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In most of the times in linear regression, the two problems of non-normality and hetroskedasticity are present both in the model.

However, the two problems could be (but not neccessarily) inter-related; if one is solved, the other could be solved automatically.

If I have a regression model, with non-normal errors (P-value of Shapiro Wilk is < .001), and hetroskedastic erros (P-value of White's test is < .001).

And I am interested to solve the problem of non-normality with bootstrapping, but am not sure whether the hetroskedasticity is solved automatically or not.

Recently, I have found bootstrap for White's test for hetroskedasticity, within the R-package "whitestrap."

If bootstrap of White's test results in a non-significant P-value (i.e., > .05), is this a good justification for us to run our regression analysis using bootstrapping in order to solve both problems?

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    $\begingroup$ Those low p-values could be misleading. While their tests might be right that the error terms do not have normal distributions or distributions with equal variances, the p-value tells you nothing about the extent to which those assumptions are violated. Depending on your sample size, it might just be that the tests are (correctly) identifying tiny deviations that have minimal impact on your work. $\endgroup$
    – Dave
    Commented Feb 14, 2023 at 2:24
  • $\begingroup$ You're right. But just assume that p-values give a good indication of non-normality or hetroskedasticity (and they support the histogram / plots) $\endgroup$
    – Hussain
    Commented Feb 14, 2023 at 2:57
  • $\begingroup$ Maybe look into pair bootstrap, look into stats.stackexchange.com/questions/604511/… $\endgroup$
    – kjetil b halvorsen ♦
    Commented Feb 18, 2023 at 2:16
  • $\begingroup$ Why not perform some transformations on the data first? $\endgroup$
    – Estimate the estimators
    Commented Feb 19, 2023 at 17:03
  • $\begingroup$ Transformation most of the times fail (from my experience) $\endgroup$
    – Hussain
    Commented Feb 20, 2023 at 11:26

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