Page 220 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV (a) Y dh X ij izrhixeu js[kk izkIr dhft, ,oa Y Kkr dhft, tcfd X = 10 gksA
(b) X dh Y ij izrhixeu js[kk izkIr dhft, ,oa X Kkr dhft, tcfd Y = 2.5 gksA
(c) dkyZ fi;lZu osQ lglEcU/ xq.kkad dk ifjdyu dhft,A
gy (Solution):
U;wure&oxZ jhfr

X Y X 2 Y 2 XY
1 6 1 36 6
5 1 25 1 5
3 0 9 0 0
2 0 4 0 0
1 1 1 1 1
1 2 1 4 2
7 1 49 1 7
3 5 9 25 15
23 16 99 68 36

ΣX ΣY ΣX 2 ΣY 2 ΣXY

Y dh X ij izrhixeu js[kk
ΣY= Na + bΣX
ΣXY = aΣX + bΣX2
16 = 8a + 23b ...(i)
36 = 23a + 99b ...(ii)
lehdj.k (i) dks 23 o lehdj.k (ii) dks 8 ls xq.kk dj ?kVkus ijμ
368 = 184a + 529b
288 = 184a + 792b
– – –
80 = – 263b
80
∴ b = – = – .304
263

lehdj.k (i) esa b dk eku j[kus ijμ
16 = 8a + (23 × – .304)
16 = 8a – 6.992 or – 8a = – 6.992 – 16
– 8a = – 22.992 or a = 2.874
Y= a + bX or Y = 2.874 – .304X
tc X = 10 gS rks Y dk eku
Y = 2.874 – .304 × 10 = 2.874 – 3.04 = – .166
X dh Y ij izrhixeu js[kk
ΣX= Na + bΣY
ΣXY = aΣY + bΣY 2
23 = 8a + 16b ...(i)
36 = 16a + 68b ...(ii)
lehdj.k (i) dks 2 ls xq.kk djosQ (ii) esa ls ?kVkus ijμ

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