# Is consecutive multiple transformation of Y variable a valid approach statistically?

I am going to run a regression analysis. But my response variable is highly right-skewed

Firstly I used a log(x+1) transformation and it increased the situation dramatically. But there is still right-skewness in my transformed data.

My question is; can I apply another transformation to my already transformed variable?

For example I have applied a sqrt transformation to my log(x+1) transformed variable and it is now very close to normality.

Is it valid in terms of data science and statistics? Can I apply such multiple data transformations to my data?

Thanks

Combining analytical transformations (say $$f$$ and $$g$$), as you suggest, is nothing else than applying a single $$u = f\circ g$$ transformation, so it is as valid as applying any simple transformation.
You just need to make sure that the transformation works (in this case, $$y>0$$ in the whole dataset and in the predictions, so that $$\sqrt{log(y+1)}$$ is real), and of course that it remains invertible, i.e. the initial variable can be retrieved from the transformed value, without ambiguity (this requires the transformation to be injective).