Page 188 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV mnkgj.k (Illustration) 7: fuEu lwpdkadksa ls laxkeh fopyu xq.kkad dh x.kuk dhft,μ
o"kZ % 1 2 3 4 5 6 7 8 9 10
ekax % 100 115 116 108 108 122 122 124 112 112
iw£r % 106 102 102 104 98 96 97 97 95 90
gy (Solution):
laxkeh fopyu&xq.kkad dh x.kuk

o"kZ ek¡x (x) fpÉ iw£r (y) fpÉ fpÉksa dk xq.kuiQy
1 100 106
2 115 + 102 – –
3 116 + 102 = –
4 108 – 104 + –
5 108 = 98 – –
6 122 + 96 – –
7 122 = 97 + –
8 124 + 97 = –
9 112 – 95 – +
10 112 = 90 – –
c = 1

N = n – 1 = 10 – 1 = 9
+ − (2c n )
r = +
c n
7
+ × (21 − ) 9 − F I 7
+
H K
= + = G J = −
n 9 9
r = – .88
c
11-4 fu'p;u xq.kkad (Coefficient of Determination)

vkfJr pj&ewY; vFkkZr~ Y-Js.kh esa gksus okys fopj.k dks ge nks Hkkxksa esa ck¡V ldrs gSaμ
(i) ,sls ifjorZu tks X-Js.kh esa gksus okys ifjorZuksa osQ iQyLo:i gksrs gSaA bUgsa Li"VhÑr ;k O;k[;s; izlj.k
dgrs gSaA
(ii) ,sls fopj.k tks X Js.kh osQ ifjorZu osQ dkj.k ugha gksrs oju~ vU; dkj.kksa ls gksrs gSa] budks vLi"VhÑr

;k vO;k[;s; izlj.k dgrs gSaμ
oqQy izlj.k = Li"VhÑr izlj.k + vLi"VhÑr izlj.k
Li"VhÑr izlj.k dk vadkRed eki fu'p;u xq.kkad ;k fu/kZj.k xq.kkad }kjk fd;k tkrk gSA ;g okLro esa
lg&lEcU/ xq.kkad dk oxZ gksrk gS] ftls bl lw=k osQ }kjk ifjdfyr fd;k tkrk gSμ
sy 2 Unexplained Variance Σ(y − ) y 2
2
c of D = r = 1 – 2 or 1 – =
oy Total Variance Σ(y + ) y 2
fu'p;u xq.kkad ls gesa ml izfr'kr dk irk pyrk gS ftl izfr'kr ls Y-Js.kh osQ ifjorZu X-Js.kh osQ ifjorZuksa
osQ dkj.k gksrs gSaA mnkgj.kkFkZ] ;fn eqnzk dh ek=kk (X) vkSj ewY;&Lrj Y esa 8 dk lg&lEcU/ xq.kkad r gS rks

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