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I am working on checking for constant variance in linear models and checking by looking at the plot of studentized residuals with fitted values. My data set via the plot looks to have a constant variance. I did a spread level plot on the data and it gives a suggested power transformation. 1.12, using this I fit a new model and checked the spread level plot again, which gives a power transformation of 1.05. I changed the power transformation to 1.05 and repeated this process many times. I finally settled on a power transformation of 1.252. After I refit the model to reflect the power transformation(1.252) and ran the spread level plot again. The suggested power transformation for this was 1.00068.

What I am wondering is If you can get the suggested power transformation to be very close to 1, does that mean the now has constant variance?

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    $\begingroup$ You have worked far too hard and have extended the spread-vs-level plot beyond its breaking point. It should be used just once and its estimate of the Box-Cox parameter should never be taken as gospel. In most cases, you should round it to the nearest multiple of $1/3$ or $1/2$. In this case, the initial result is good evidence that no transformation was needed, because $1.12$ is comfortably close to $1$. Stop with that and go on your way with the diagnosis of your model's fit. $\endgroup$ – whuber Aug 13 '14 at 15:30

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