▁and ▁W ▁is ▁the ▁diagonal ▁matrix ▁of ▁such ▁weights . ▁ ▁The ▁weights ▁should , ▁ide ally , ▁be ▁equal ▁to ▁the ▁reci pro cal ▁of ▁the ▁variance ▁of ▁the ▁measurement . ▁( This ▁implies ▁that ▁the ▁observations ▁are ▁un cor related . ▁If ▁the ▁observations ▁are ▁correl ated , ▁the ▁expression ▁ ▁applies . ▁In ▁this ▁case ▁the ▁weight ▁matrix ▁should ▁ide ally ▁be ▁equal ▁to ▁the ▁inverse ▁of ▁the ▁variance - cov ar iance ▁matrix ▁of ▁the ▁observations ). ▁The ▁normal ▁equations ▁are ▁then : ▁ ▁This ▁method ▁is ▁used ▁in ▁iter atively ▁re weight ed ▁least ▁squares . ▁ ▁Parameter ▁errors ▁and ▁correlation ▁The ▁estimated ▁parameter ▁values ▁are ▁linear ▁combinations ▁of ▁the ▁observed ▁values ▁ ▁Therefore , ▁an ▁expression ▁for ▁the ▁estimated ▁variance - cov ar iance ▁matrix ▁of ▁the ▁parameter ▁estimates ▁can ▁be ▁obtained ▁by ▁error ▁propag ation ▁from ▁the ▁errors ▁in ▁the ▁observations . ▁Let ▁the ▁variance - cov ar iance ▁matrix ▁for ▁the ▁observations ▁be ▁denoted ▁by ▁M ▁and ▁that ▁of ▁the ▁estimated ▁parameters ▁by ▁M β . ▁Then ▁ ▁When ▁W ▁= ▁M − 1 , ▁this ▁simpl ifies ▁to ▁ ▁When ▁unit ▁weights ▁are ▁used ▁( W ▁= ▁I , ▁the ▁identity ▁matrix ), ▁it ▁is ▁imp lied ▁that ▁the ▁experimental ▁errors ▁are ▁un cor related ▁and ▁all ▁equal : ▁M ▁= ▁ σ 2 I , ▁where ▁ σ 2 ▁is ▁the ▁a ▁pri ori ▁variance ▁of ▁an ▁observation . ▁In ▁any ▁case , ▁ σ 2 ▁is ▁approxim ated ▁by ▁the ▁reduced ▁chi