▁is ▁viol ated ▁the ▁re gress ors ▁are ▁called ▁linear ly ▁dependent ▁or ▁perfectly ▁mult icol linear . ▁In ▁such ▁case ▁the ▁value ▁of ▁the ▁regression ▁coefficient ▁ β ▁cannot ▁be ▁learned , ▁although ▁prediction ▁of ▁y ▁values ▁is ▁still ▁possible ▁for ▁new ▁values ▁of ▁the ▁re gress ors ▁that ▁lie ▁in ▁the ▁same ▁linear ly ▁dependent ▁sub space . ▁▁ ▁S pher ical ▁errors : ▁▁ ▁where ▁ ▁is ▁the ▁identity ▁matrix ▁in ▁dimension ▁n , ▁and ▁ σ 2 ▁is ▁a ▁parameter ▁which ▁determ ines ▁the ▁variance ▁of ▁each ▁observation . ▁This ▁ σ 2 ▁is ▁considered ▁a ▁n uis ance ▁parameter ▁in ▁the ▁model , ▁although ▁usually ▁it ▁is ▁also ▁estimated . ▁If ▁this ▁assumption ▁is ▁viol ated ▁then ▁the ▁O LS ▁estimates ▁are ▁still ▁valid , ▁but ▁no ▁longer ▁efficient . ▁It ▁is ▁custom ary ▁to ▁split ▁this ▁assumption ▁into ▁two ▁parts : ▁ ▁Hom os ced astic ity : ▁, ▁which ▁means ▁that ▁the ▁error ▁term ▁has ▁the ▁same ▁variance ▁ σ 2 ▁in ▁each ▁observation . ▁When ▁this ▁requirement ▁is ▁viol ated ▁this ▁is ▁called ▁heter os ced astic ity , ▁in ▁such ▁case ▁a ▁more ▁efficient ▁estim ator ▁would ▁be ▁weight ed ▁least ▁squares . ▁If ▁the ▁errors ▁have ▁infinite ▁variance ▁then ▁the ▁O LS ▁estimates ▁will ▁also ▁have ▁infinite ▁variance ▁( although ▁by ▁the ▁law ▁of ▁large ▁numbers ▁they ▁will ▁non eth eless ▁tend ▁toward ▁the ▁true ▁values ▁so ▁long ▁as ▁the ▁errors ▁have ▁zero ▁mean ). ▁In ▁this ▁case , ▁robust ▁estimation ▁techniques ▁are