Page 337 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—23% dky Js.kh dh xzkfdd ,oa vFkZ &eè;d jhfr

ΣY = Na + bΣX uksV
ΣXY = aΣX + bΣX 2
mnkgj.k (Illustration) 5. U;wure oxZ fof/ osQ iz;ksx }kjk fuEu leadksa ls nh?kZdkyhu izo`fÙk ewY;ksa dh x.kuk
dhft,μ
o"kZ : 1970 1971 1972 1973 1974 1975 1976
mRiknu (Vu esa) : 40 45 46 41 48 49 46
2
mnkgj.k (Solution): fn, gq, leadksa ls ΣX, ΣY, ΣX rFkk ΣXY Kkr dj izlkekU; lehdj.kksa osQ iz;ksx }kjk
‘a’ rFkk ‘b’ vpj ewY;ksa dk ewY; Kkr dj izo`fÙk dh x.kuk dh tk,xhA

izo`fÙk ewY; dk ifjdyu (U;wure oxZ jhfr)

o"kZ mRiknu (Vuksa esa) X X 2 XY izo`fÙk ewY;
Y a + bX = Y c
1970 40 1 1 40 41 + 1 = 42
1971 45 2 4 90 41 + 2 = 43
1972 46 3 9 138 41 + 3 = 44
1973 41 4 16 164 41 + 4 = 45
1974 48 5 25 240 41 + 5 = 46
1975 49 6 36 294 41 + 6 = 47
1976 46 7 49 322 41 + 7 = 48
315 ΣY 28 ΣX 140 ΣX 2 1288 ΣXY ΣY = 315
c
ΣY= Na + bΣX ...(i)
ΣXY = aΣX + bΣX 2 ...(ii)
lehdj.k esa ewY; j[kus ijμ
315 = 7a + 28b ...(i)

1288 = 28a + 140b ...(ii)
lehdj.k (i) dks pkj ls xq.kk djosQ lehdj.k (ii) esa ls ?kVkus ijμ
1288 = 28a+ 140b
1260 = 28a + 112b
– – –
28 = 28b
∴ b = 1
lehdj.k (i) esa b dk eku j[kus ijμ
315 = 7a + 28b or 315 = 7a + 28
315 – 28 = 7a or 287 = 7a
a = 41 ∴ a = 41 rFkk b = 1

ljy js[kk osQ lehdj.k Y = a + bX osQ vk/kj ij Kkr izo`fÙk ewY; Øe'k% 42, 43, 44, 45, 46, 47, 48 gksaxsA ewy
leadksa ,oa izo`fÙk ewY;ksa dks fcUnq js[kk i=k ij fuEu izdkj izkafdr fd;k tk,xkμ

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