▁when ▁comparing ▁two ▁alternative ▁models , ▁smaller ▁values ▁of ▁one ▁of ▁these ▁criteria ▁will ▁indicate ▁a ▁better ▁model . ▁▁ ▁Standard ▁error ▁of ▁regression ▁is ▁an ▁estimate ▁of ▁ σ , ▁standard ▁error ▁of ▁the ▁error ▁term . ▁ ▁Total ▁sum ▁of ▁squares , ▁model ▁sum ▁of ▁squ ared , ▁and ▁resid ual ▁sum ▁of ▁squares ▁tell ▁us ▁how ▁much ▁of ▁the ▁initial ▁variation ▁in ▁the ▁sample ▁were ▁explained ▁by ▁the ▁regression . ▁ ▁F - stat istic ▁tries ▁to ▁test ▁the ▁hypothesis ▁that ▁all ▁coefficients ▁( except ▁the ▁intercept ) ▁are ▁equal ▁to ▁zero . ▁This ▁stat istic ▁has ▁F ( p – 1 , n – p ) ▁distribution ▁under ▁the ▁null ▁hypothesis ▁and ▁normal ity ▁assumption , ▁and ▁its ▁p - value ▁indicates ▁probability ▁that ▁the ▁hypothesis ▁is ▁indeed ▁true . ▁Note ▁that ▁when ▁errors ▁are ▁not ▁normal ▁this ▁stat istic ▁becomes ▁invalid , ▁and ▁other ▁tests ▁such ▁as ▁Wald ▁test ▁or ▁L R ▁test ▁should ▁be ▁used . ▁ ▁Ord inary ▁least ▁squares ▁analysis ▁often ▁includes ▁the ▁use ▁of ▁di agnostic ▁plots ▁designed ▁to ▁detect ▁depart ures ▁of ▁the ▁data ▁from ▁the ▁assumed ▁form ▁of ▁the ▁model . ▁ ▁These ▁are ▁some ▁of ▁the ▁common ▁di agnostic ▁plots : ▁ ▁Res id uals ▁against ▁the ▁explan atory ▁variables ▁in ▁the ▁model . ▁A ▁non - linear ▁relation ▁between ▁these ▁variables ▁suggests ▁that ▁the ▁linear ity ▁of ▁the ▁conditional ▁mean ▁function ▁may ▁not ▁hold . ▁ ▁D ifferent ▁levels ▁of ▁vari ability ▁in ▁the ▁resid uals ▁for ▁different ▁levels ▁of