Page 204 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV mnkgj.k (Illustration) 4: 7 dLcksa esa Vh-oh- lsV dh ekax osQ ,d vUos"k.k ls fuEu vkadM+s izkIr gq, %
tula[;k (gtkj esa)
[Population (in thousands)] x : 11 14 14 17 17 21 25
Vh-oh- lsVksa dh ekax
[No. of T.V. Sets demanded)] y : 15 27 27 30 34 38 46
y dk x ij izrhixeu lehdj.k Kkr dhft,A rhl gtkj tula[;k okys dLcs esa Vh-oh- lsVksa dh ekax dks
vuqekfur dhft,A
gy (Solution):

tula[;k d x d x 2 Vh-oh- lsV d y d y 2 d d
x y
(’000) x (x = 17) y ( y = 31)
11 –6 36 15 –16 256 + 96
14 –3 9 27 –4 16 + 12
14 –3 9 27 –4 16 + 12
17 0 0 30 –1 1 0
17 0 0 34 + 3 9 0
21 + 4 16 38 + 7 49 28
25 + 8 64 46 + 15 225 120
2
2
Σx = 119 Σd = 134 Σy = 217 Σd = 572 Σd d = 268
x
x y
y
Σ x 119 Σ y 217
x = = = 17 y = = = 31
N 7 N 7
Σd 2 Σd 2
σ = N x σ = N y
x
y
134 572
.
.
= = 19 14 = 4.37 = = 8171 = 0.04
7 7
Σdd 268 268 268
r = x y = = = = .97
.
Σ 2 x Σd × d 2 y 134 × 572 76 648 277
y dk x ij izrhixeu lehdj.k (y on x)
σ
y − y = r y x ( − x)
σ x
. 904
eku j[kus ij] y – 31 = .97 (x − 17 )
. 437
⇒ y – 31 = 2.06(x – 17)
⇒ y = 2.06x – 35.02 + 31

;k y = 2.06x – 4.02
tula[;k 30 gtkj gksus ij Vh-oh- lsVksa dh vkSlr ekax fudkyus osQ fy, lehdj.k (y on x) esa x osQ LFkku ij
30 j[krs gSa %

198 LOVELY PROFESSIONAL UNIVERSITY