c andid ate " ▁value ▁for ▁the ▁parameter ▁vector ▁ β . ▁The ▁quantity ▁, ▁called ▁the ▁resid ual ▁for ▁the ▁i - th ▁observation , ▁measures ▁the ▁vertical ▁distance ▁between ▁the ▁data ▁point ▁ ▁and ▁the ▁hyper plane ▁, ▁and ▁thus ▁ass esses ▁the ▁degree ▁of ▁fit ▁between ▁the ▁actual ▁data ▁and ▁the ▁model . ▁The ▁sum ▁of ▁squ ared ▁resid uals ▁( SS R ) ▁( also ▁called ▁the ▁error ▁sum ▁of ▁squares ▁( E SS ) ▁or ▁resid ual ▁sum ▁of ▁squares ▁( R SS )) ▁is ▁a ▁measure ▁of ▁the ▁overall ▁model ▁fit : ▁▁ ▁where ▁T ▁denotes ▁the ▁matrix ▁trans pose , ▁and ▁the ▁rows ▁of ▁X , ▁den oting ▁the ▁values ▁of ▁all ▁the ▁independent ▁variables ▁associated ▁with ▁a ▁particular ▁value ▁of ▁the ▁dependent ▁variable , ▁are ▁X i ▁= ▁x i T . ▁ ▁The ▁value ▁of ▁b ▁which ▁minim izes ▁this ▁sum ▁is ▁called ▁the ▁O LS ▁estim ator ▁for ▁ β . ▁The ▁function ▁S ( b ) ▁is ▁quadratic ▁in ▁b ▁with ▁positive - defin ite ▁H ess ian , ▁and ▁therefore ▁this ▁function ▁poss esses ▁a ▁unique ▁global ▁minimum ▁at ▁, ▁which ▁can ▁be ▁given ▁by ▁the ▁explicit ▁formula :[ proof ] ▁▁▁▁ ▁The ▁product ▁N = XT ▁X ▁is ▁a ▁normal ▁matrix ▁and ▁its ▁inverse , ▁Q = N – 1 , ▁is ▁the ▁c of actor ▁matrix ▁of ▁ β , ▁closely ▁related ▁to ▁its ▁cov ar iance ▁matrix , ▁C β . ▁The ▁matrix ▁( XT ▁X ) –