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When transforming the dependent variables, I know R^2 and related criterion is not suitable for model selection. Then which one should I use?

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    $\begingroup$ the question is not clear... model selection for what? $\endgroup$
    – ABK
    Mar 6 '20 at 10:49
  • $\begingroup$ In a simple linear regression, I want to select the best lambda when doing box-cox transformation for the dependent variable . Thank you. $\endgroup$
    – Eva
    Mar 6 '20 at 10:58
  • $\begingroup$ See stats.stackexchange.com/questions/242526/… or the list. Probably a dup in there $\endgroup$ Mar 6 '20 at 13:14
  • $\begingroup$ This question is so general that it deserves a general answer, which is provided by the duplicate. $\endgroup$
    – whuber
    Mar 9 '20 at 14:31
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Unless you are exclusively interested in prediction (and not at all in explanation) then I think you should only transform variables for substantive reasons, not statistical ones.

EDIT 2 For instance, it often makes sense to take logs of money variables such as income or price.

EDIT 1 Note that not all statisticians share my views.

If the assumptions of OLS regression are not met, then, rather than transform, you can use a different model, such as quantile regression or robust regression.

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  • $\begingroup$ Thank you for your suggestion. But I have to do some transformation for the response and compare them, which the requirement of my hw. $\endgroup$
    – Eva
    Mar 9 '20 at 13:58
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    $\begingroup$ It is worth noting that your opinion very well may be a minority one among statisticians, especially those exposed to Tukey's work on EDA. Tukey advocated using exploratory analysis to uncover effective ways of re-expressing data. This was one of the cornerstones of his approach to all data analysis. $\endgroup$
    – whuber
    Mar 9 '20 at 14:33
  • $\begingroup$ OK, I edited my answer. But Tukey didn't have the tools that we have - at least, not in any practical way. I know quantile regression is very old in theory, but it only became practical with computer. $\endgroup$
    – Peter Flom
    Mar 9 '20 at 18:59
  • $\begingroup$ There are many situations e.g fitting power functions or exponentials where taking logs first is natural and convenient and often the best thing to do. I don't know whether you call that circumstance substantive or statistical. The same applies, although on the whole with less force, to several other transformations. $\endgroup$
    – Nick Cox
    Mar 9 '20 at 19:09
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    $\begingroup$ With many kinds of data being willing to use logarithmic scale arises from past experience that it is a good idea. Some people call that theory. $\endgroup$
    – Nick Cox
    Mar 9 '20 at 19:20

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