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I assume that this graph doesn't support the assumption of homoscedasticity. Am I right? Does it make sense to carry out another test to be sure?

y-axis: Regression Standardized Residual, x-axis: Regression Standardized Predicted Value, dependent variable: Score of a questionnaire measuring rage attacks, n=156

enter image description here

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  • $\begingroup$ Welcome to the site. For those of us who don't speak German (I think it's German) could you translate the axis label? I think I understand most of it, but not "geschatzer Wert" and "think I understand" is not really good. $\endgroup$ – Peter Flom Dec 16 '19 at 13:56
  • $\begingroup$ Sure, it's in my text: y-axis: Regression Standardized Residual, x-axis: Regression Standardized Predicted Value. $\endgroup$ – AppleSeed Dec 16 '19 at 14:05
  • $\begingroup$ You should have a look at this $\endgroup$ – MGP Dec 16 '19 at 14:13
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    $\begingroup$ Does this answer your question? Chart indicates homoscedasticity but Breusch-Pagan test p<.001 $\endgroup$ – Nick Cox Dec 16 '19 at 14:27
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    $\begingroup$ There is a presumably a constraint on the response, say no score is lower than zero. Hence, residuals must plot above some line that in spirit is residual = minimum observed $-$ fitted. (Standardization affects details only.) This alone inhibits or prohibits homoscedasticity. If there is an upper bound only, all the more reason to consider a generalized linear model with appropriate link rather than plain regression. For more, see the thread suggested just above as duplicate. $\endgroup$ – Nick Cox Dec 16 '19 at 14:32
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Two essential assumptions of regression are being unbiased and variance independence with observations. Mathematically, $\varepsilon \in \mathbb{R}^{n}$ is:

$$ \varepsilon \sim \mathcal{N} (0, \sigma^{2} I_{n}). $$

In your case, it seems that the estimated variance increase with observations. Two possibilities : the first one is a problem of heteroscedasticity and maybe a problem of sampling.

I hope it helps.

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