ared ▁is ▁the ▁coefficient ▁of ▁determ ination ▁indicating ▁good ness - of - fit ▁of ▁the ▁regression . ▁This ▁stat istic ▁will ▁be ▁equal ▁to ▁one ▁if ▁fit ▁is ▁perfect , ▁and ▁to ▁zero ▁when ▁re gress ors ▁X ▁have ▁no ▁explan atory ▁power ▁what so ever . ▁This ▁is ▁a ▁bi ased ▁estimate ▁of ▁the ▁population ▁R - squ ared , ▁and ▁will ▁never ▁decrease ▁if ▁additional ▁re gress ors ▁are ▁added , ▁even ▁if ▁they ▁are ▁irrelevant . ▁ ▁Ad just ed ▁R - squ ared ▁is ▁a ▁slightly ▁modified ▁version ▁of ▁, ▁designed ▁to ▁pen al ize ▁for ▁the ▁excess ▁number ▁of ▁re gress ors ▁which ▁do ▁not ▁add ▁to ▁the ▁explan atory ▁power ▁of ▁the ▁regression . ▁This ▁stat istic ▁is ▁always ▁smaller ▁than ▁, ▁can ▁decrease ▁as ▁new ▁re gress ors ▁are ▁added , ▁and ▁even ▁be ▁negative ▁for ▁poor ly ▁fitting ▁models : ▁▁▁ ▁Log - lik elihood ▁is ▁calculated ▁under ▁the ▁assumption ▁that ▁errors ▁follow ▁normal ▁distribution . ▁Even ▁though ▁the ▁assumption ▁is ▁not ▁very ▁reasonable , ▁this ▁stat istic ▁may ▁still ▁find ▁its ▁use ▁in ▁conduct ing ▁L R ▁tests . ▁ ▁Dur bin – W at son ▁stat istic ▁tests ▁whether ▁there ▁is ▁any ▁evidence ▁of ▁serial ▁correlation ▁between ▁the ▁resid uals . ▁As ▁a ▁rule ▁of ▁thumb , ▁the ▁value ▁smaller ▁than ▁ 2 ▁will ▁be ▁an ▁evidence ▁of ▁positive ▁correlation . ▁ ▁A ka ike ▁information ▁criter ion ▁and ▁Schwar z ▁criter ion ▁are ▁both ▁used ▁for ▁model ▁selection . ▁Gener ally