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I am performing a total least squares regression in which I have many x observations for a given y observation. The x observations are normally distributed.

I am aware I could do some sort of weighting using the variance of x at each y, but do I have to? Could I not just input every each x,y pair and run the regression? Would the results be the same?

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  • $\begingroup$ Can you give an example of your data set? If I understand correctly, you have more than one value of $x_1$ for a single value of $y$? If that's the case, I guess I would ask why that is, which would influence how you create your model. $\endgroup$ Sep 16, 2016 at 19:50
  • $\begingroup$ The dataset is ground penetrating radar measurements(GPR) (~x) taken over asphalt with a known air void content(~y). There are thousands of individual measurements taken over a single location. I do not have a sample of the dataset at this time. $\endgroup$
    – rconway91
    Sep 16, 2016 at 19:57
  • $\begingroup$ You seem to have flipped the response and predictor here. The $y$ in your experiment is not a random variable (you say it's known) -- the $x$'s are. Presumably the reason why you're calling it the $y$ here is you want to later use the derived relationship to predict air void content from GPR measurements (like inverse regression). $\endgroup$
    – Glen_b
    Sep 17, 2016 at 3:02
  • $\begingroup$ Glen_b, you are correct, that is the end goal of the regression. Is it incorrect to use the GPR data as the x value? $\endgroup$
    – rconway91
    Sep 17, 2016 at 12:46

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