Can you provide more details. Typically you have a single vector for dependent variable. So you have 16 dependent and also independent variables? If so, what is your research question?

Let me explain with an example

say A is a matrix

[ 1 2 3

4 5 6

7 8 9 ]

B is another matrix

[ 5 6 8

8 9 2

1 2 5 ]

I am looking for an analysis that allow me to predict every columns in B by using the corresponding column in A.

For example, predict [ 5 8 1 ] (first column in B) by using [1 4 7](first column in A).

As there are three column altogether, i want to do it by using one analysis instead of running 3 linear regression.