One approach in notation:

A(s,q,i,d) means Answer according to indices s=subject index, q=question index, i=independent variable index, d=dependent variable index.

So, you have a 4-dimensional space of answer values.

A(1,1,1,1) to A(n,3,8,3).

I don't think this is what's needed for a couple of reasons:

1) Any question regarding the dependent variable must be in the context of at least the one independent variable or it's out of context. Isn't that right?

2) A question about an independent variable has no meaning without the dependent variable. This may be the same as #1 said another way.

You might consider the following:

n subjects

8 independent variables of q values each

(where you should ask if q values reasonably represents the independent variable span)

1 dependent variable of m values

(where you should ask if m values reasonably represents the dependent variable span)

Then each question or test would be posed GIVEN each of the m dependent variable values.

So, there will be m tests per independent variable.

That's also a total of nxqxm questions .... or "tests"

The notation might be:

Q(s,i,d) > A(s,i,d) Where the matrix is nxqxm Presumably you will want to combine the subject data into a single test result. So, I would be thinking along the lines of:

A(1,i,d) + A(2,i,d) + ......... + A(n,i,d) = P(i,d)

which is the sum of all subjects for EACH indenpendent variable value and EACH dependent variable value.

and, of course, you could use the square root of the sum of the squares or some such measure instead of a simple sum - depending on what you want / need.

Now you have a 2-dimensional matrix that's pretty easy to handle / envision.

The tests were done with alignment of the columns by stating a specific value for the independent variable in each case.

You said:

I'd like to prove there is (or is not) a positive/negative correlation between each independent variable and the dependent variable.

This suggests correlating the dependent variable vector (which I've not made notation for yet) and each independent variable vector.

So, the have I(1, ....,m) which is the vector of independent variable values.

Compute the correlation of I with A in order to get the correlation coefficient for each independent variable. Something like:

i=8 d=m

C(i) = sum[I(i)*P(i,d)]

i=1 d=1

I've not been too careful here and I'm a bit worried about mixing up the number of variables and the number of VALUES of each variable that's being use.

But, I hope it's a nudge in the right direction.