Box-Cox transform doesn't make data normal I'm working with the famous diamonds dataset and the target value is non-normal:

After applying the Box-Cox transform, the shape of the histogram is closer to a normal distribution but the quantile plot is far from it:

Also, all normality tests fail to reject non-normality with tiny p-values. This happens after I have filtered the outliers in my data using the IQR criterion.
Is there a way to fix the normality of my target variable? Why is the Box-Cox transform failing?

Quick points about the issues you raised:

*

*There is no guarantee that the Box-Cox transformation will transform your data to look more like a normal distribution.

*Do not remove "outliers" because they do not fit your model, change your model.

*Often times there is nothing you can do (no transformation) that can make a variable "normal".

More importantly:


*Why are you trying to transform your variable into a normal distribution?

*Why are you removing "outliers"?

*Your data is bounded from below by 0 (or close to 0, so it appears), so there is no way to make this normal in any way, shape, or form.

