Let's assume we have an OLS regression y(x). 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

Let's assume we have a 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

Let's assume we have an OLS regression y(x). Is there a way to obtain a distribution 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

Let's assume we have an OLS regression y(x). 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