Page 201 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—12% js[kh; izrhixeu fo'ys"k.k % ifjp; ,oa izrhixeu dh js[kk,¡

izrhixeu js[kkvksa dks O;Dr djrs gSaA ftl izdkj x dh y ij izrhixeu js[kk y osQ fn, gq, ewY;ksa osQ fy, vfr uksV
lEHkkfor x osQ ewY;ksa dk izn'kZu djrh gS vkSj blh Hkkafr y dh x ij izrhixeu js[kk osQ fn;s gq, ewY;ksa osQ
led{k y osQ ewY; crkrh gSA blh izdkj dk ij izrhixeu lehdj.k osQ ewY;ksa esa fopj.k izdV djrk gS tks
x esa ifjorZu gksus ij visf{kr gksaxsA js[kh; izrhixeu lehdj.k mu loksZi;qDr js[kkvksa osQ lehdj.k gksrs gSa ftUgsa
U;wure oxZ i¼fr osQ vk/kj ij cuk;k tkrk gSμ
(i) x dk y ij izrhixeu lehdj.k (Regression Equation of x on y) :
x = c + dy
blh lehdj.k osQ }kjk y (Lora=k pj&ewY;) osQ fn;s gq, ewY;ksa osQ vk/kj ij x (vkfJr pj&ewY;) osQ
rRlEcU/h loksZÙke ekè; ewY; Kkr fd, tkrs gSaA bl lehdj.k dks lglEcU/ xq.kkad] izeki fopyu vkSj
lekUrj ekè;ksa osQ ekuksa osQ :i esa fuEufyf[kr <ax ij fy[kk tk ldrk gS %
σ
x = x = r x ( y − y)
σ y

;gk¡ ij x vkSj y Øe'k% leadekykvksa osQ lekUrj ekè;ksa dks izVd djrs gSa vkSj σ rFkk σ muosQ izeki
y
x
fopyuksa dks vkSj r mu nksuksa osQ eè; lglEcU/ xq.kkad dks izdV djrk gSA
vpj&ewY; ‘c’ vUr%[k.M (intercept) gS vFkkZr~ og fcUnq gS ftl ij izrhixeu js[kk x = c + dy Hkqtk&v{k (x-
axis) dks Li'kZ djrh gSA vpj&ewY; ‘d’ izrhixeu js[kk dk <ky izn£'kr djrk gSA bls x dk y ij izrhixeu
xq.kkad (Regression Coefficient of x on y) dgrs gSaA izk;% bls b ls izdV djrs gSaA bl izdkj]
xy
σ
x = x = r x ( y − y)
σ y

osQ vUrxZr c = x − dy, d = r σ x = b xy
σ y

x − dy dks vUr%[k.M (c) dk chtxf.krh; eki dgk tk ldrk gSA
(ii) y dk x ij izrhixeu lehdj.k (Regression Equation of y on x):
y = a + bx

bl lehdj.k osQ }kjk x (Lora=k pj&ewY;) osQ fy, gq, ewY;ksa osQ vk/kj ij y (vkfJr pj&ewY;) osQ
rRlEcU/h loksZÙke ewY; Kkr fd, tkrs gSaA bl lehdj.k dks fuEu izdkj j[kk tkrk gS %
σ
y
y − = r y x ( − x)
σ x
σ y
tgka a = y − bx, b = r = b yx
σ x
bu lehdj.kksa esa ‘a’ vkSj ‘b’ vpj&ewY; (constant) gSaA vpj&ewY; ‘a’ vUr%[k.M (intercept) gS vFkkZr~ og
fcUnq gS ftl ij izrhixeu js[kk dksfV&v{k (y-axis) dks Li'kZ djrh gSA js[kkfp=k ij ewyfcUnw (O) osQ
dksfV&v{k ij izrhixeu js[kk osQ Li'kZ fcUnq dk vUrj gh vUr%[k.M dgykrk gSA tc a dk ewY; /ukRed gksrk
gS rks js[kk y-axis dks ewY;fcUnq (O) ls mQij dh vksj Li'kZ djrh gS rFkk tc a dk ewY; 'kwU; gks] rks js[kk
ewyfcUnq ls izkjEHk gksrh gSA
nwljk vpj&ewY; ‘b’ izrhixeu js[kk dk <ky (Slope of the line) izn£'kr djrk gSA bls y dk x ij izrhixeu
xq.kkad (Regression Coefficient of y on x) dgrs gSaA izk;% bls b ls izdV djrs gSaA blls ;g Kkr gksrk gS
yx

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