Page 349 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

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

gy (Solution): miufr ewY;ksa (Trend Values) dk vkdyu (y?kq&jhfr) uksV
Year Employees Dev. 1973 Squares Product Trend (T)

X Y X X 2 XY Y = a + bX Y c
1971 100 – 2 4 – 200 130 + (14 × – 2) = 102
1972 120 – 1 1 – 120 130 + (14 × – 1) = 116
1973 130 0 0 0 130 + (14 × 0) = 130
1974 140 + 1 1 + 140 130 + (14 × 1) = 144
1975 160 + 2 4 + 320 130 + (14 × 2) = 158
2
N = 5 ΣY = 650 ΣX = 0 ΣX = 10 ΣXY = 140 SYc = 650
ΣY 650 ΣXY 140
a = = = 130 b = = = 14
N 5 ΣX 2 10
miufr lehdj.k (Trend Equation)—Y = 130 + 14X

ewwy o"kZ = 1973, X bdkbZ = 1 o"kZ] Y bdkbZ = deZpkjh&la[;k
1 tqykbZ 1976 dks deZpkfj;ksa dh la[;k dk vuqekuμ
o"kZ 1976 osQ fy, X = + 3 or Y = 130 + (14 × 3) = 172

24-3 le;&bdkb;ksa dh la[;k ;qXe gksuk (Even Number of Time Units)

tc voyksduksa ;k le;&bdkb;ksa dh la[;k ;qXe gks (tSls 6, 8, 10 ;k 12 vkfn) rks ,slh fLFkfr esa y?kq jhfr
osQ vUrxZr fopyu osQ fy, X dh bdkbZ vkèks&o"kZ (le;&pØ ok£"kd gksus ij) osQ cjkcj gh eku yh tkrh
gSA blls fopyu n'keyo (tSlsμ 0.5, – 1.5 rFkk + 0.5, + 1.5 vkfn) esa vk,axs ijUrq x.ku&fØ;k dks ljy
cukus osQ fy, mUgsa nqxuk dj fy;k tkrk gSA 'ks"k&fØ;k iwoZor~ jgrh gSA mnkgj.k uhps nsf[k,A
mnkgj.k (Illustration) 5% fuEu vk¡dM+ksa dks U;wure oxZ jhfr }kjk ljy js[kh; miufr iznku dhft, vkSj
miufr ewY; Kkr dhft,A ifjorZu dh leku&nj ekurs gq, o"kZ 2000 osQ fy, lEHkkO; vk; vuqekfur dhft,μ
Year : 1991 1992 1993 1994 1995 1996 1997 1998
Income (Lakh Rs.) : 38 40 65 72 69 60 87 95
gy (Solution): pw¡fd ;gk¡ le;&bdkb;ksa dh la[;k ;qXe (even) gSA vr% ewy&fcUnq (origin) chp osQ nks o"kks±
(1994 rFkk 1995) dk eè;&o"kZ 1994.5 gksxkA mlls fopyu ysus osQ ckn fopyuksa dks lqfoèkk dh n`f"V ls nqxuk
dj fy;k x;k gSA lw=kkuqlkjμ

t − (X dk eè; fcUnq ) t − (mid point of X )
X = ;k =
/ 12 (vUrjky ) / 12 (interval )
;gk¡ vUrjky ls vk'k; o"kks± vFkkZr~ X osQ ewY;ksa esa le;≤ (times-difference) ls gS tks ;gk¡ 1 o"kZ gSA vr%
izFke X (1991) dk eku fuEu gksxkμ
.
.
t − 1994 5 1991 − 1994 5 − 35
.
for t = 1991, X = = = = – 7
.
/
12 1) 05 05
(
.

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