I have yet to find a good intuitive explanation of TLS. Online resources tend to focus on the vertical vs. perpendicular square error pictures (I don't need to see perpendicular lines to understand what that means) and quickly move to PCA formulas showing how to calculate TLS betas.

I would like an intuitive explanation that answers these questions:

  1. 'TLS accounts for both the error in the dependent variable and the independent variable'. What does that mean?
  2. Why is the OLS beta from Y ~ X not the inverse of X ~ Y (intuition)?
  3. How does TLS help to solve practical regression modeling problems compared to OLS?

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