如果你已经知道有两个隐含因子，但不知道a,b，也不知道X,Y具体是什么，那就是confirmatory factor analysis. a and b are factor load, X and Y are latent variables.

If you want to know what X and Y are, one way is to do the principle component analysis with some rotation method. You can guess something from the first two largest component.

One group of 500 points will give you an estimate a b, and something about X and Y.

ten group of data will give you an estimate of average a, b. or if you prefer, do separate analysis.