Engineer here, so apologies for my simplistic stats language.
I am missing some experimental data that I would like to "fill in" based on a linear regression to other data. I need to do this because I am measuring a process over a year, and a running sum of some measured quantities is required.
Let's say I have a set of x and y variables. There is a linear relationship between the variables. Both x and y have experimental errors attached to them (3-5% for y, ~5% for x, 95% confidence). I would like to be able to predict y based on x and provide a 95% prediction interval on that prediction.
I know I can calculate a prediction interval based on my data, e.g.: https://onlinecourses.science.psu.edu/stat414/node/298/
However, this doesn't seem to consider errors in my data. Am I correct to assume I'd need to look into "errors-in-variables" regression? If so, any easy-to follow examples would be appreciated.