Prove that if an additional regressor X k1 is added to X , Theils adjusted R 2 increases if and only if jTk1j 1,

Prove that if an additional regressor X kÅ1 is added to X , Theil’s adjusted R 2

increases if and only if jTkÅ1j È 1, where TkÅ1 Æ b¯kÅ1/s( b¯kÅ1) is the t-ratio for b¯kÅ1 and s( b¯kÅ1) Æ

¡

s2[(X 0X )¡1]kÅ1,kÅ1

¢1/2 is the homoskedasticity-formula standard error.