Propagate error with prediction interval

I have a linear dataset with known values of X & Y in R. I treat the dataset as a linear model.

I have a data point with a known value of X and an unknown value of Y. The X value has an associated instrument error.

Goal: compute the prediction interval (of Y) for the data point based on the known value of X and its associated error.




This allows me to compute the prediction interval for a data point, based on a known value of X, but does not propagate the error associated with X.

I need a method in R to include/propagate the error associated with X.

Note - The X,Y dataset is subject to the same type of associated error as the input variable, X. However, we do not wish to include the dataset's associated error in this prediction interval.