How to write R formula for multivariate response?

Question

In R I want to do some regression on multivariate response on all predictors, for univariate response, I know the formula is like

y~., this is to use all predictors to regress y, what if now I face 100 response, I can not type 100 yi like y1+y2+y3...+y4~x, so how to use all predictors to regress multivariate response?

Answer 1

In R, the multivariate formula is to use cbind() for your Y variable. Thus, the formula would be:

model <- lm(cbind(y1, y2, y3, y4)~x)

Answer 2

That's relatively easy if y is a matrix with 100 columns. In that case you do it the same way. For example:

lm(y ~ x)

will do a linear regression of y onto the columns of x.