Final Step: Prediction new values using model I'm about to finish up a machine learning challenge, but I'm suck on the final part. Before running my model I did a simple power transformation ($dependent ~variable^{1/4}$)  on the dependent variable in the training set to make it look more like a standard normal distribution. Do I do the inverse transformation ($predicted~scores^4$) to my prediction scores (my test set does not have the dependent variable)?
I had negative values in my original dependent variable in my training set, will I not be able to predict these?
 A: It sounds like something has gone wrong a bit/the transformation does not achieve entirely what you want it to do, because I would guess that the model "thinks" that values <0 correspond to values of the back-transformed variable <0 (when they probably should just be closer to zero), but with the inverse transformation being $f(y) = y^4$, they actually end up being values that are higher than (some) values >0. Some transformation can be okay for inferential analyses, but problematic for prediction (e.g. square-root transformation for integer valued count data).
I would be tempted to consider an alternative transformation - e.g. if all values are strictly positive a log-transformation could be a candidate (then a machine learning model can predict any number in $(-\infty, \infty)$ and they all map to a number in $(0, \infty)$).
Alternatives include using an output-/final-activiation-/link-/loss-function in your machine learning model that implicitly does a meaningful transformation.
A: The answer is yes you should. The model you have fitted is of the form $g(y)=f(x)$, and hence you predicted values are of the form $\hat{g(y)}$. To get $\hat{y}$ the back  transformation  is necessary. 
