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I am running some data in R that is intended for multiple regression. However my data is not normally distributed. Most of my independant variables are continuous, however one is a catagorical factor containing two groups. The issue is that when looking at my dependent variable in terms of these groupings, there is a strong positive skew with one group and a strong negative skew with another group. I have included histogram images below to get an idea. Is there a transformation that I can apply that can help resolve this type of non-normality and how can I do this in R? I tried a log transformation, square root transformation, cube root transofrmation... no luck.

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    $\begingroup$ What about the residuals of your regression? Those are what matter. $\endgroup$
    – Dave
    Jun 26, 2020 at 11:32
  • $\begingroup$ Do you know anything about the process generating the data? $\endgroup$
    – user289381
    Jun 26, 2020 at 11:42
  • $\begingroup$ As @Dave commented: Data do not need to be normaly distributed for linear regression or else you could not even think of binary predictors. $\endgroup$
    – Bernhard
    Jun 26, 2020 at 11:58
  • $\begingroup$ Added residials via an edit. This has not been adjusted for outliers. $\endgroup$
    – Guest
    Jun 26, 2020 at 12:56
  • $\begingroup$ I would't worry based on these plots. For tests/confidence intervals, you could try bootstrapping. $\endgroup$ Jun 27, 2020 at 2:36

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There is an R package called trafo that may give some ideas. I have not used it but it tests model assumptions using residuals (see @dave comment).

The dependent variable and group two look candidates for preprocessing by taking logarithms.

The Q-Q plot is not bad as far as these things go. The heteroscedasity in the residuals can be tested for using the Breusch–Pagan test.

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