# Can I iteratively transform a variable with log10 until it fits a linear model?

I have a response variable, $Z$, for which I'm trying to make a linear model.

Here are some of the fit diagnostics plots: From the fan-like shape of the residual-vs-predicted value plots, I concluded that a $log_{10}$ transformation should be appropriate, so I transformed $Z$ and got the following plots: Then I iteratively applied $log_{10}$ to form a new variable $W = log_{10}(1+log_{10}log_{10}Z)$ and got this: The lack-of-fit $p$ value also improves: from $0.01$ with no transformations, to $0.08$ for the last one.

Now, my questions is as follows:

1. Is it a good practice to iteratively apply transformations until variance is stabilized enough, and $p$ value of the lack-of-fittests improves over $0.05$?
2. Would it be acceptable to proceed with the analysis of the linear model for $W$, or it would be better to try to fit nonlinear models to $Z$?
• If you simply care about prediction and not interpretation and you have validated your data against a validation dataset, I see nothing wrong with this approach. – StatsStudent May 21 '16 at 19:00

Is it a good practice to iteratively apply transformations until variance is stabilized enough, and $p-$value of the lack-of-fittests improves over 0.05?
Would it be acceptable to proceed with the analysis of the linear model for $W$, or it would be better to try to fit nonlinear models to $Z$?
If you are interested in the behavior of $Z$ I think it would be better to try to fit non-linear models to $Z$. This is unless you expect the functional form of $W$ for $Z$. If you believe that to best represent $Z$ then you should go with that.