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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

AppleSeed
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    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. – Peter Flom Dec 16 '19 at 13:56
  • Sure, it's in my text: y-axis: Regression Standardized Residual, x-axis: Regression Standardized Predicted Value. – AppleSeed Dec 16 '19 at 14:05
  • You should have a look at [this](https://en.wikipedia.org/wiki/Breusch%E2%80%93Pagan_test) – MGP Dec 16 '19 at 14:13
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    Does this answer your question? [Chart indicates homoscedasticity but Breusch-Pagan test p<.001> – Nick Cox Dec 16 '19 at 14:27
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    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. – Nick Cox Dec 16 '19 at 14:32
  • Thanks for your help! Breusch-Pagan-test shows a significance of 0.187, the modified Breusch-Pagan p= 0.242 and the White-test p= 0.587. So, can I assume homoscedasticity? But the problem which Nick Cox wrote about stays...so is it still advisable to run a generalized linear model instead of a multiple linear regression? – AppleSeed Dec 16 '19 at 15:08
  • I don't think this is a duplicate because in the question marked as a potential duplicate the N was much larger and the Breusch Pagan test was statistically significant. – Peter Flom Dec 17 '19 at 11:34

1 Answers1

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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.

Nick Cox
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Rémi Coulaud
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