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Suppose a linear model for Y in a single predictor var, X. If the residuals show a pattern of increasing variance (wrt X), sometimes a transformation of Y, Y'=f(Y) is considered (where f is sq rt, log, etc), which we can express in the general form Y' = Y$^\alpha$, for $\alpha \in (0,1)$

My question is the following: has anyone ever researched the method for finding the best value of the parameter $\alpha$?

I don't see many references to this topic in my texts, yet it seems like such a simple question, that someone must have worked on it. Any references or something to point me in the right direction would be greatly appreciated.

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    $\begingroup$ I would point you towards power transforms such as the Box Cox and Yeo-Johnson transforms. Both are implemented in the R package car $\endgroup$
    – user603
    Commented Oct 29, 2014 at 15:43
  • $\begingroup$ I'm a student and had heard this term but was not familiar with it. I actually derived something similar to what they did (but figured it was too easy not to have been done already) Thanks! $\endgroup$ Commented Oct 29, 2014 at 15:55
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    $\begingroup$ I suggest that you follow the threads in stats.stackexchange.com/questions/121592/… $\endgroup$
    – IrishStat
    Commented Oct 29, 2014 at 16:08
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    $\begingroup$ ...or any of these other threads $\endgroup$
    – user603
    Commented Oct 29, 2014 at 16:11
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    $\begingroup$ The best ones to focus on mention Box-Cox transformations. $\endgroup$
    – whuber
    Commented Oct 29, 2014 at 16:13

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