Page 234 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV ls ek=k 7 ;k 8 lseh- gh vf/d Fkh (vFkkZr~ 1 lseh- ls de Fkh)A ljy 'kCnksa esa] tgk¡ firkvksa dh ekè;&Å¡pkbZ
lexz dh ekè;&Å¡pkbZ ls de ;k vf/d gksrh Fkh Hkh ogk¡ iq=kksa dh ekè;&Å¡pkbZ lexz dh ekè;&Å¡pkbZ osQ
lfUudV gksus dh FkhA vr% fu"d"kZ :i esa iq=kksa dh Å¡pkbZ osQ lkekU; ;k lexz&ekè; osQ fudV gksus ;k okfil
ykSVus dh bl izo`fÙk dks gh xkYVu us ^eè;erk dh vkSj izrhixeu vFkkZr~ okilh* (Regression towards
Mediocrity) dk uke fn;k gSA
ikfjHkkf"kd :i esa] ;k&yqu pkÅ (Ya-Lun Chou) osQ vuqlkj ¶izrhixeu fo'ys"k.k pjksa osQ chp ^lEcU/ dh
izÑfr* dk fu:i.k djus dk iz;kl djrk gSμvFkkZr~ ;g pjksa esa iQyukRed lEcU/ dk vè;;u djrk gS vkSj
muosQ ckjs esa Hkfo";ok.kh ;k iwokZuqeku gsrq jpukrU=k izLrqr djrk gSA¸ 1

14-4 izrhixeu fo'ys"k.k dk egÙo ,oa mi;ksx (Importance and Uses of Regres-
sion Analysis)

izrhixeu fo'ys"k.k lkaf[;dh; fl¼kUr dh ,d egRoiw.kZ 'kk[kk gS ftldk vuqiz;ksx yxHkx lHkh izkÑfrd]
HkkSfrd rFkk lkekftd foKkuksa esa fd;k tkrk gSA ;g rduhd vc osQoy iSÙk`d fo'ks"krkvksa rd gh lhfer ugha
gS cfYd bldk iz;ksx mu lHkh {ks=kksa eas fd;k tkus yxk gS tgk¡ nks ;k vf/d ijLij lEc¼ Jsf.k;ksa eas fofHkUu
in&ewY;ksa dh lkekU; ekè; dh vksj okfil ykSVus dh izo`fÙk ik;h tkrh gSA vFkZ'kkL=k rFkk O;kolkf;d txr
esa ;g vkfFkZd pjksa osQ chp lEcU/ ekius ;k vuqekfur djus dh ,d vk/kjHkwr rduhd gS tks oLrqr% vkfFkZd
fl¼kUr ,oa vkfFkZd thou dk lkj gSA mnkgj.k osQ rkSj ij] ;fn ge tkurs gSa fd nks pkj tSls dher (X) rFkk
ekax (Y) ijLij ?kfu"B :i ls lEcfU/r gSa rks bl rduhd ls ge Y osQ fdlh fuf'pr ;k iznÙk ewY; osQ fy,
X dk loksZi;qDr eku Kkr dj ldrs gSa vFkok blh izdkj X osQ fy, Y dk loksZi;qDr eku vuqekfur fd;k
tk ldrk gSA blh izdkj fdlh oLrq osQ mRiknu ;k iw£r esa fuf'pr ek=kk esa ifjorZu (o`f¼ ;k deh) gksus ij
mlosQ ewY; esa lEHkkfor ifjorZu dk vuqeku yxk;k tk ldrk gSA blh izdkj o"kkZ dh ek=kk] cht] moZjd vkfn
osQ vk/kj ij Ñf"k mit dk vkSj iw¡th osQ vk/kj ij ykHk vkfn dk vuqeku yxkus esa ;g rduhd vR;f/d
mi;ksxh gSA lp rks ;g gS fd O;kolkf;d txr esa izrhixeu fo'ys"k.k ,d ^fu;U=k.k midj.k* (Control
Tool) dh Hkk¡fr dk;Z djrk gSA blosQ }kjk iwokZuqeku rFkk fu.kZ;u (Forecasting and Decision-making) esa
i;kZIr lqfo/k gksrh gS vkSj lkFk&gh fy, x, fu.kZ;ksa dks O;kogkfjdrk dh dlkSVh ij j[kk tk ldrk gS vkSj
;g lewph&izfØ;k fdlh Hkh O;olk; dh vk/kjf'kyk gSA gk¡! Lej.k jgs] ;fn nks Jsf.k;ksa eas ijLij ?kfu"B
lglEcU/ ugha gS rks fiQj vuqeku vf/d ;FkkFkZ ugha gksrsA izrhixeu fo'ys"k.k osQ fofHkUu mi;ksx (Uses) bl
izdkj gSaμ
(1) izrhixeu fo'ys"k.k dk ,d egRoiw.kZ mi;ksx izrhixeu js[kk (Regression Line) osQ mik; osQ :i esa
LorU=k pj osQ ewY;ksa ls vkfJr pj osQ ewY;ksa osQ vuqeku miyC/ djkuk gSA izrhixeu js[kk X rFkk Y
pjksa osQ chp fo|eku vkSlr lEcU/ksa dh O;k[;k djrh gS vFkkZr~ ;g Y osQ iznÙk ewY;ksa osQ fy, X osQ
ekè; ewY;ksa dks n'kkZrh gSA bl js[kk dk lehdj.k] ftls izrhixeu lehdj.k dgrs gSa] esa LorU=k pj
osQ ewY; vkfn"V djus ij vkfJr pj osQ vuqeku miyC/ gks tkrs gSaA
(2) izrhixeu fo'ys"k.k dk nwljk è;s; ml foHkze (=kqfV) dk eki djuk gS tks vuqeku yxkrs le; izrhixeu
js[kk osQ iz;ksx osQ dkj.k mRiUu gksrk gSA blosQ fy, vuqeku dk izeki foHkze Kkr fd;k tkrk gSA
(3) rhljk] ge izrhixeu xq.kkadksa dh lgk;rk ls lglEcU/ xq.kkad Kkr dj ldrs gSaA lglEcU/ xq.kkad
(r) dk oxZ] fuf'p;u&xq.kkad (Coefficient of Determination, r ) dgykrk gS vkSj ;g nks pjksa osQ chp
2
fo|eku lglEcU/ dh ijLij ?kfu"Brk dh ek=kk dk eki djrk gS vkSj vkfJr pj esa izlj.k
(Variance) osQ vuqikr dks crkrk gSA lkekU; :iksa eas] r dk ewY; ftruk vf/d gksrk gS vUok;kstu

1. “Regression analysis attempts to establish the ‘nature of the relationship’ between variables—
that is, to study the functional relationship between the variables and thereby provide a
mechanism for prediction or forecasting.” —Ya-Lun Chou

228 LOVELY PROFESSIONAL UNIVERSITY