▁the ▁errors ▁on ▁both ▁variables ▁are ▁the ▁same , ▁then ▁the ▁resid ual ▁represents ▁the ▁short est ▁distance ▁between ▁the ▁data ▁point ▁and ▁the ▁fitted ▁curve , ▁that ▁is , ▁the ▁resid ual ▁vector ▁is ▁per pend icular ▁to ▁the ▁tang ent ▁of ▁the ▁curve . ▁For ▁this ▁reason , ▁this ▁type ▁of ▁regression ▁is ▁sometimes ▁called ▁two ▁dimensional ▁E uclidean ▁regression ▁( Ste in , ▁ 1 9 8 3 ) ▁or ▁orthogonal ▁regression . ▁ ▁Sc ale ▁invariant ▁methods ▁ ▁A ▁serious ▁difficulty ▁ar ises ▁if ▁the ▁variables ▁are ▁not ▁measured ▁in ▁the ▁same ▁units . ▁First ▁consider ▁meas uring ▁distance ▁between ▁a ▁data ▁point ▁and ▁the ▁line : ▁what ▁are ▁the ▁measurement ▁units ▁for ▁this ▁distance ? ▁If ▁we ▁consider ▁meas uring ▁distance ▁based ▁on ▁P yth ag or as ' ▁Theorem ▁then ▁it ▁is ▁clear ▁that ▁we ▁shall ▁be ▁adding ▁quantities ▁measured ▁in ▁different ▁units , ▁which ▁is ▁ ▁meaning less . ▁Second ly , ▁if ▁we ▁res c ale ▁one ▁of ▁the ▁variables ▁e . g ., ▁measure ▁in ▁gr ams ▁rather ▁than ▁kil og rams , ▁then ▁we ▁shall ▁end ▁up ▁with ▁different ▁results ▁( a ▁different ▁line ). ▁To ▁avoid ▁these ▁problems ▁it ▁is ▁sometimes ▁suggested ▁that ▁we ▁convert ▁to ▁dimension less ▁variables — this ▁may ▁be ▁called ▁normal ization ▁or ▁standard ization . ▁However ▁there ▁are ▁various ▁ways ▁of ▁doing ▁this , ▁and ▁these ▁lead ▁to ▁fitted ▁models ▁which ▁are ▁not ▁equivalent ▁to ▁each ▁other . ▁One ▁approach ▁is ▁to ▁normal ize ▁by ▁known ▁(