I'll start by saying that I'm a software engineer, and while I took statistics courses, I'm far of an expert in it.
My job is to essentially build software for data scientists in my team to help them with their research.
One of the data scientists recently asked me for a tool that will do the following:
- Given $K$ features (large number), run a regression of them on $Y$.
- Compute the $t$ stat and $p$ value of each of these features.
- If any feature has $p$ value greater than $0.05$, remove it from the set of features.
- Rerun this procedure until the $p$ value is $\leq 0.05$ for all features. Report this model.
Now I can easily build this, but honestly, I am questioning the soundness of this technique.
I recall my stat professor mentioning that you can't compare the $t$ value in multiple regression across multiple features and you should only use it to test the significance of one variable, not a group of variables. I also researched a bit online and it seems like the most common way to selecting features is either 1) Forward selection 2) Backward Selection and 3) Stable selection, none of which use the $p$ value as a basis of removing variables.
Any idea if I am making a fuss out of nothing?