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A response $y$ has been measured using 25 electronic devices.

For 8 of them, the response was heavily flawed. It was usually equal to a third of the response measured from the other devices.

So, I removed them and did my main analysis. I then thought, could I use the data from the other 8 responses (i.e., the covariates), and use them to predict new data, and then I would take a third of that data, and compare with the responses from the 8 devices I actually got?

If that's a good fit, then that would seem to confirm the hypothesis that the 8 devices give responses equal to a third of the "actual" response (assuming our model is correct)?

Is this a good idea?

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In order to find a sensible answer to your question, "is it a good idea?", I would want to know what we are talking about. Imagine your $y$ is the result of function that is carried out, defined by a number of characteristics. The answer to "what is $y$?", is therefore not only defined by the attribute it is supposed to represent, but also by a number of characteristics describing the context:

  • what object(s) are the measurements taken from? E.g. water samples, some rat's brain, some people in a company's customers panel, a piece of aluminum foil put in a microwave that is running at 700W.
  • what instruments were used?
  • when were the measurements taken?
  • given the time of measurement, should the measurements have the same result and why?
  • who was pushing the buttons?
  • etc.

If 8 of the measurements show different outcomes (bias?), in a consistent pattern, I would say that your measurement theory is incomplete or incorrect.

It's generally not a good idea to assume that any model is correct. Remember, it's a model!

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