Page 173 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—10% lglaca/ % fo{ksi&fp=k fof/] dkyZ fi;lZu dk lglaca/ xq.kkad

ekudj fopyu ysus gksaxsA tSlk fd mnkgj.k 4 esa gSA lqfo/k dh n`f"V ls ;g vf/d vPNk gS fd dfYir uksV
ekè; dksbZ ,slh la[;k yh tk;s rks Js.kh osQ chp esa gks vkSj dksbZ ,slk ewY; gks tks Js.kh esa gksA ;g Bhd mlh
izdkj ls fd;k tkrk gS tSlk fd izeki fopyu fudkyrs le; ge ns[k pqosQ gSaA ijUrq dfYir ekè; ls fopyu
ysus ij nks Jsf.k;ksa osQ izR;sd ewY;ksa osQ fopyuksa osQ xq.kuiQyksa dk ;ksx (Σd d ) Hkh fHkUu vkrk gS vkSj blosQ
x y
ewY; dks 'kq¼ djus osQ fy, lw=k esa FkksM+s ifjorZu dh vko';drk gksrh gSA bls (Σd d ), 'kq¼ djus osQ fy, blesa
x y
ls nksuksa leadekykvksa osQ Øe'k% okLrfod vkSj dfYir ekè;ksa osQ vUrjksa osQ xq.kuiQyksa dks inksa dh oqQy la[;k
ls xq.kk djosQ ?kVk fn;k tkrk gSA blosQ fuEu lw=k gSaμ
Σdd − ( − NX X − A )( A )
izFke lw=kμ r = x y 1 1 2 2
Nσσ y
x
where, X = Actual Mean of X-Series (X-Js.kh dk okLrfod lekUrj ekè; )
1
A = Assumed Mean of X-Series (X-Js.kh dk dfYir ekè; )
1
X = Actual Mean of Y-Series (Y-Js.kh dk okLrfod lekUrj ekè; )
2
A = Assumed Mean of Y-Series (Y-Js.kh dk dfYir ekè; )
2
Σd d = Sum of the products of deviations from assumed averages (dfYir ekè;ksa ls inksa osQ
x y
fopyuksa osQ xq.kuiQyksa dk ;ksx)
σ = Standard Deviation of X-Series (X-Js.kh dk izeki fopyu)
x
σ = Standard Deviation of Y-Series (Y-Js.kh dk izeki fopyu)
y
N = Number of the pairs of items (inksa osQ tksM+ksa dh la[;k)

dkyZ fi;lZu osQ lglaca/ xq.kkad Kkr djus dh ljy izR;{k jhfr dk lw=k fyf[k,A

f}rh; lw=kμizFke lw=k esa okLrfod lekUrj ekè; vkSj izeki fopyu Kkr djus gksrs gSa ftuosQ dkj.k x.kuk
fØ;k c<+ tkrh gSA vr% lw=k esa okLrfod vkSj dfYir ekè; osQ vUrj vkSj izeki fopyuksa osQ LFkku ij muosQ
lw=kksa ls fopyuksa osQ ekè; vkSj foypuksa osQ oxks± osQ ekè; dk iz;ksx dj lw=k dks ljy cuk fy;k tkrk gS tks
bl izdkj gSμ
Σd F
Σdd − G H N xI J G Σd F yI J K
N
y
x
K H N
r =
d
Σ 2 Σd F I 2 Σ 2 y Σd F d I 2
y
H K
N x −G J × x − G J
N N N H N K
where, Σd = Sum of the deviations from assumed mean in X-Series (X-Js.kh esa dfYir ekè; ls
x
eqY;ksa osQ fopyuksa dk ;ksx)
Σd = Sum of the deviations from assumed mean in Y-Series (Y-Js.kh esa dfYir ekè; ls
y
eqY;ksa osQ fopyuksa dk ;ksx)
Other symbols stad for the same things as in the first formula.

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