# Prediction intervals with experimental errors

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.

• Hi, welcome to CV, and thanks for a nice first question! I took the liberty of changing the CI to a PI; the two concepts are similar but different. Unfortunately, plain vanilla errors-in-variables models only account for errors in the independent variables, whereas you have errors in both the independent and dependent variables, so you will need to do something more fancy. I am not an expert about this, though, so I hope someone will chime in. – Stephan Kolassa Jun 8 '18 at 19:20
• This may be helpful: Systematic/measurement error on a linear regression. Not a duplicate, though, because it doesn't go into prediction. – Stephan Kolassa Jun 8 '18 at 19:23
• Or this one: Methods for fitting a “simple” measurement error model. Unfortunately, the link in the answer is dead. – Stephan Kolassa Jun 8 '18 at 19:26
• Thanks for the pointers! That gives me a starting point. It's curious to me that I can't find any sort of "standard" method for this - I would've thought it to be a common problem. Maybe I'm looking in the wrong places. – cmeister Jun 11 '18 at 12:54