▁order ▁for ▁R 2 ▁to ▁be ▁meaning ful , ▁the ▁matrix ▁X ▁of ▁data ▁on ▁re gress ors ▁must ▁contain ▁a ▁column ▁vector ▁of ▁ones ▁to ▁represent ▁the ▁constant ▁whose ▁coefficient ▁is ▁the ▁regression ▁intercept . ▁In ▁that ▁case , ▁R 2 ▁will ▁always ▁be ▁a ▁number ▁between ▁ 0 ▁and ▁ 1 , ▁with ▁values ▁close ▁to ▁ 1 ▁indicating ▁a ▁good ▁degree ▁of ▁fit . ▁ ▁The ▁variance ▁in ▁the ▁prediction ▁of ▁the ▁independent ▁variable ▁as ▁a ▁function ▁of ▁the ▁dependent ▁variable ▁is ▁given ▁in ▁the ▁article ▁Pol ynomial ▁least ▁squares . ▁▁ ▁Simple ▁linear ▁regression ▁model ▁▁ ▁If ▁the ▁data ▁matrix ▁X ▁contains ▁only ▁two ▁variables , ▁a ▁constant ▁and ▁a ▁scalar ▁re gress or ▁x i , ▁then ▁this ▁is ▁called ▁the ▁" simple ▁regression ▁model ". ▁This ▁case ▁is ▁often ▁considered ▁in ▁the ▁beginner ▁statistics ▁classes , ▁as ▁it ▁provides ▁much ▁simpler ▁formulas ▁even ▁suitable ▁for ▁manual ▁calculation . ▁The ▁parameters ▁are ▁commonly ▁denoted ▁as ▁: ▁▁ ▁The ▁least ▁squares ▁estimates ▁in ▁this ▁case ▁are ▁given ▁by ▁simple ▁formulas ▁▁▁ ▁where ▁Var ( .) ▁and ▁Cov ( .) ▁are ▁sample ▁parameters . ▁▁ ▁Altern ative ▁deriv ations ▁ ▁In ▁the ▁previous ▁section ▁the ▁least ▁squares ▁estim ator ▁ ▁was ▁obtained ▁as ▁a ▁value ▁that ▁minim izes ▁the ▁sum ▁of ▁squ ared ▁resid uals ▁of ▁the ▁model . ▁However ▁it ▁is ▁also ▁possible ▁to ▁derive ▁the ▁same ▁estim ator ▁from ▁other ▁approaches . ▁In ▁all ▁cases ▁the ▁formula ▁for ▁O LS ▁estim ator ▁remains ▁the ▁same : ▁; ▁the