▁functions ▁of ▁the ▁re gress ors ▁X , ▁and ▁generally ▁are ▁une qual . ▁The ▁observations ▁with ▁high ▁weights ▁are ▁called ▁influ ential ▁because ▁they ▁have ▁a ▁more ▁pron ounced ▁effect ▁on ▁the ▁value ▁of ▁the ▁estim ator . ▁ ▁To ▁analyze ▁which ▁observations ▁are ▁influ ential ▁we ▁remove ▁a ▁specific ▁j - th ▁observation ▁and ▁consider ▁how ▁much ▁the ▁estimated ▁quantities ▁are ▁going ▁to ▁change ▁( similar ly ▁to ▁the ▁jack kn ife ▁method ). ▁It ▁can ▁be ▁shown ▁that ▁the ▁change ▁in ▁the ▁O LS ▁estim ator ▁for ▁ β ▁will ▁be ▁equal ▁to ▁▁▁ ▁where ▁ ▁is ▁the ▁j - th ▁diagonal ▁element ▁of ▁the ▁hat ▁matrix ▁P , ▁and ▁x j ▁is ▁the ▁vector ▁of ▁re gress ors ▁corresponding ▁to ▁the ▁j - th ▁observation . ▁Similarly , ▁the ▁change ▁in ▁the ▁predicted ▁value ▁for ▁j - th ▁observation ▁resulting ▁from ▁om itting ▁that ▁observation ▁from ▁the ▁dataset ▁will ▁be ▁equal ▁to ▁▁▁▁ ▁From ▁the ▁properties ▁of ▁the ▁hat ▁matrix , ▁, ▁and ▁they ▁sum ▁up ▁to ▁p , ▁so ▁that ▁on ▁average ▁. ▁These ▁quantities ▁h j ▁are ▁called ▁the ▁lever ages , ▁and ▁observations ▁with ▁high ▁h j ▁are ▁called ▁le verage ▁points . ▁Usually ▁the ▁observations ▁with ▁high ▁le verage ▁ought ▁to ▁be ▁scr ut in ized ▁more ▁carefully , ▁in ▁case ▁they ▁are ▁err one ous , ▁or ▁out liers , ▁or ▁in ▁some ▁other ▁way ▁at yp ical ▁of ▁the ▁rest ▁of ▁the ▁dataset . ▁▁ ▁Part ition ed ▁regression ▁ ▁Sometimes ▁the ▁variables