Page 345 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—24% dky&Js.kh dh fof/ % U;wure oxZ jhfr osQ fl¼kar ,oa mlosQ vuqiz;ksx

24-2 vpj&ewY;ksa dh ifjx.kuk (Calculation of Constant Values) uksV

U;wure oxZ jhfr esa eq[; leL;k vpj&ewY;ksa dh ifjx.kuk dh gksrh gSA bl lEcUèk esa izk;% nks jhfr;k¡ (v)
nh?kZ jhfr rFkk (c) y?kq jhfr izpfyr gSa] ftudk fofèkor~ vè;;u ge uhps djsaxsμ

(v) nh?kZ jhfr (Least Square Long Method)μbl jhfr osQ vuqlkj ifjx.ku&fØ;k bl izdkj gSμ
(i) lcls igys LorU=k py&ewY;ksa vFkkZr~ le; fcUnqvksa dks X Js.kh ekurs gq,] muosQ fy, izkjEHk ls Øe
la[;k,¡ 1, 2, 3, 4...iz;qDr dh tkrh gSaA okLro esa] ,slk djus dk vFkZ ;g gS izFke dky ,dd ls fiNys
,dd dks ewy fcUnq (origin-0) eku fy;k x;k gSA
(ii) bu Øe&la[;kvksa dks X }kjk O;Dr fd;k x;k gS vkSj budk ;ksx ΣX dj fy;k tkrk gSA
(iii) fiQj Øe&la[;kvksa osQ oxks± dk ;ksx ΣX fudkyk tkrk gSA
2
(iv) X vkSj ewy leadksa vFkkZr~ Y Js.kh osQ rRlaoknh ewY;ksa dh xq.kk djosQ mudk tksM+ ΣXY fudky fy;k
tkrk gSA
(v) Y Js.kh osQ ewY;ksa dk ;ksx djosQ ΣY izkIr fd;k tkrk gSA
2
(vi) tc ΣX, ΣX , ΣXY rFkk ΣY ewY; izkIr gks tk,¡ rks blosQ ckn izlkekU; lehdj.kksa esa bu ewY;ksa dks
vkfn"V (substitute) djosQ ‘a’ rFkk ‘b’ osQ ewY; izkIr dj fy, tkrs gSaA fuEu izlkekU; lehdj.kksa dk
iz;ksx fd;k tkrk gSμ
ΣY= Na + bΣX ...(i)
ΣXY = aΣX + bΣX 2 ...(ii)
(vii) vUr esa ‘a’ rFkk ‘b’ osQ ewY; Kkr gks tkus osQ ckn ljy js[kk osQ vkèkkjHkwr lehdj.k (Y = a + bX) dk
iz;ksx djosQ izo`fÙk ewY; fudky fy;s tkrs gSaA

vpj ewY;ksa dh ifjx.kuk ls vki D;k le>rs gSa\

mnkgj.k (Illustration) 1: fuEu leadksa ls U;wure&oxZ jhfr }kjk miufr ewY; Kkr dhft,μ
o"kZ : 1974 1975 1976 1977 1978 1979
mRiknu (yk[k Vu) : 5 7 9 10 12 17
gy (Solution).

miufr ewY;ksa dk ifjdyu (U;wure oxZ nh?kZ jhfr)

o"kZ mRiknu X oxZ xq.kuiQy miufr ewY;
Y X 2 XY a + bX = Y e
1974 5 1 1 5 2.3 + (2.2 × 1) 4.5
1975 7 2 4 14 2.3 + (2.2 × 2) 6.7
1976 9 3 9 27 2.3 + (2.2 × 3) 8.9
1977 10 4 16 40 2.3 + (2.2 × 4) 11.1
1978 12 5 25 60 2.3 + (2.2 × 5) 13.3
1979 17 6 36 102 2.3 + (2.2 × 6) 15.5

;ksx 60 21 91 248 60.0

ΣY = Na + bΣX ...(i) ΣXY = aΣX + ΣX 2 ...(ii)

LOVELY PROFESSIONAL UNIVERSITY 339