It's sometimes said (e.g. in this talk) that doing univariate analysis before multiple regression may lead to kicking off useful features and other mistakes. So, my questions are as follows.
- Are there any simple example models showing that such an effect may occur?
- If so, does it mean I need not to make univariate analysis at all? Or it just means that I can't reject a feature only due to the bad result of a univariate test?
EDIT: by univariate analysis I mean feature selection