best estimate of that linear fit you can do this for multivariate gaussians again the math is going to be more hairier to this higher dimensional and so forth but only it's just very linear map there's no trickery happening you're just saying this is my density there's my data just plug away at it and out comes some result for these kind of solutions in nice closed form and again conditional multivariate Gaussian y equals C times X will come something that looks like least squares solution for the C matrix and then for the covariance matrix we'll