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Errors in independent variables

In the section Errors in independent variables in this lecture, there are a couple things I do not understand:

  1. Why not simply get rid of u by conversion to rolling mean?
  2. What is the difference between u and ϵ?

In addition, it would be great if there was some indication of how to apply the knowledge in the section.

I would also appreciate any other comments or resources about this topic.