Page 344 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV ;|fi dky&Js.kh fo'ys"k.k dh rduhd osQ fodkl osQ fy, vFkZ'kkL=kh fo'ks"k :i ls mÙkjnk;h gS fdUrq dky
Js.kh dk vè;;u vU; dbZ {ks=kksa osQ deZpkfj;ksa] mnkgj.kkFkZ O;olk;h] lekt'kkL=kh] tho foKkuosÙkk Hkw&xHkZ'kkL=kh]
lkoZtfud LokLF; deZpkjh ,oa vU; osQ fy, Hkh :fpdj gSA dky&Js.kh fof/ dh izo`fÙk dks ekius dh fofHkUu
fof/;k¡ gSaA bUgha fof/;ksa esa ls nh?kZdkyhu izo`fÙk dks ukius osQ fy, U;wure oxZ jhfr dk iz;ksx fd;k tkrk gSA

24-1 U;wure oxZ jhfr osQ fl¼kar (Principle of Least Square)

U;wure oxZ jhfr miufr osQ eki dh loZJs"B jhfr gSA bl jhfr osQ vUrxZr xf.krh; lehdj.kksa osQ iz;ksx }kjk]
U;wure oxZ ekU;rk osQ vkèkkj ij dky&Js.kh osQ fy, lokZfèkd mi;qDr js[kk (line of the best fit) [khaph tkrh
gSA Lej.k jgs ;g js[kk ljy (straight) Hkh gks ldrh gS vkSj ijoyf;d oØ (parabolic curve) osQ :i esa Hkh
[khaph tk ldrh gSA izlkekU; lehdj.kksa (normal equations) dh lgk;rk ls [khaph tkus okyh U;wure oxZ
js[kk] ,d ,slh js[kk gS ftlls ewy leadksa osQ fcUnqvksa osQ fopyuksa osQ oxks± dk tksM+ vU; fdlh Hkh js[kk dh
vis{kkÑr U;wure gksrk gSA ;gh dkj.k gS fd bl jhfr dks ^U;wure oxZ jhfr* dh laKk nh tkrh gSA lw=kkuqlkjμ
Σ(Y – Y ) = minimum, Y = Original Values
2
c
Y = Trend Values of Y series
c
ljy js[kh; izo`fÙk&vUok;kstu (Fitting a Straight Line Trend)μbl jhfr osQ vuqlkj izo`fÙk Kkr djus osQ
fy, fuEu vkèkkjHkwr lehdj.k (Key Equation) dk iz;ksx fd;k tkrk gSμ
Y = a + bX X = Unit of Time (dky ,dd)

a and b = Two constants (vpj ewY;)
vpj ewY; ‘a’ tksfd Y-vUr%[k.M (Y-intercept) Hkh dgykrk gS ewy fcUnq (0) vkSj Y-v{k ij fLFkr ml fcUnq
dk vUrj gS] tgk¡ ls miufr js[kk vkjEHk gksrh gSA blh izdkj ‘b’ izo`fÙk js[kk (trend line) osQ <yku dh vksj
laosQr djrk gSA nwljs 'kCnksa esa] ;g bl ckr dks Li"V djrk gS fd le; dh ,d bdkbZ c<+us ls miufr js[kk
fdruh Åij vFkok fdruh uhps dh vksj vxzlj gksrh gSA uhps bl rF; dks fp=k }kjk Hkh Li"V fd;k x;k
gSμ

b
b
b
a b
b
Y
b
b b b b b
b +6
+ +2 +3 +4 +5
a a a a a a a

o 1 2 3 4 5 6
x

fp=k 24-1- ljy js[kk dk izfr:i fp=k

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