This is the Normal Probability Plot I've obtained for some data:


As you can see the points seem to osciallate, as in a period, around the line of slope 1 and passing through the origin. I've obtained this plot by trying to fit a simple linear regression model. Can I deduce from this peculiar behaviour (just as an Anzat, or a guess, waiting for further tests) that this can indicate that there is a polynomial relationship? (for example the grade of the polynomial might be equal to the number of times the oscillation crosses the line)

Or otherwise, what does this suggest? That there is a trigonometric relationship?


Basically Ive fitted a linear model data.lm <- lm(y~x, data=data) , then Ive created the standardized residuals data.lm$sr <- rstandard(data.lm) and finally plotted the qqplot qqnorm(data.lm$sr) and I've added abline(0,1)

  • $\begingroup$ It may be random, or it may be a degree of clustering in your residuals. One possible cause could be some rounding in your original data $\endgroup$ – Henry Apr 12 '17 at 20:42
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    $\begingroup$ I think you're reading way more into your small sample than you have evidence for; those little wiggles do happen with random data. You may have somewhat shorter tails but even that can happen sometimes. See here (where even in larger samples, plots g, i and u among others show such wiggles); also see here which gives advice on reading the plots $\endgroup$ – Glen_b -Reinstate Monica Apr 13 '17 at 1:44
  • $\begingroup$ @Henry Actually there is some rounding involved in the acquisition of data! $\endgroup$ – Euler_Salter Apr 13 '17 at 2:40
  • $\begingroup$ ... probably worth mentioning in the question. It looks like you have 3 pairs of duplicated values. $\endgroup$ – Glen_b -Reinstate Monica Apr 13 '17 at 2:54
  • $\begingroup$ @Glen_b where do you see that from? $\endgroup$ – Euler_Salter Apr 13 '17 at 8:42

It is true that a qq plot from a multimodal distribution would look like this (with bumps), but assuming that none of the points in the picture are on top of each other, you only have 29 data points. The data could easily be normally distributed and yet have a qq plot that looks just like this. To check, you can simulate data sets of size 30 from a normal distribution and make qq plots of them.

Here are 16 which I made with the commands

for (i in 1L:16){x<-rnorm(30);qqnorm(x);abline(0,1)}

enter image description here

By coincidence, in this case the bottom left hand plot looks very much like yours!

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    $\begingroup$ +1 ... though I guess you mean "multimodal" in the first sentence? (you might enjoy the first answer I linked in comments above) $\endgroup$ – Glen_b -Reinstate Monica Apr 13 '17 at 1:45

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