Say I have the following multiple linear regression:
Y ~ X1 + X2 + X3 + X4
All X variables are independent, but X1 and X2 look kind of linearly related when plotted against one another (e.g., R-squared ~0.5, if I fit a simple linear regression to X1 ~ X2). Will BIC or AIC throw out one of the variables because this? How much collinearity is too much? Is there a formal procedure for identifying and dealing with such collinearity?