Let's assume we have a [simple linear regression](http://en.wikipedia.org/wiki/Simple_linear_regression) y(x) = a + bx. Is there a way to obtain a probability density function of y for any given x? Would the concept of confidence regions be useful here in any way?


I'm not a big expert in statistics and your help will be very much appreciated


Thank you



Distribution function of dependent variable, confidence regions
You need to make your answer more precise. First, the regression should be  

y = a + bx + e  

where e has some distribution, let's say described by a density g(e)


Now, do you mean:


1) Obtaining the density f(y|x) theoretically?  

This one is easy. By the transformation of densities  

f(y|x) = 1/(a+bx)\*g(y/(a+bx))


2) Estimating the density when you do not know the parameters of the regression model?  

This one will depend on what you know and what you don't know, and what data you have at hand, and is a more complex issue, so you need to provide more information.


