiple regression corresponds to the case where we have 1 dependent variable and multiple independent variables. Multivariate regression, on the other hand, corresponds to the case where we have 1 independent variable and multiple dependent variables. So, my question is, what do we call it if a regression method learns the coefficients of multiple independent variables learned from multiple dependent variables at a time (in a multi-task fashion where the dependent variables are the tasks)? Is it both multivariate and multiple regression?
Multiple regression, a term first used by Pearson, 1908, is to learn more about the relationship between several independent or predictor variables and one dependent or criterion variable.
Multivariate regression is a technique that estimates a single regression model with more than one outcome variable.
Ans. When there is more than one predictor variable in a multivariate regression model, the model is a multivariate multiple regression.