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Could you please help me interpret the following residual plot and P-P plot from a multiple regression analysis?

I'd say that this shows evidence of heteroscedasticity as the residuals are grouped together, but I'm not sure.

enter image description here

enter image description here

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    $\begingroup$ The discreteness of the top plot strongly indicates the need for a GLM rather than OLS model. This needs to be taken care of before considering heteroscedasticity. $\endgroup$
    – whuber
    Nov 14, 2019 at 23:56
  • $\begingroup$ Existence of extreme values suggest the distribution deviate from symmetry. $\endgroup$ Sep 15, 2020 at 11:43

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Heteroskedasticity is not about errors being grouped together but about unequal variance (variability) of the errors. In your plot errors seem to have different variability at the beginning of the plot then in the end so I would say there is heteroskedasticity there.

Probability-probability (p-p) plot measures how closely two distributions match together. If you get perfect straight lines the distributions are perfect match. However, p-p plots are used to test normality of errors by comparing the error distribution to normal one not to test heteroskedasticity.

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    $\begingroup$ Right, thanks for your explanation, now I think I understand the difference between checking for homoskedasticity and checking for normality (I'm a student, still learning all this!). What does the P-P plot indicate then? There is a deviation from the diagonal around the middle, does this mean that the distribution is not normal? $\endgroup$
    – Cyrille
    Nov 14, 2019 at 23:55
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    $\begingroup$ @Cyrille yes the more it deviates from straight line the more are the distributions different - however, you get straight line only with identical distributions so small deviations are ok. On more sophisticated p-p plot you would have an acceptance region based on some test and say that the distribution is non normal only when you get outside that. Just eyeballing it it looks like it’s not normal. In real life I would always do some supplementary tests looking at graphs is arbitrary $\endgroup$
    – 1muflon1
    Nov 15, 2019 at 0:00

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