Page 346 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV 60 = 6a + 21b 248 = 21a + 91b
lehdj.k (i) dks 7 ls vkSj lehdj.k (ii) dks 2 ls xq.kk djosQ mu nksuksa dks ?kVkus ijμ
420 = 42a + 147b
496 = ± 42a ± 182b 76 = 35b ∴ b = 2.2
–

vc ‘a’ dk eku Kkr djus osQ fy;s ‘b’ dk ewY; leh- (i) esa j[kus ijμ
60 = 6a + (21 × 2.2) or 6a = 13.8∴ a = 2.3
∴ Y = 2.3 + 2.2X ewy fcUnq 1974 : X bdkbZ = 1 o"kZ]

Y bdkbZ % mRiknu (yk[k Vu)

uksV~l ;g irk yxkus osQ fy, fd x.ku&fØ;k Bhd gS ;k ugha vFkkZr~ mÙkj 'kq¼ gS ;k v'kq¼ gS] bldh
dlkSVh ;g gS fd miufr ewY;ksa dk ;ksx (ΣY ) ewy leadksa vFkkZr~ Y Js.kh osQ ;ksx (ΣY) osQ cjkcj
c
gksuk pkfg;sA ;fn ;s nksuksa ;ksx cjkcj ugha gSa vFkkZr~ ΣY ≠ ΣY rks le> yhft;s fd dgha dksbZ
c
xyrh gks x;h gSA
(c) y?kq jhfr (Least Squares Short-cut Method)μnh?kZ jhfr dh vis{kk y?kq jhfr ljy gksus osQ
lkFk&gh&lkFk 'kh?kzxkeh Hkh gSA vr% fo|k£Fk;ksa dks lnSo bl jhfr dk gh iz;ksx djuk pkfg;sA fØ;k&fofèk
bl izdkj gSμ
(i) loZizFke chp okys o"kZ vFkkZr~ eè;dk&o"kZ (middle or median year) dks 'kwU; ekurs gq, lHkh o"kks±
;k le;&fcUnqvksa osQ dkfyd fopyu (time deviations) fudky fy;s tkrs gSaA Lej.k jgs] 'kwU; ls Åij
okys fopyu Í.kkRed rFkk uhps osQ fopyu èkukRed gksaxsA ijUrq mudk chtxf.krh; ;ksx
(Σ/X) lnSo 'kwU; gksxkA
(ii) ΣY, ΣXY rFkk ΣX dh x.kuk dh tk;sxhA
2
(iii) ‘a’ rFkk ‘b’ dk ewY; fudkyus osQ fy, mi;qZDr lehdj.kksa osQ iz;ksx dh vko'drk ugha gksrh_ cfYd

budh x.kuk fuEu izdkj ls dh tk;sxhμ
ΣY ΣXY
a = b =
N ΣX 2
(iv) vUr esa vkèkkjHkwr lehdj.k (Y = a + bX) esa Øe'k% X osQ ewY;ksa dks vkfn"V djosQ izo`fÙk&ewY; Kkr dj
fy;s tkrs gSa rFkk mudks fcUnq js[kk ij izkafdr dj nsrs gSaA
mnkgj.k (Illustration) 2: fuEu leadksa dks U;wure oxZ jhfr }kjk ljy js[kk miufr iznku dhft, rFkk miufr
ewY;ksa vkSj ewy leadksa dks xzkiQ isij ij izn£'kr dhft,μ

o"kZ : 1961 1962 1963 1964 1965 1966 1967
mRiknu (dqVy) : 80 90 92 83 94 99 92

340 LOVELY PROFESSIONAL UNIVERSITY