A followup to my previous post on university retention and males.
Assume boys and girls are identical, except: there's something in the water at high schools that causes boys to do worse than girls; and there's something in the water at universities that causes boys to do worse than girls.
Suppose you had a data set for all university students, that told you for each student i: that student's performance at university Ui; that student's performance at high school Hi; and that student's sex Si (Si=1 for male, Si=0 for female).
Suppose you ran a multiple regression of Ui on Hi and Si:
Ui = a + bHi + cSi + ei
What would you expect to find?