In a very basic problem or linear regression y= mx + q one can define an Confidence Interval around the line. This has a characteristic shape: narrow at the center getting bigger at the extremities. Instead of just those boundaries, I would like to calculate a probability density function of the line to be pass through a point (xi,yi)

In brief my question is: How can I calculate a PDF around the line ? To be clearer this is the probability function of which the CDF=0.95 would correspond to the 95% C.I.

Sorry for my ignorance if this is very basic.



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