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I have a multiple regression model and when I check its residuals vs fitted I have determined a transformation of some kind needs to take place ... but I don't know which variable to start with (4 variables in total).

I was thinking I first need to make a a matrix where I can see each variable plotted against each other to see if any are linearly related.

I also thought I'd should make models of each variable against the dependent variable and check the residuals for each of these.

Is this going too far or rather making the process more complex than it needs to be ?

I guess my ultimate question is, is there an initial procedure you typically follow to determine which variable to transform ?

Scortchi - Reinstate Monica
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B.Miller
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  • What is the evidence for a transformation? Are you trying to achieve homoscedastic residuals, to linearize the relationship between the response and the regressors, or perhaps--because you mention exploring relationships among the regressors themselves--are you trying to cure some problem of collinearity? – whuber Sep 02 '15 at 15:18
  • My inital impressions from plotting the data are that I need to achieve homoscedastic residuals. I am not entirely confidnet in how collinearity works but thought comparing the variables against each other may help determine if they were making teh data be non-homoscedastic. – B.Miller Sep 02 '15 at 23:26

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The residuals vs. fitted plot is used to diagnose heteroscedasticity. If you believe there is sufficient heteroscedasticity to merit action, transformations are [only] one of the possible options (see my answer to: Alternatives to one-way ANOVA for heteroscedastic data). If you do choose a transformation as the right strategy for your situation, we are talking about transforming the $Y$ variable, not the $X$ variables. A standard way to select the transformation to use is to perform a Box-Cox analysis. It is commonly recommended to select not necessarily the optimal transformation, but the nearest interpretable transformation and see if it suffices.

gung - Reinstate Monica
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