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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.

user603
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Matt Brenneman
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    I would point you towards [power transforms](http://en.wikipedia.org/wiki/Power_transform) such as the Box Cox and Yeo-Johnson transforms. Both are implemented in the R package [car](http://cran.r-project.org/web/packages/car/) – user603 Oct 29 '14 at 15:43
  • 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! – Matt Brenneman Oct 29 '14 at 15:55
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    I suggest that you follow the threads in http://stats.stackexchange.com/questions/121592/determine-when-time-series-should-be-logged-or-any-other-transformation-and-ap/121595#121595 – IrishStat Oct 29 '14 at 16:08
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    ...or any of these [other threads](http://stats.stackexchange.com/questions/tagged/data-transformation) – user603 Oct 29 '14 at 16:11
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    The best ones to focus on mention [Box-Cox transformations](http://stats.stackexchange.com/search?tab=votes&q=Box-cox). – whuber Oct 29 '14 at 16:13
  • FWIW, my question wasn't HOW to do the transformation, but rather IF there was a method whereby one can obtain the best parameter for a power transformation. I know (now) the former answers the latter, but this specific form of my question (AFAIK) has not been asked. For this reason, it might be useful to leave up, in case anyone else is thinking along the lines I was. – Matt Brenneman Oct 29 '14 at 23:31

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