# How can I predict a distribution (from a set of predictors) that I can simulate from?

Let's say I have the following regression problem:

Given a person's age and height, I want to predict how many years they've spent playing basketball. However, instead of just regressing on these features, I'd like to actually predict a distribution that I can simulate from: for each sample, I'd like to predict a distribution (for instance, predict the parameters for the normal distribution) for each specific test sample, that I can then draw samples from to simulate on.

More explicit example: after training my model, if I have a test sample with [age=25, height=72"], I'd like to predict the distribution for how many years that person has spent playing basketball, so I can draw samples from that predicted distribution for simulation purposes. Seems similar to quantile regression but I'd like to predict an explicit distribution that I can sample from...

Any tips for how to go about solving this?

• @defcal almost. It's the sum of squared errors divided by $n-2$ (rather than just $n$). Oct 28 '15 at 2:59