es ▁optim ality ▁among ▁both ▁linear ▁and ▁non - linear ▁estim ators , ▁but ▁only ▁in ▁the ▁case ▁of ▁normally ▁distributed ▁error ▁terms . ▁ ▁The ▁estim ator ▁s 2 ▁will ▁be ▁proportional ▁to ▁the ▁chi - squ ared ▁distribution : ▁▁ ▁The ▁variance ▁of ▁this ▁estim ator ▁is ▁equal ▁to ▁, ▁which ▁does ▁not ▁att ain ▁the ▁C ram ér – R ao ▁bound ▁of ▁. ▁However ▁it ▁was ▁shown ▁that ▁there ▁are ▁no ▁un bi ased ▁estim ators ▁of ▁ σ 2 ▁with ▁variance ▁smaller ▁than ▁that ▁of ▁the ▁estim ator ▁s 2 . ▁If ▁we ▁are ▁willing ▁to ▁allow ▁bi ased ▁estim ators , ▁and ▁consider ▁the ▁class ▁of ▁estim ators ▁that ▁are ▁proportional ▁to ▁the ▁sum ▁of ▁squ ared ▁resid uals ▁( SS R ) ▁of ▁the ▁model , ▁then ▁the ▁best ▁( in ▁the ▁sense ▁of ▁the ▁mean ▁squ ared ▁error ) ▁estim ator ▁in ▁this ▁class ▁will ▁be ▁, ▁which ▁even ▁be ats ▁the ▁C ram ér – R ao ▁bound ▁in ▁case ▁when ▁there ▁is ▁only ▁one ▁re gress or ▁( ). ▁ ▁Moreover , ▁the ▁estim ators ▁ ▁and ▁s 2 ▁are ▁independent , ▁the ▁fact ▁which ▁comes ▁in ▁useful ▁when ▁construct ing ▁the ▁t - ▁and ▁F - tests ▁for ▁the ▁regression . ▁▁ ▁In flu ential ▁observations ▁▁ ▁As ▁was ▁mentioned ▁before , ▁the ▁estim ator ▁ ▁is ▁linear ▁in ▁y , ▁meaning ▁that ▁it ▁represents ▁a ▁linear ▁combination ▁of ▁the ▁dependent ▁variables ▁y i . ▁The ▁weights ▁in ▁this ▁linear ▁combination ▁are