Page 336 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV (iii) ewy leadksa dks izkafdr djus ls ;fn mÙky (Convex) oØ izkIr gks rks py&ekè;ksa ls izkIr oØ mlls
Åij gksxkA
(iv) ;fn py&ekè; vkSj fu;fer mPpkopuksa dh vof/ leku gS rks ;s ekè; fu;fer mPpkopuksa dks
iw.kZ :i ls nwj dj nsrs gSaA
(v) py&ekè;ksa ls vfu;fer mPpkopuksa dks de fd;k tk ldrk gS] nwj ughaA
xq.k&nks"kμbl jhfr osQ vè;;u ls ;g Li"V gks tkrk gS fd bl jhfr }kjk izkIr ifj.kke vf/d lgh gksrs gSa]
D;ksafd bu ij O;fDrxr i{kikr dh Hkkouk dk izHkko ugha iM+rk gSA bl jhfr }kjk izo`fÙk Kkr djus dh izfØ;k
dks le>uk Hkh ljy gSA bu xq.kksa osQ gksrs gq, Hkh bl jhfr esa fuEu nks"k ik, tkrs gSaμ

(i) py&ekè;ksa dh vof/ dk fu/kZj.k djuk dfBu dk;Z gS] ;fn mi;qDr jhfr ls py&ekè;ksa dh vof/
dk fu/kZj.k ugha fd;k x;k rks ifj.kke vokLrfod gksrs gSaA

(ii) bl jhfr dk iz;ksx fu;fer mPpkopuksa okyh Js.kh osQ fy, gh mi;qDr gS D;ksafd py ekè;ksa ls
vfu;fer mPpkopuksa dks nwj ugha fd;k tk ldrk gSA
(iii) izo`fÙk osQ eki esa vkjEHk osQ ,oa vUr osQ oqQN izo`fÙk ewY; NqV tkrs gSaA
(4) U;wure oxZ jhfr (Method of Least Squares)μU;wure oxZ jhfr }kjk nh?kZdkyhu izo`fÙk dk vuqeku
xf.krh; lehdj.kksa osQ vk/kj ij yxk;k tkrk gSA bl jhfr esa U;wure oxZ dh ekU;rk osQ vkèkkj ij
loksZi;qDr js[kk (Line of Best Fit) [khaph tkrh gSA loksZi;qDr js[kk nks izdkj dh gks ldrh gSA
(i) ljy js[kk (Straight Line)
(ii) ijoyf;d oØ (Parabolic Curve)

U;wure oxZ jhfr nks mís';ksa dks iwjk djrh gSμ
(i) voyksfdr ewY;ksa osQ loksZi;qDr js[kk ls mnxz fopyuksa dk ;ksx 'kwU; gksrk gSA
Σ(Y – Y ) = 0
c
(ii) loksZi;qDr js[kk ls Kkr fopyuksa osQ oxZ dk ;ksx vU; fdlh ljy js[kk ls Kkr fopyuksa osQ oxZ dh
rqyuk esa U;wure gksrk gSA
Σ(Y – Y ) = 0 U;wure (Minimum)
2
c
nwljh fo'ks"krk osQ dkj.k gh bl jhfr dks U;wure oxZ jhfr dgk tkrk gSA
Y laosQrk{kj dk rkRi;Z vkfJr pj osQ ewy leadksa ls gSA
Y laosQrk{kj dk rkRi;Z vkfJr pj osQ U;wure oxZ jhfr }kjk Kkr laxfBr ewY;ksa ls gSA
c
ljy js[kh; izo`fÙk (Straight Line Trend)μU;wure oxZ jhfr }kjk ljy js[kh; izo`fÙk ljy js[kk osQ fuEu
lehdj.k }kjk Kkr dh tkrh gSμ
Y = a + bX

lehdj.k esaμ
Y = izo`fÙk ewY; (Trend Value)

X = le; bdkbZ (Unit of Time)
a rFkk b = vpj ewY; (Constants)
vpj ewY; a rFkk b esa ls ‘a’ vUr%[k.M (Intercept) gS rFkk ‘b’ izo`fÙk js[kk osQ <yku (Slope) dks O;Dr djrk
gSA izo`fÙk ewY; Kkr djus osQ fy, a rFkk b vpj ewY;ksa dk ifjdyu djuk gksrk gSA a rFkk b vpj ewY;ksa dk
ifjdyu fuEu izlkekU; lehdj.kksa dh lgk;rk ls fd;k tkrk gSμ

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