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bdkbZ—14% lglaca/ fo'ys"k.k cuke izrhixeu fo'ys"k.k

Jsf.k;ksa esa) oqQN lEcU/ ik;k tkrk gS vkSj ik;k tk ldrk gS rks Hkh bu izek.kksa dh cM+h lko/kuh ls tkap djuh uksV
pkfg,A¸ rHkh lgh fu"d"kZ ij igqapk tk ldrk gSA lkaf[;dh esa lglEcU/ dk fl¼kUr cgqr egÙoiw.kZ gSA bl
fl¼kUr dks fodflr djus o vk/qfud :i nsus dk Js; Úkafll xkYVu rFkk dkyZ fi;lZu dks gSA bl
fl¼kUr osQ vk/kj ij izR;sd {ks=k esa nks ;k vf/d ?kVukvksa osQ ijLij lEcU/ksa dk Li"Vhdj.k gksrk gSA
lglEcU/ fo'ys"k.k ls gesa ;g irk pyrk gS fd nks lEcfU/r py&ewY;ksa esa fdruk o fdl izdkj dk lEcU/
gSA izrhixeu (Regression) vkSj fopj.k vuqikr (Ratio of Variation) dh /kj.kk,a lglEcU/ lEcUèkh fl¼kUr
ij gh vk/kfjr gSaA budh lgk;rk ls nks lEcfU/r Jsf.k;ksa esa ls ,d esa fn;s gq, fuf'pr py&ewY; osQ vkèkkj
ij nwljh Js.kh osQ lEHkkfor py&ewY;ksa dk fo'oluh; vuqeku yxk;k tk ldrk gSA bl izdkj O;kogkfjd
thou osQ izR;sd {ks=k esa nks ;k nks ls vf/d lEcfU/r ?kVukvksa osQ ikjLifjd lEcU/ dk foospu djus esa ;g
fl¼kUr cgqr mi;ksxh fl¼ gksrk gSA

lglEcU/ dk izHkko gekjh Hkfo";ok.kh dh vfuf'prrk osQ foLrkj dks de djrk gSA

14-2 lglEcU/ fo'ys"k.k dk egÙo (Importance of Correlation Analysis)

lglEcU/ fo'ys"k.k dk iz;ksx mu leLr {ks=kksa (vkfFkZd] lkekftd] O;kolkf;d] vkfn) esa fd;k tkrk gS tgka
nks ;k vf/d pjksa osQ eè; dkj.k&ifj.kke lEcU/ ik;k tkrk gS ijUrq vFkZ'kkL=k esa bl rduhd dk fo'ks"k egÙo
gSA ewY; rFkk ekax] mRiknu rFkk jkstxkj] etnwjh rFkk ewY; lwpdkad] fofu;ksftr iwath ,oa vftZr ykHk rFkk vU;
,sls gh rF;ksa esa fudV dk lEcU/ ik;k tkrk gSA vFkZ'kkL=k es lglEcU/ osQ mi;ksx osQ ckjs esa uhloSaxj
(Neiswanger) fy[krs gSa] ¶lglEcU/ fo'ys"k.k vkfFkZd O;ogkj dks le>us esa ;ksx nsrk gS] fo'ks"k egÙoiw.kZ
pjksa ftu ij vU; pj fuHkZj djrs gSa] dks [kkstus esa lgk;rk nsrk gS] vFkZ'kkL=kh mu lEcU/ksa dks Li"V djrk gS
ftuls xM+cM+h iSQyrh gS rFkk mls mu mik;ksa osQ lq>ko nsrk gS ftuosQ }kjk fLFkjrk ykus okyh 'kfDr;ka izHkkoh
gks ldrh gSaA¸

14-3 izrhixeu fo'ys"k.k (Regression Analysis)

izrhixeu ;k lekJ;.k dk 'kkfCnd vFkZ gSμokfil ykSVuk ;k ihNs gVuk (going back or returning)A bl
vo/kj.kk dk iz;ksx loZizFke izfl¼ oSKkfud lj Úkafll xkYVu (Sir Francis Galton) us lu~ 1877 esa vius
'kks/i=kμ^iSr`d Å¡pkbZ esa eè;erk dh vksj izrhixeu vFkkZr~ okilh* (Regression towards Mediocrity in
Heriditary Stature) esa fd;k FkkA xkYVu }kjk fd, x, ,d gtkj firkvksa vkSj muosQ iq=kksa dh Å¡pkbZ osQ
vè;;u ls ,d jkspd ,oa egÙoiw.kZ fu"d"kZ ;g fudy dj vk;k fd ;|fi yEcs firkvksa osQ iq=k yEcs vkSj
NksVs firkvksa osQ iq=k NksVs gksrs gSa (vFkkZr~ nksuksa esa ?kfu"B lglEcU/ gksrk gS)A ijUrq yEcs firkvksa okys lewg osQ
iq=kksa dh vkSlr yEckbZ firkvksa ls de gksrh gS vkSj NksVs firkvksa okys lewg osQ iq=kksa dh vkSlr yEckbZ firkvksa
ls vf/d gksrh gSA nwljs 'kCnksa esa] ;|fi firk ,oa iq=kksa dh Å¡pkbZ eas ?kfu"B lglEcU/ Fkk ijUrq fiQj Hkh lkekU;
;k lexz&ekè; ls nksuksa osQ fopyuksa esa i;kZIr vUrj FkkA tgk¡ lexz dh ekè;&Å¡pkbZ ls firkvksa dh Å¡pkbZ osQ
fopyu vf/d Fks] ogk¡ iq=kksa dh Å¡pkbZ osQ fopyu vis{kkÑr de FksA ;fn firkvksa dh ekè;&Å¡pkbZ lexz dh
ekè;&Å¡pkbZ ls ekuk 1 lseh- vf/d Fkh rks muosQ iq=kksa (vkfJr Js.kh) dh ekè;&Å¡pkbZ lexz dh ekè;&Å¡pkbZ

1. “Whenever some definite connections exist between the two or more groups, classes or series
of data. there is said to be correlation.”
—A. L. Boddington
2. “The whole subject of correlation refers to that inter-relation between separate character by

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