### Regression with multiple dependent variables?

• Jeff

10 years ago

Is it possible to have a (multiple) regression equation with two or more dependent variables? Sure, you could run two separate regression equations, one for each DV, but that doesn't seem like it would capture any relationship between the two DVs? As in SUR or 3SLS?

• Brett Correct answer

10 years ago

Yes, it is possible. What you're interested is is called "Multivariate Multiple Regression" or just "Multivariate Regression". I don't know what software you are using, but you can do this in R.

Here's a link that provides examples.

http://www.public.iastate.edu/~maitra/stat501/lectures/MultivariateRegression.pdf One might add that fitting the regressions separateley is indeed equivalent to the multivariate formulation with a matrix of dependent variables. In R with package mvtnorm installed (1st: multivariate model, 2nd: separate univariate models): library(mvtnorm); X <- rmvnorm(100, c(1, 2), matrix(c(4, 2, 2, 3), ncol=2)); Y <- X %*% matrix(1:4, ncol=2) + rmvnorm(100, c(0, 0), diag(c(20, 30))); lm(Y ~ X[ , 1] + X[ , 2]); lm(Y[ , 1] ~ X[ , 1] + X[ , 2]); lm(Y[ , 2] ~ X[ , 1] + X[ , 2]) If it's equivalent, what's the purpose? @JoshuaRosenberg one reason for running a multivariate regression over separate regressions with single dependent variables is the ability to conduct tests of the coefficients across the different outcome variables. For example, you can perform an F-test to see if a predictor has the same effect on one outcome variable as it has on another outcome variable.

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