Page 340 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV izlkekU; lehdj.k %
ΣY= Na + cΣX 2 ...(i)
ΣXY = bΣX 2 ...(ii)
ΣX Y= aΣX + cΣX 4 ...(iii)
2
2
117 = 9a + 60c ...(i)
131 = 60b ...(ii)
831 = 60c + 708c ...(iii)
lehdj.k (ii) lsμ
131 = 60b
131
b = = 2.183
60
lehdj.k (i) dks 20 rFkk lehdj.k (iii) dks 3 ls xq.kk djus ijμ
2340 = 180a + 1200c
2493 = 180a + 2124c
– 924c = – 153
c = 0.166
lehdj.k (i) esa c eku j[kus ijμ
117 = 9a + 60 × .166 or 117 = 9a + 9.96
– 9a = 9.69 – 117 or – 9a = – 107.04 or a = 11.89
vr% izo`fÙk ewY; Kkr djus dk lehdj.k
2
Y = 11.89 + 2.183X + .166X gksxkA
f}?kkrh; izo`fÙk ewY;

X X 2 izo`fÙk ewY;
a + bX + cX = Yc
2
– 4 16 11.89 – 8.732 + 2.656 = 5.814
– 3 9 11.89 – 6.549 + 1.494 = 6.835
– 2 4 11.89 – 4.366 + 0.664 = 8.188
– 1 1 11.89 – 2.183 + 0.166 = 9.873
0 0 11.89 + 0 + 0 = 11.890
1 1 11.89 + 2.183 + 0.166 = 14.229
2 4 11.89 + 4.366 + 0.664 = 16.920
3 9 11.89 + 6.549 + 1.494 = 19.833
4 16 11.89 + 8.732 + 2.6 56 = 223.278

ewy leadksa ,oa izo`fÙk ewY; dks fcUnq js[kk i=k ij Hkh izkafdr fd;k x;k tk ldrk gSA

r`rh; ?kkr osQ ijoyf;d&oØ (Parabolic curve of the third degree)μr`rh; ?kkr osQ ijoyf;d&oØ dk
vUok;kstu fuEu lehdj.k }kjk fd;k tkrk gSμ
2
Y = a + bX + cX + dX 3
a, b, c rFkk d vpj ewY;ksa dh x.kuk fuEu izlkekU; lehdj.kksa }kjk Kkr dh tkrh gSμ

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