▁true ▁coefficient ▁value ▁ 9 5 % ▁that ▁the ▁interval ▁ ▁en comp ass es ▁the ▁true ▁coefficient ▁value ▁ 9 9 % ▁that ▁the ▁interval ▁ ▁en comp ass es ▁the ▁true ▁coefficient ▁value ▁The ▁assumption ▁is ▁not ▁un reason able ▁when ▁m   >>   n . ▁If ▁the ▁experimental ▁errors ▁are ▁normally ▁distributed ▁the ▁parameters ▁will ▁belong ▁to ▁a ▁Student ' s ▁t - distribution ▁with ▁m   −   n ▁degrees ▁of ▁freedom . ▁When ▁m   >>   n ▁Student ' s ▁t - distribution ▁approxim ates ▁a ▁normal ▁distribution . ▁Note , ▁however , ▁that ▁these ▁confidence ▁limits ▁cannot ▁take ▁system atic ▁error ▁into ▁account . ▁Also , ▁parameter ▁errors ▁should ▁be ▁quoted ▁to ▁one ▁significant ▁figure ▁only , ▁as ▁they ▁are ▁subject ▁to ▁sampling ▁error . ▁ ▁When ▁the ▁number ▁of ▁observations ▁is ▁relatively ▁small , ▁Che by chev ' s ▁inequality ▁can ▁be ▁used ▁for ▁an ▁upper ▁bound ▁on ▁prob abilities , ▁regardless ▁of ▁any ▁assumptions ▁about ▁the ▁distribution ▁of ▁experimental ▁errors : ▁the ▁maximum ▁prob abilities ▁that ▁a ▁parameter ▁will ▁be ▁more ▁than ▁ 1 , ▁ 2 ▁or ▁ 3 ▁standard ▁devi ations ▁away ▁from ▁its ▁expectation ▁value ▁are ▁ 1 0 0 %, ▁ 2 5 % ▁and ▁ 1 1 % ▁respectively . ▁ ▁Res id ual ▁values ▁and ▁correlation ▁▁ ▁The ▁resid uals ▁ ▁are ▁related ▁to ▁the ▁observations ▁by ▁ ▁where ▁H ▁is ▁the ▁ide mp ot ent ▁matrix ▁known ▁as ▁the ▁hat ▁matrix : ▁ ▁and ▁I ▁is