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Based on the graph, would you say that there is some sort of heteroscedasticity in the data? Y-axis is residual squared and X-axis is predicted values of Y

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  • $\begingroup$ This looks like a hard case: there is some concentration of larger residuals around the centre of the range of predicted Y values, but not so much that it couldn't plausibly be due to random variation. A little more detail might be helpful. What is your predictive model? Are you concerned about possible heteroscedasticity because ít may affect the reliability of standard errors of regression parameter estimates, or perhaps for some other reason? $\endgroup$ – Adam Bailey Apr 14 '16 at 9:12
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    $\begingroup$ Have you tried a White test to test for heteroskedasticity? $\endgroup$ – DornerA Apr 14 '16 at 12:13
  • $\begingroup$ I'm voting to close this question as off-topic because this is not about economics. If anything, this is about data analysis and should be migrated to cross.validated. $\endgroup$ – Martin Van der Linden Apr 15 '16 at 3:46
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The question should be: Does there appear to be enough heteroskedasticity so that not taking it into account would lower the quality of inference? And this is because "taking heteroskedasticity into account" (even if only for robust standard errors) is not without costs -with small sample sizes it may worsen the reliability of results. And it becomes even riskier if you want to implement the more traditional approach where you will specify a functional relationship between the error variances and the regressors.

From the graph, my initial conjecture would be "no, not enough". But peform an "influential observations" analysis, since you obvioulsy have a few large residuals. Also, with today's software, it is cheap to estimate a heteroskedasiticity robust variance covariance matrix, and see whether standard errors differ visibly or not, whether they reverse statistical sigificance tests or not, etc.

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