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I am aware that one should transform percentages and proportions when using them in an ANOVA, due to the values being bounded by 0 and 1. I have seen suggestions that the best transformations are logit and arcsine (with benefits/problems with both).

However, I have two linked questions about a multiple linear regression.

1) Does one still need to transform the percentages and proportions when using them as predictor variables in a multiple linear regression? Or can they be left in their raw form?

2) How about when using percentages/proportions as an outcome variable in a multiple linear regression?

Clarification: As discussed in my original question, I am particularly interested in whether the guidance depends on the percentages/proportions being used as an outcome or predictor variable in a linear regression.

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It is less of an issue whether a variable is expressed as a percentage then the underlying distribution of that variable and the residuals of linear regression. In fact, it may be argued that most variables measured are in some way bounded (eg max possible temperature) and discrete. In some cases proportional variables lend themselves to linear regression without transformations and in some cases they can be so clustered or skewed that none of the transformations can mitigate that. Arcsine and logit will work for intermediate cases, particularly when there are a lot of values close to 0 and 1.

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  • $\begingroup$ Thank you katya. Does the guidance differ dependent on whether the the proportion(s) is an outcome or predictor variable? $\endgroup$ Commented Jul 29, 2015 at 14:06
  • $\begingroup$ analyzing the distribution of residuals incorporates both; however for extreme cases with very few categories, the choice of the model will differ depending on whether it is response (logistic model) or one of multiple predictors. $\endgroup$
    – katya
    Commented Jul 29, 2015 at 16:35
  • $\begingroup$ Thank you for your response. The model that I am running is exploring the relationship between multiple predictors (expressed as proportions) with a single continuous outcome variable, hence why I am using a linear regression. $\endgroup$ Commented Jul 29, 2015 at 17:39
  • $\begingroup$ related, asked by same OP: stats.stackexchange.com/questions/163822/… $\endgroup$
    – Helix123
    Commented Jan 28, 2016 at 21:46

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