Regression with multiple dependent variables?
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.
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])
@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.