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?
Terminology for regression with more than 1 independent variable and more than 1 dependent variable?
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1 Answer
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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.
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$\begingroup$ I said "multiple regression corresponds to the case where we have 1 dependent variable and multiple independent variables" and "multivariate regression corresponds to the case where we have 1 independent variable and multiple dependent variables.". So, I think it is not "the other way around", what you said is exactly the same as what I stated in the question. I recommend editing your response accordingly. $\endgroup$– user5054Commented Nov 27, 2017 at 1:14
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$\begingroup$ OK, edited just for you. Thus, you should now admit that the question is answered by voting for it and accepting the answer. $\endgroup$– CarlCommented Nov 27, 2017 at 1:23
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1$\begingroup$ Of course I would do this, even if you do not ask me to do. But I also want to note that editing "just for me" does not make any sense. We all, including you as well, should be concerned about the true knowledge without any confusing pieces. This is why Stack Exchange exists in the first place. $\endgroup$– user5054Commented Nov 27, 2017 at 1:29
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$\begingroup$ Happy to oblige 1) you asked the question 2) you asked for a better answer. Moreover, all models are wrong is a more exacting standard than the truth. $\endgroup$– CarlCommented Nov 27, 2017 at 2:04
terminologytag which is about to hit 700 questions. [Edit: I just added the tag to your Q, so now our site does indeed have 700 terminology questions.] $\endgroup$