Page 225 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—13% lk/kj.k izrhixeu xq.kkad fof/

gy (Solution): y osQ fn, gq, ewY;ksa dks x osQ y ij lehdj.k esa rFkk x osQ ewY;ksa dks y osQ x ij lehdj.k esa uksV
vkfn"V djus ij Øe'k% x vkSj y osQ laxf.kr ewY; x o y fudky fy, tk;saxs fiQj fuEufyf[kr lkj.kh cukbZ
c
c
tk,xhμ
vuqeku&izeki =kqfV (U;wure oxZ jhfr)

U;wure oxZ jhfr fopyu fopyu fopyu
x }kjk xf.kr ewY; (x – x ) (x – x ) 2 y y (y – y ) (y – y ) 2
c 2 c c c
x = 0.5 + 0.5y
c
1 .5 – 0.5 0.25 2 2.4 – 0.4 0.16
2 3.0 – 1.0 1.00 5 3.7 1.3 1.69
3 2.0 + 1.0 1.00 3 5.0 – 2.0 4.00
4 4.5 – 0.5 0.25 8 6.3 1.7 2.89
5 4.0 + 1.0 1.00 7 7.6 – 0.6 0.36
3.50 9.10

Σ(x − x ) 2 . 350 Σ(y − y ) 2 . 910
S = c = S = c =
xy
N 5 yx N 5
.
S xy = 070 = .84 S = 182. = 1.35
yx
iznÙk lehdj.kksa ls ekè;&ewY; izrhixeu Kkr djuk (Find the mean-value Regression by
given Equation)
xq.kkadksa dh x.kukμ;fn nksuksa izrhixeu lehdj.k Kkr gksa rks mudks gy djosQ x vkSj y osQ ekè; (x o y )

fudkys tkrs gSaA ijUrq x osQ y ij lehdj.k ls bxy vkSj y osQ x ij lehdj.k ls byx Hkh Kkr fd;s tk ldrs gSaA
ijUrq dHkh&dHkh lehdj.k bl izdkj fn, tkrs gSa fd muosQ fujh{k.k ls ;g fuf'pr ugha fd;k tk ldrk gS
fd muesa ls dkSu&lk x dk y ij vkSj y dk x ij izrhixeu izLrqr djrk gSA ,slh fLFkfr esa fdlh ,d dks x
dk y ij izrhixeu lehdj.k ekudj byx Kkr dj fy;k tkrk gS vkSj blh izdkj nwljs lehdj.k dh lgk;rk
ls byx fudky fy;k tkrk gSA ;fn bxy vkSj byx dk xq.kuiQy 1 ls vfèkd gS rks gekjh ifjdYiuk xyr gS D;ksafd
2
r > 1. ;fn ,slk gks rks iz'u dks fiQj ls gy djuk iM+rk gSA bl ckj ml lehdj.k dks Y dk X ij lehdj.k
ekuuk gksxk ftls igys X dk Y ij ekuk FkkA bl izdkj byx vkSj bxy dh xq.kk 1 ls vfèkd ugha gksxh vkSj ifj.kke
'kq¼ gksaxsA
mgkgj.k (Illustration) 10: ;fn nks izrhixeu lehdj.k fuEu izdkj gksa rks x o y osQ ekè; ewY; fudkfy, vkSj
lg&lEcUèk xq.kkad fudkfy,μ
4y – 15x + 530 = 0
20x – 3y – 975 = 0
gy (Solution)% x o y osQ ekè; ewY;
4y – 15x ± – 530 ...(1)
– 3y + 20x = 975 ...(2)

leh- (1) esa 3 rFkk leh- (2) esa y dk xq.kk djus ij]
12y – 45x = – 1590
– 12y + 80x = 3900
35x = 2310

LOVELY PROFESSIONAL UNIVERSITY 219