Page 339 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

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

2.5 gksaxsA ;s vk/s o"kZ osQ fopyu gksrs gSa_ vr% x.ku fØ;k dks ljy cukus osQ fy, bUgsa 2 ls xq.kk dj iwjs o"kZ uksV
osQ fopyu esa cny fy;k tkrk gSA
ijoy;&pØh; ;k v&js[kh; izo`fÙk (Parabolic or Non-linear trend)—ljy js[kh; izo`fÙk dks ,d ?kkrh;
izo`fÙk Hkh dgk tkrk gSA ftu ifjfLFkfr;ksa esa nh?kZ&dkyhu izo`fÙk dk fo'ys"k.k ljy js[kk ls ugha fd;k tk ldrk]
mu ifjfLFkfr;ksa esa f}rh;] r`rh;k prqFkZ ?kkr osQ ,osQUnz oØksa dk iz;ksx fd;k tkrk gSA

vjs[kh; izo`fÙk dh x.kuk osQ fy, ,osQUnz oØksa dk iz;ksx fd;k tkrk gSA
f}rh; ?kkr osQ ijoyf;d&oØ f}?kkrh; izo`fÙk (Parabolic Curve of the second degree or Quadratic

trend)μf}?kkrh; izo`fÙk dh x.kuk fuEu lehdj.k }kjk dh tkrh gSμ
Y = a + bX + cX 2

a, b rFkk c vpj ewY;ksa dh x.kuk fuEu lehdj.kksa dh lgk;rk ls dh tkrh gSμ
izR;{k jhfr y?kq jhfr (eè; o"kZ = 0)
(i) ΣY = Na + bΣX + cΣX 2 ΣY= Na + cΣX 2
2
(ii) ΣXY = aΣX + bΣX + cΣX 3 ΣXY = bΣX 2
3
2
2
3
2
2
(iii) ΣX Y = aΣX + bΣX + cΣX 4 ΣX Y= aΣX + cΣX 4 (pw¡fd ΣX = ΣX = 0)
O;ogkj esa y?kq jhfr dk iz;ksx vf/d fd;k tkrk gSA
mnkgj.k (Illustration) 10: fuEu osQ fy, f}?kkrh; ijoyf;d oØ dk vUok;kstu dhft,μ
X : 1970 1971 1972 1973 1974 1975 1976 1977 1978
Y : 4 8 9 12 11 14 16 17 26
gy (Solution): f}?kkrh; ijoyf;d oØ dk lehdj.k % Y = a + bX + cX 2

a, b vkSj c dk eku fuEu izdkj Kkr fd;k tk,xkμ
f}?kkrh; ijoyf;d oØ dk vUok;kstu

eè; o"kZ ls
2
o"kZ Y le; fopyu XY X 2 X 3 X 3 X Y
X a + bX = Y c
1970 4 – 4 – 16 16 – 64 256 64
1971 8 – 3 – 24 9 – 27 81 72
1972 9 – 2 – 18 4 – 8 16 36
1973 12 – 1 – 12 1 – 1 1 12
1974 11 0 0 0 0 0 0
1975 14 1 14 1 + 1 1 14
1976 16 2 32 4 + 8 16 64
1977 17 3 51 9 + 27 81 153
1978 26 4 104 16 + 64 256 416
N = 9 117 0 131 60 0 708 831
2
ΣY ΣX ΣXY ΣX 2 ΣX 3 ΣX 4 ΣX Y

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