# How to find proper weights for summation of 3 dependent variables

I have time series for 3 variables, say energies from 3 sources (e1, e2, e3). I have checked their dependency using the calculation of the correlation of each pair and found that their dependency is not ignorable (correlation varies between 0.3 to 0.7). They must be summed with their own weights (w1,w2, and w3, respectively) to retrieve total energy (E_total= w1*e1 + w2*e2 + w3*e3). I have also a benchmark to evaluate the total energy. The problem is that I don't know how to define the proper weights to sum those 3 variables. I really appreciate any help.

• Hi and welcome to Cross validated. The question IMHO cannot really be answered as posed - the answer would depend heavily on: what are the 3 variables, what exactly is their dependency structure and what do you want to do with the new variable. Could you clarify? Note that it is well possible that formulating those as precisely as you can would help you find the answer yourself. – Martin Modrák Jan 10 at 13:29