Let's say I have a matrix of values for many different variables Y1..Y1000 at X=1,2,3..,10. Some of these variables are directly correlated with X, some follow different shapes (e.g. a normal distribution) and some are just random. I want to build a model to predict X based on given values of Y1..Y1000.
What would be the correct approach for this? I assume a simple linear regression would not be feasible because of the number of variables and the fact that not all variables are linearly dependent on X.