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Based on this y vs. residual plot, where residual = y - prediction, it appears that my linear regression model is systematically under-predicting on y > 0.02. Could it be due to heteroskedastic errors? I'm modeling time series data, and I've plotted the residuals time series plot underneath the y vs. residual plot. I'd specifically like to know why the residuals are strictly positive for large y.

y_resid resid resid autocor y autocor y dist resid dist

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    $\begingroup$ You data has strong autocorrelation. $\endgroup$
    – SmallChess
    Commented Apr 24, 2018 at 8:00
  • $\begingroup$ Both x and y are positively skewed which will give you positively skewed residuals. $\endgroup$
    – dbwilson
    Commented Apr 24, 2018 at 11:49
  • $\begingroup$ How can we tell that the residuals are "strictly positive for large y"? None of your plots conveys that information and it's inadequately quantified: how large is "large" and how many such observations are involved? BTW, there's little evidence of any autocorrelation, either, so that's unlikely to be a factor. $\endgroup$
    – whuber ♦
    Commented Apr 24, 2018 at 15:29
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    $\begingroup$ I disagree that the residuals are autocorrelated - I've added some new plots to demonstrate. However, I agree that the dependent variable is positively skewed - is this ok if my only goal is prediction? $\endgroup$
    – tmakino
    Commented Apr 24, 2018 at 15:30
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    $\begingroup$ Your dependent variable is negatively skewed. The skewness appears reversed in some of the plots because you (or your software) has computed the negatives of the residuals. $\endgroup$
    – whuber ♦
    Commented Apr 24, 2018 at 15:31

1 Answer 1

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I think it can be one of two things (I would have to take a look at your data to say for sure):

  • either your data has high homoskedasticity
  • or your data is strongly auto-correlated (a typical characteristic of time series)
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  • $\begingroup$ You cannot have high homoskedasticity. You are either homoskedastic or you are not homoskedastic. It is a binary choice. $\endgroup$
    – Dave Harris
    Commented Apr 24, 2018 at 16:04
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    $\begingroup$ @DaveHarris If you only consider p-value cutoffs (e.g. p < 0.05) as the magic number, then it is binary. But if you look at the correct measure (the effect size, e.g. the actual value of W or F for the Levene's test), then a distribution can most certainly be highly homoskedastic versus not much. Even though it is traditional to only consider p < 0.05, it is always more meaningful to actually consider the value of the effect size. $\endgroup$
    – Tripartio
    Commented Apr 24, 2018 at 16:46

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