Page 151 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—9% lglacaèk% ifjHkk"kk] izdkj ,oa vFkZ'kkfL=k;ksa dh iz;qDr fof/;k¡

uksV

nks cjkcj fpÉksa dks xq.kk osQ le; laxkeh fpÉ eku fy;k tkrk gSA lglEcUèk Kkr
djus dh laxkeh fopyu jhfr ljy gS] blls vYidkyhu mPpkopuksa esa lglEcUèk
Kkr gks tkrk gS] blls lglEcUèk dh fn'kk dk gh Kku gks ikrk gS bldh la[;kRed
eki lEHko ugha gS] vr% bldk iz;ksx cgqr de fd;k tkrk gSA

vU; jhfr;k¡μlglEcUèk Kkr djus dh xf.krh; jhfr;ksa esa dkyZ fi;lZu }kjk izfrikfnr jhfr vfèkd yksdfiz;
gSA mDr jhfr;ksa osQ vfrfjDr oqQN vU; jhfr;ksa }kjk Hkh lglEcUèk xq.kkad dh x.kuk dh tk ldrh gS] buesa eq[;
U;wure oxZ jhfr gSA
U;wure oxZ jhfr }kjk lglEcUèk (Correlation by the Method of Least Squares)

U;wure oxZ fofèk osQ vkèkkj ij [khaph xbZ loksZÙke js[kk ij (Line of Best Fit) ;g fofèk vkèkkfjr gSA bl fofèk
esa fn, x, x osQ ewY;ksa osQ fy, y osQ loZJs"B lEHkkfor ewY; Kkr dj lglEcUèk Kkr fd;k tkrk gSA loksZÙke
js[kk ls izkIr fopyuksa osQ oxZ dk ;ksx Kkr fopyuksa osQ oxZ osQ ;ksx ls gj le; U;wure gksrk gS] vr% bls
U;wure oxZ jhfr dgk tkrk gSA
U;wure oxZ jhfr }kjk lglEcUèk Kkr djus dh izfØ;kμU;wure oxZ jhfr }kjk lglEcUèk xq.kkad fuEu izdkj
Kkr fd;k tkrk gSμ
(i) loZizFke ljy js[kk osQ lehdj.k dh lgk;rk ls x osQ fn, gq, ewY;ksa osQ fy, y osQ lEHkkfor ewY; (y )
c
Kkr fd, tkrs gSaμ
ljy js[kk dk lehdj.k : y = a + bx. bl lehdj.k osQ nks vpj (Constant) ewY; a ,oa b dk eku fuEu
nks izlkekU; lehdj.kksa }kjk Kkr fd;k tkrk gSμ
Σy = Na + bΣx
Σxy = Σxa + bΣx 2
(ii) y osQ fn, gq, ewY;ksa esa ls y osQ lEHkkfor ewY;ksa dks ?kVk dj fopyu Kkr fd, tkrs gSaA
d = y – y c
2
2
(iii) izkIr fopyuksa dk oxZ djosQ mldk ;ksx Σ(y – y ) ;k Σd Kkr dj fy;k tkrk gSA
c
(iv) y Js.kh osQ okLrfod ewY;ksa osQ vkèkkj ij izlj.k Kkr fd;k tkrk gSμ
Σ d 2
2
Variance of y ;k σ = N y
y
(v) loksZi;qDr js[kk izlj.k ftls vLi"VhÑr izlj.k (unexplained variance) Hkh dgrs gSa] fuEu izdkj Kkr
fd;k tkrk gSμ
Σ(y − y ) 2
S = c
2
y N
2
Sy dk oxZewy (S ) dks ^vuqeku dk izeki foHkze* (Standard error of the estimates) dgk tkrk gSA
y
(vi) fuEu lw=k osQ iz;ksx }kjk lglEcUèk xq.kkad dh x.kuk dh tkrh gSμ
S 2
r = 1 − y
σ y 2

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