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I'm currently working on an assignment for a course in Statistics and was wondering anyones thoughts on this. My friends and I keep going back and forth on which one it is. I think it's true for the pattern but I don't understand why that would be the case.

True or False: The pattern of the residuals vs predicted values and the residuals vs a predictor based on a 2nd order model are exactly the same.

What I have thought of so far is that the patterns would be the same because of the fact that it is the only variable within the model.

I don't have a clue so any kind of help would be appreciated.

Thanks!!!

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    $\begingroup$ Please add the [self-study] tag & read its wiki. $\endgroup$
    – gung - Reinstate Monica
    Commented Dec 4, 2019 at 14:11
  • $\begingroup$ Why not make up some data and give it a try? $\endgroup$
    – Sal Mangiafico
    Commented Dec 4, 2019 at 15:23

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False

If the pattern of residuals vs. predicted values is the same as residuals vs. an individual predictor, there must be a linear relationship between the predictor and the predicted values. If this relationship between predictor and prediction is non-linear, then the two graphs will have different shapes. Because this is a second-order model, we know that the relationship between predictor and prediction is non-linear. Therefore, the pattern of residuals vs. predicted values is not the same as residuals vs. a predictor - essentially, you're taking the residuals vs. predictor graph, and performing a non-linear transformation of one of the axes (because the predictor to prediction transformation is non-linear).

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