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For linear regression:

If the variable is right skewed, a log transformation of the data is suitable. If the variable is left skewed, square, cubic or higher powers is suitable.

Source: http://fmwww.bc.edu/repec/bocode/t/transint.html

For the independent variables:

I applied higher powers for my left skewed data, but they are still left skewed. What do I do? Do I just leave the data as it is when I run my linear regression? Well certainly, my AICs are better without the transformation.

When I got rid off the transformation, the linear regression results are the same as before with the transformation.

kjetil b halvorsen
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lusicat
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    Does the skewness in data collected even matter in a linear regression? – lusicat Dec 26 '16 at 01:27
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    Do you talk about response or predictor variables, or both? Could you make the Q a little bit more specific by specifying your regression model (with equations), and telling us what the variables represent, that is, what they are supposed to measure? – kjetil b halvorsen Dec 26 '16 at 01:32
  • Question updated... – lusicat Dec 26 '16 at 01:34
  • You make some statements in your question. Are you quoting some source, or are you asserting these to be facts? – Glen_b Dec 26 '16 at 01:49
  • Yes, these are facts from my results... – lusicat Dec 26 '16 at 01:50
  • It is interesting after applying a transformation for my left skewed independent variables, the linear regression coefficients and AIC did not change in R. – lusicat Dec 26 '16 at 01:56
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    There is no assumption in regression that the predictor variables should have any specific distribution! So no need to transform. See for instance http://stats.stackexchange.com/questions/1444/how-should-i-transform-non-negative-data-including-zeros/1452#1452 and serach this site, there are many good posts about transformations. – kjetil b halvorsen Dec 26 '16 at 02:05
  • but what if I assume it in my linear model...for my study purposes? – lusicat Dec 26 '16 at 02:11
  • Are variables skewed or regression residuals? The latter should be all that matters. – Björn Dec 26 '16 at 06:07
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    @Delta: if you make such assumptions, then your model is not a stanfard linear model, and you shiold ecålain to us why you need those assuptions. – kjetil b halvorsen Dec 28 '16 at 11:47

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