Page 208 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV 13-1 lk/kj.k izrhixeu xq.kkad (Co-efficient of Simple Regression)

izrhixeu xq.kkad ;g crykrs gSa fd ,d pj esa ,d bdkbZ dk ifjorZu gksus ij nwljs pj esa vkSlr :i ls fdruk
ifjorZu gksxkA izrhixeu lehdj.k dh rjg izrhixeu xq.kkad Hkh nks gksrs gSaμ

(i) X dk Y ij izrhixeu xq.kkadμbls bxy laosQrk{kj }kjk O;Dr fd;k tkrk gSA ;g xq.kkad crykrk
gS fd Y pj esa ,d bdkbZ dk ifjorZu gksus ij X esa fdruk ifjroZu gksxk] bldh x.kuk fuEu izdkj ls dh
tkrh gSμ
σ
bxy = r x
σ y

lw=k esaμ
bxy = X dk Y ij izrhixeu xq.kkad
σ = X pj dk izeki fopyu
x
σ = Y pj dk izeki fopyu
y
r = lglEcU/ xq.kk¡d 5

bxy dk eki X dh Y ij izrhixeu js[kk osQ <ky dks Hkh O;Dr djrk gS] bls b laosQrk{kj }kjk Hkh O;Dr fd;k
1
tkrk gSA
(i) Y dk X izrhixeu xq.kkadμbls byx laosQrk{kj }kjk O;Dr fd;k tkrk gSA ;g xq.kkad crykrk gS fd X pj
esa ,d bdkbZ dk ifjorZu gksus ij Y esa fdruk ifjorZu gksxkA byx dk eki Y dh X ij izrhixeu js[kk osQ <ky
dks Hkh O;Dr djrk gSA bldh x.kuk osQ fy, fuEu lehdj.k dk iz;ksx fd;k tkrk gSμ
σ
byx = r y
σ z
byx = Y dk X ij izrhixeu xq.kkadA
bl xq.kkad dh b laosQrk{kj }kjk Hkh O;Dr fd;k tkrk gSA
2
mnkgj.k (Illustration) 1: fuEu leadksa dh lgk;rk ls izrhixeu xq.kkad Kkr dhft,μ
r = 0.6 σ = 16 σ = 48
x
y
gy (Solution): X dk Y ij izrhixeu xq.kkad
σ 16
bxy = r x = .6 = .2
σ y 48

vFkkZr~ Y esa ,d bdkbZ dk ifjorZu gksus ij X esa vkSlr :i ls .2 osQ cjkcj ifjorZu gksxkA Y dk X ij izrhixeu
xq.kkad
σ 48
byx = r x = .6 = 1.8
σ y 16
vFkkZr~ X esa ,d bdkbZ dk ifjorZu gksus ij Y esa vkSlr :i ls 1.8 dk ifjorZu gksxkA

izrhixeu xq.kkad ls lglEcU/ xq.kkad dh x.kukμizrhixeu xq.kkad Kkr gksus ij lglEcU/ xq.kkad (r) dh
x.kuk ljyrk ls dh tk ldrh gSA lglEcU/ xq.kkad Kkr djus dh izfØ;k fuEu izdkj gSμ
(i) loZizFke nksuksa izrhixeu xq.kkadksa dk xq.kuiQy Kkr fd;k tkrk gSμ
(bxy × byx )

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