I'm just wondering if it's possible to analyse and interpret variables that have been transformed using different transformations (eg log and square-root) or if all variables in the analysis have to have been transformed with the same method in order to interpret the results. Thanks, Suzie

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    $\begingroup$ Yes to the first, No to the second. A number of threads on this site with the 'data-transformation' tag should be helpful, e.g., stats.stackexchange.com/questions/18480/… (see Charlie and jthetzel's answers). $\endgroup$ – rolando2 Mar 11 '12 at 13:44

Just a simple example to see why data can be transformed in any suitable way for the analysis:

Imagine we want to find out the dependency between the size of a car and its price. For some reason you measure the area (or volume), whereas the effect perhaps can be explained better when looking at the length. Let's assume also that the marginal utility of additional income decreases, hence we would expect a dependency between $\log(income)$ and the length. The only way to capture this correctly is to apply different transformations to the variables.

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