Page 156 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV fu'p;u&xq.kkad (Coefficient of Determination)
2
lglEcUèk xq.kkad dk oxZ (r ) fu'p;u xq.kkad dgykrk gSA fu'p;u xq.kkad dh eki ;g Kkr djus osQ fy,
dh tkrh gS fd Y pj ewY; esa gksus okys fdrus ifjorZu X pj ewY; esa gksus okys ifjorZuksa osQ ifj.kkeLo:i
gksrs gSaA Y pj ewY; esa gksus okys ifjorZuksa dks nks Hkkxksa esa foHkDr fd;k tk ldrk gSμ
(i) ,sls ifjorZu X pj ewY; esa gksus okys ifjorZuksa ls lEcfUèkr gSaA
(ii) ,sls ifjorZu tks Y pj ewY; esa gksus okys ifjorZuksa ls lEcfUèkr gSaA

X pj ewY; ls lEcfUèkr ifjorZu ;k fopj.k dks ^Li"VhÑr izlj.k* (Explained Variance) rFkk nwljs izdkj osQ
ifjorZu tks X ls lEcfUèkr ugha gSa ^vLi"VhÑr izlj.k* (Unexplained Variance) dgykrs gSaA Li"VhÑr ,oa
vLi"VhÑr izlj.k dk ;ksx oqQy izlj.k dks O;Dr djrk gSμ
2
Σ Y ) = 2 [ Σ(Y − c Y ) + 2 Σ(Y − (Y − Y c ) ]
Σ(Y – Y ) = oqQy izlj.k σ ej
2
2
y
Σ(Y – Y ) = Li"VhÑr izlj.k σY ej
2
2
c
c
Σ(Y – Y ) = vLi"VhÑr izlj.k S ej
2
2
c y
vLi"VhÑr izlj.k dk eki rks U;wure oxZ jhfr }kjk lglEcUèk Kkr djrs le; gks tkrk gS] Li"VhÑr izlj.k
dk eki fu'p;u xq.kkad (Coefficient of Determination) }kjk fd;k tkrk gS] vU; 'kCnksa esa fu'p;u xq.kkad
oqQy izlj.k osQ ml vuqikr dh eki gS ftls Li"VhÑr fd;k x;k gSA fu'p;u xq.kkad dk fuèkkZj.k fuEu lw=k
}kjk fd;k tkrk gSμ
S 2
Coefficient of Determination = 1 – y = r 2
σ y 2

Σ(Y − Y) 2
Li"Vhdj.k izlj.k c
;k = 2
oqQy izlj.k Σ(Y − Y)

mnkgj.kkFkZ] ;fn iw£r dh ek=kk (X) ,oa dher Lrj (Y) osQ eè; lglEcUèk xq.kkad 9 gS rks bldk oxZ = 81
fu'p;u xq.kkad gksxkA fu'p;u xq.kkad bl ckr dks Li"V djrk gS fd dherksa esa gksus okys 81% ifjorZu iw£r
esa gksus okys ifjorZuksa osQ dkj.k mRiUu gksrs gSaA bl izdkj fu'p;u xq.kkad ls ge ml izfr'kr dks Kkr dj ldrs
gSa ftlosQ cjkcj Y pj ewY; osQ ifjorZu x pj ewY; osQ ifjorZu osQ dkj.k gksrs gSaA lglEcUèk dh rqyuk djus
osQ fy, fu'p;u xq.kkad dk iz;ksx vfèkd mi;qDr ekuk tkrk gSA
vfu'p;u xq.kkad (Coefficient of Non-Determination)μY osQ tks ifjorZu x osQ ifjorZuksa ls lEcfUèkr ugha
2
gSa] mudh eki vfu'p;u xq.kkad }kjk dh tkrh gS_ bls K }kjk O;Dr fd;k tkrk gSμ
lw=k osQ :i esaμ
S 2 Σ(Y − Y ) 2
2
K = y ;k c
σ 2 y Σ(Y − X ) 2
2
;k (1 – r )
vfu'p;u xq.kkad ls og izfr'kr izkIr gksrk gS ftlosQ cjkcj y pj ewY; osQ ifjorZu x pj ewY; osQ ifjorZuksa
osQ dkj.k u gksdj vU; dkj.kksa ls gksrs gSaA

150 LOVELY PROFESSIONAL UNIVERSITY