2 , ▁is ▁the ▁O LS ▁estimate ▁for ▁ σ 2 , ▁whereas ▁the ▁second , ▁, ▁is ▁the ▁M LE ▁estimate ▁for ▁ σ 2 . ▁The ▁two ▁estim ators ▁are ▁quite ▁similar ▁in ▁large ▁samples ; ▁the ▁first ▁estim ator ▁is ▁always ▁un bi ased , ▁while ▁the ▁second ▁estim ator ▁is ▁bi ased ▁but ▁has ▁a ▁smaller ▁mean ▁squ ared ▁error . ▁In ▁practice ▁s 2 ▁is ▁used ▁more ▁often , ▁since ▁it ▁is ▁more ▁convenient ▁for ▁the ▁hypothesis ▁testing . ▁The ▁square ▁root ▁of ▁s 2 ▁is ▁called ▁the ▁regression ▁standard ▁error , ▁standard ▁error ▁of ▁the ▁regression , ▁or ▁standard ▁error ▁of ▁the ▁equation . ▁ ▁It ▁is ▁common ▁to ▁assess ▁the ▁good ness - of - fit ▁of ▁the ▁O LS ▁regression ▁by ▁comparing ▁how ▁much ▁the ▁initial ▁variation ▁in ▁the ▁sample ▁can ▁be ▁reduced ▁by ▁re gress ing ▁onto ▁X . ▁The ▁coefficient ▁of ▁determ ination ▁R 2 ▁is ▁defined ▁as ▁a ▁ratio ▁of ▁" exp la ined " ▁variance ▁to ▁the ▁" total " ▁variance ▁of ▁the ▁dependent ▁variable ▁y , ▁in ▁the ▁cases ▁where ▁the ▁regression ▁sum ▁of ▁squares ▁equals ▁the ▁sum ▁of ▁squares ▁of ▁resid uals : ▁▁ ▁where ▁T SS ▁is ▁the ▁total ▁sum ▁of ▁squares ▁for ▁the ▁dependent ▁variable , ▁, ▁and ▁ 1 ▁is ▁an ▁n × 1 ▁vector ▁of ▁ones . ▁( L ▁is ▁a ▁" centering ▁matrix " ▁which ▁is ▁equivalent ▁to ▁regression ▁on ▁a ▁constant ; ▁it ▁simply ▁subtract s ▁the ▁mean ▁from ▁a ▁variable .) ▁In