▁ ▁or ▁in ▁vector ▁form , ▁▁ ▁where ▁ β ▁is ▁a ▁p × 1 ▁vector ▁of ▁unknown ▁parameters ; ▁the ▁ ε is ▁are ▁un ob ser ved ▁scalar ▁random ▁variables ▁( errors ) ▁which ▁account ▁for ▁influ ences ▁upon ▁the ▁responses ▁y i ▁from ▁sources ▁other ▁than ▁the ▁explan ators ▁x i ; ▁and ▁ ▁is ▁a ▁column ▁vector ▁of ▁the ▁it h ▁observations ▁of ▁all ▁the ▁explan atory ▁variables . ▁This ▁model ▁can ▁also ▁be ▁written ▁in ▁matrix ▁notation ▁as ▁▁ ▁where ▁y ▁and ▁ ε ▁are ▁n × 1 ▁vectors ▁of ▁the ▁values ▁of ▁the ▁response ▁variable ▁and ▁the ▁errors ▁for ▁the ▁various ▁observations , ▁and ▁X ▁is ▁an ▁n × p ▁matrix ▁of ▁re gress ors , ▁also ▁sometimes ▁called ▁the ▁design ▁matrix , ▁whose ▁row ▁i ▁is ▁x i T ▁and ▁contains ▁the ▁it h ▁observations ▁on ▁all ▁the ▁explan atory ▁variables . ▁ ▁As ▁a ▁rule , ▁the ▁constant ▁term ▁is ▁always ▁included ▁in ▁the ▁set ▁of ▁re gress ors ▁X , ▁say , ▁by ▁taking ▁ ▁for ▁all ▁. ▁The ▁coefficient ▁ β 1 ▁corresponding ▁to ▁this ▁re gress or ▁is ▁called ▁the ▁intercept . ▁ ▁There ▁may ▁be ▁some ▁relationship ▁between ▁the ▁re gress ors . ▁For ▁instance , ▁the ▁third ▁re gress or ▁may ▁be ▁the ▁square ▁of ▁the ▁second ▁re gress or . ▁In ▁this ▁case ▁( ass uming ▁that ▁the ▁first ▁re gress or ▁is ▁constant ) ▁we ▁have ▁a ▁quadratic ▁model ▁in ▁the ▁second ▁re gress or . ▁But ▁this