Can someone help me understand? I know that you don't want to add variables to a model if they don't actually assist in predicting the dependent variable, but what is the mathematical reason behind this as it pertains to this question? What is R^2adj, and how is it interpreted? It's been a long time since I've taken a statistics course and I'm trying to teach myself. Detailed explanation appreciated!!! Thank you.

If adding predictor variables to a regression model never reduces R2 why not just include all the available predictor variables in the model? Also, remark on the meaning of Radi