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I'm doing a project which involves multiple regression, and I'm aware (as far as I understand) that the residuals should be normally distributed with a constant variance. From my study, the residuals look as follows

Residuals vs Fitted Values QQplot

However, the second plot (the QQ-plot) indicates that the residuals are not normally distributed. I've tried to transform some of my continuous explanatory variables and also tried to fit variables with a spline function, both attempts without any success. I've read these posts which concern the subject

Post1, Post2, Post3, Post4, Post5 and finally, a post where the author seem to have the same problem as myself; Post6.

From these posts, I've reached these conclusions:

  • Rarely is it the case that you see a QQ plot that lines up along a straight line. Even if you have tried all kinds of transformations/fittings, a QQ-plot that doesn't fit with a straight line is not a substantial issue in practical terms. Thus, I should not be fixated on fixing the residuals.

  • There are other methods, such as Box-Tidwell, which can help me. But using this method can often result in models which are hard to interpret.


Question By looking at my plots above, do you see any obvious transformation that can be used? Or is there any other way to make sure that the residuals fulfill the assumption of normally distributed residuals? Or should I just leave it and try to explain why the residuals aren't normal?

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  • $\begingroup$ If there is any, what's the distribution you assumed when running regression? Poisson/Gamma/Tweedie? From the residual plots, the residual range for fitted value 190 above are narrower, this may be an indicator of too higher order of distribution power under a GLM model structure. $\endgroup$ – Sixiang.Hu Feb 28 '18 at 13:52
  • $\begingroup$ One of my friends agree with you, that I should use GLM and see if the residuals perhaps are Gamma-distributed (or any other distribution that are scewed). I will try to use this method and see what happens. Thank you! $\endgroup$ – Aerdennis Mar 1 '18 at 10:08
  • $\begingroup$ Use of R here seems incidental. There is no good reason to make R the first word in the title. $\endgroup$ – Nick Cox Mar 18 at 17:09
  • $\begingroup$ Lack of symmetry here implies that you might be better off working on a different scale. Although this thread may be dead (OP asked just this one question and hasn't visited the site since January), I would want to know much more about the response or outcome variable and whether it is bounded, in practice if not in principle. Also, all "multiple regression" implies is two or more predictors; without more of a story there, it's hard to advise. $\endgroup$ – Nick Cox Mar 18 at 17:12
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My advice would be to stop trying to force the data to fit your model and choose a model that fits your data.

For example: Quantile regression or various robust regression methods could be used.

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Although I am not 100%, what I would do in this scenario is split up the variables you included in your multiple regression, then graph a scatter plot of them individually. This will help you see what kind of data you are dealing with without the other variables clouding up your analysis. Determine if only one variable, or all of them need to be transformed, transform them individually, then regress the new variables on each other.

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  • $\begingroup$ Thanks for the answer! I did, one of the variables was fitted with a polynomial of second degree and the other with a log. Though, the result was the same. I will try to use GLM and also approach the datamaterial in another way to see if I get a better result. $\endgroup$ – Aerdennis Mar 1 '18 at 10:15

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