Page 203 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—12% js[kh; izrhixeu fo'ys"k.k % ifjp; ,oa izrhixeu dh js[kk,¡

mRiknu o o"kkZ osQ chp lglEcU/ xq.kkad uksV
r = 0.5
lEHkkfor mRiknu crkb, tcfd o"kkZ 9 lseh gksA
gy (Solution):

ekuk x = mit] y = o"kkZ
Kkr gS % x = 10, y = 8, σ = 8, σ = 2, r = 0.5
x y
x dk y ij izrhixeu lehdj.k (x on y)
σ
x − x = x y ( − y)
σ y
8
Kkr eku j[kus ij] x – 10 = .5 × (y – 8)
2
;k x – 10 = 2(y – 8) ;k x – 10 = 2y – 16 ;k x = 2y – 6
lEHkkfor mit tcfd o"kkZ 9 lseh gks]
x = 2 × 9 – 6 = 18 – 6 = 12 fdxzk izfr bdkbZ {ks=kiQy
mnkgj.k (Illustration) 3: fuEu vkadM+ksa osQ vk/kj ij tks izrhixeu js[kk,a izkIr gksrh gSa muls (i) ifr dh
izR;kf'kr vk;q Kkr djsa tc iRuh dh vk;q 12 o"kZ gS rFkk (ii) iRuh dh izR;kf'kr vk;q Kkr djsa tc ifr dh
vk;q 33 o"kZ gSA
ekè; izeki fopyu
(Mean) (Standard deviation)
ifr dh vk;q (Husband’s age) 25 o"kZ (years) 4 o"kZ (yeas)
iRuh dh vk;q (Wife’s age) 32 o"kZ (years) 5 o"kZ (years)

ifr vkSj iRuh dh vk;q osQ chp lglEcU/ xq.kkad
= 0.8
gy (Solution):
ekuk x = ifr dh vk;q] y = iRuh dh vk;q

fn;k gqvk gS % x = 25, σ = 4, σ = 5, r = .8
x dk y ij lehdj.k (x on y) y dk x ij izrhixeu lehdj.k (y on x)
σ σ
x = x = r x ( y − y) y = y = r y ( x − x)
σ y σ x
4 5
x – 25 = 0.8 × (y – 22) y – 22 = 0.8 × (x – 25)
5 4
;k x – 25 = 0.64(y – 22) ;k ny – 22 = 1.0(x – 25)
;k x = 0.64y + 14.08 y = x – 25 + 22

;fn iRuh dh vk;q 12 o"kZ gks rks] ;k y = x – 3
ifr dh vk;q x = 0.64 × 12 + 14.08 ;fn ifr dh vk;q 33 o"kZ gks] rks
= 7.68 + 14.08 = 21.76 o"kZ iRuh dh vk;q y = 33 – 3 = 30 o"kZ

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