Page 165 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—10% lglaca/ % fo{ksi&fp=k fof/] dkyZ fi;lZu dk lglaca/ xq.kkad

fd;k FkkA uksV
nksuksa Jsf.k;ksa osQ lg&fopj.k (Co-variance) dh eki dks Jsf.k;ksa osQ izeki fopyuksa (standard deviations)
osQ xq.kuiQy ls Hkkx nsus ij izkIr HkkxiQy dks dkyZ fi;lZu dk lglEcU/ xq.kkad dgk tkrk gS rFkk bls
r ls iznf'kZr fd;k tkrk gSA vFkkZr~
y
cov ( , )
x
r =
σ x , σ y
lg&fopj.k dh eki] nksuksa Jsf.k;ksa osQ lekUrj ekè;ksa ls fy;s x;s fopyuksa osQ xq.kuiQyksa osQ ;ksx esa inksa dh
la[;k ls Hkkx nsdj Kkr dh tkrh gSA vFkkZr~
tgka] d = x – x , x Js.kh osQ lekUrj ekè; ls fudkys x;s fopyu
x
dy = y – y , y Js.kh osQ lekUrj ekè; ls fudkys x;s fopyu

dkyZ fi;lZu osQ lglEcU/ xq.kkad dks xq.kk ifj?kkr lglEcU/ xq.kkad (Product

Moment Correlation Coefficient) Hkh dgrs gSaA
dkyZ fi;lZu osQ lglEcU/ xq.kkad osQ eq[; y{k.k
(Main Characteristics of Karl Pearson’s Coefficient of Correlation)

dkyZ fi;lZu osQ lglEcU/ xq.kkad osQ izeq[k y{k.k fuEu gSμ
(1) lg&fopj.k dk vPNk ekiμ;g xq.kkad Js.kh osQ lHkh inksa ij vk/kfjr gS vkSj lHkh dks egÙo iznku
djrk gSA lg&fopj.k dh ek=kk] nksuksa Jsf.k;ksa osQ lekUrj ekè;ksa ls fy;s x;s fopyuksa osQ xq.kuiQyksa osQ
;ksx esa inksa dh la[;k ls Hkkx nsdj Kkr dh tkrh gSA
lglEcU/ xq.kkad dks ifjHkkf"kr djrs le; lg&fopj.k (co-variance) dh fujis{k eki dks xq.kkad esa
ifjofrZr djus osQ fy, bls nksuksa Jsf.k;ksa osQ izeki fopyuksa osQ xq.kuiQy ls Hkkx fn;k tkrk gSA vr%
lglEcU/ xq.kkad okLro esa lg&fopj.k osQ eki dk gh xq.kkad gS vFkkZr~ lglEcU/ xq.kkad lg&fopj.k
dh ek=kk dks Hkh Li"V :i ls O;Dr djrk gSA
(2) fn'kk dk ekuμxq.kkad osQ /u dk fpÉ (+) /ukRed lglEcU/ rFkk Í.k dk fpÉ (–) Í.kkRed
lglEcU/ iznf'kZr djrk gSa
(3) lhekvksa o ek=kk dk Kkuμ + 1 vkSj – 1 osQ chp lglEcU/ xq.kkad lnSo jgrk gSA + 1 iw.kZ /ukRed
lglEcU/ vkSj – 1 iw.kZ Í.kkRed lglEcU/ izdV djrk gSA lglEcU/ xq.kkad 'kwU; gks rks ogka
lglEcU/ dk vHkko gksrk gSA
(4) vko`fÙk dk egÙoμ;g xq.kkad lead Jsf.k;ksa dh fn'kkvksa ( + vkSj –) osQ lkFk&lkFk mudh vko`fÙk dks
Hkh egÙo nsrk gS vFkkZr~ izR;sd ewY; osQ fopj.k dh ek=kk dks è;ku esa j[krk gSA
(5) dk;Z&dkj.k lEcU/ ugha crkrkμ;g xq.kkad lglEcU/ crkrk gS] ijUrq bl fo"k; ij oqQN Hkh izdk'k
ugha Mkyrk fd Jsf.k;ksa osQ chp dk;Z&dkj.k lEcU/ gS ;k ughaA
(6) vkn'kZ ekiμ;g xq.kkad lekUrj ekè; rFkk izeki fopyu ij vk/kfjr gS] vr% bls lglEcU/ dk
vkn'kZ eki dgk tk ldrk gSA
(7) x.kuk dfBuμbl xq.kkad dks fudkyuk dfBu gS D;ksafd bldks ogh fudky ldrk gS ftls xf.kr dk
lkekU; Kku gksA

LOVELY PROFESSIONAL UNIVERSITY 159