No clue. All we know is that you like letters for the variable names. You have to talk about the research if you want assistance. Best, David

1)Try to diagonalise the autocorrelation matrix

E(XX) E(YX) E(ZX)

E(XY) E(YY) E(ZY)

E(XZ) E(YZ) E(ZZ)

This will give you a new coordinate system x, y, z

with E(xy) =0 idem for each non diagonal term.

2) X and Y seem to be independent but not Z

How about a model like X +iZ =r exp(i alpha)

Y+iZ =s exp(i beta)

or look for f and g such that

f(X) +iZ =r exp (i alpha)

g(Y) +iZ =s exp(i beta)

Here is the idea: you know the Euler angles of articulated systems? A right model for these is obtained with three angles psi, theta, phi. If you were to stay in x, y, z, you would struggle, but with the angles, you have a canonical representation and nice decoupling...

Therefore change your representation to follow the canonicity of your problem.

Look at the physics of it: constraints, degrees of freedom.

Let me know if it helps

Hi Neto,

This may not the answer to your question directly, it is rather a comment on Regression and correlation. Correlation is symmetric and you can interchange the variables like Cor(x, y)=Cor(y,x) but in regression it is not the same. Because in regression you gona chaeck the impacts of independent variable(s) on dependent variable(s). Just take care when you change variables in your analysis. It is depend what is the objectives of your research. According to the objectives of your study you decide about the variables (Independent and dependent).

Best of luck