Page 196 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV ijUrq vkt osQ ;qx esa izrhixeu dh èkkj.kk osQoy firkxr fo'ks"krkvksa osQ vè;;u rd gh lhfer ugha gS vfirq
bldk iz;ksx mu lHkh {ks=kksa esa fd;k tkrk gS ftuesa nks ;k vfèkd lEcfUèkr Jsf.k;ksa esa fofHkUu in&ewY;ksa dh
lkekU; ekè; dh vksj okil tkus dh izo`fÙk ikbZ tkrh gSA izrhixeu osQ vkèkkj ij lkekftd] vk£Fkd o
O;kolkf;d {ks=kksa esa fofHkUu ?kVukvksa osQ ekè; lEcUèkksa dk fo'ys"k.k djosQ izrhixeu&lehdj.k dh lgk;rk
ls ,d in&ewY; ls lEcfUèkr nwljk vkfJr ewY; vuqekfur fd;k tk ldrk gSA
12-1 izrhixeu dk vFkZ ,oa izrhixeu fo'ys"k.k (Meaning of Regression and
Regression Analysis)

lkaf[;dh esa ^izrhixeu* dk 'kkfCnd vFkZ okil vkus ;k ihNs ykSVus ls gSA bl 'kCn osQ iz;ksx dk Js; lj
izQkafll xYVu (Sir Francis Galton) dks fn;k tkrk gSA bUgksaus gh loZizFke izrhixeu dk fo'ys"k.kkRed
vè;;u fd;kA firkvksa vkSj iq=kksa dh m¡Qpkb;ksa dk vè;;u djrs le; mUgksaus ;g ns[kk osQ yEcs firkvksa osQ iq=k
yEcs ,oa fBxus firkvksa osQ iq=k Hkh fBxus gksrs gSa] ijUrq yEcs firkvksa osQ iq=kksa dh vkSlr maQpkbZ muosQ vkSlr
maQpkbZ ls de gksrh gS rFkk fBxus firkvksa osQ iq=kksa dh vkSlr maQpkbZ muosQ firkvksa dh vkSlr maQpkbZ ls vf/d
gksrh gSA xkYVu us ;g irk yxk;k fd ekuo tkfr esa lkekU; vkSlr maQpkbZ dh vksj okil vkus dh izo`fÙk gksrh
gS] bl izo`fÙk dks gh izrhixeu (Regression) dgrs gSaA
okfyl rFkk jkWcV~lZ us dgk gS fd ¶izk;% ;g Kkr djuk vf/d egRoiw.kZ gksrk gS fd nks ?kVukvksa esa
okLrfod lEcU/ D;k gS ftlls ,d py&ewY; (Lora=k py&ewY;) osQ Kku osQ vk/kj ij nwljs
py&ewY; (vkfJr py&ewY;) dk iwokZuqeku yxk;k tk losQ vkSj bl izdkj dh fLFkfr esa iz;ksx dh
1
tkus okyh mi;qDr rduhd ^izrhixeu fo'ys"k.k* dgykrh gSA¸
izrhixeu fo'ys"k.k osQ izdkj (Kinds of Regression Analysis)

izrhixeu rduhd }kjk Lora=k pj osQ vk/kj ij vkfJr pj dk vuqeku yxk;k tkrk gSA izrhixeu fo'ys"k.k
nks izdkj dk gks ldrk gSμ
(i) js[kh; o oØh; izrhixeu (Linear and Curvilinear Regression)μnks lEcfU/r leadekykvksa esa
izrhixeu dk vè;;u vf/drj fcUnqjs[kh; <ax ls fd;k tkrk gSA x vkSj y Jsf.k;ksa osQ py&ewY;ksa dks
fcUnqjs[k& i=k ij vafdr djus ls ,d fo{ksi fp=k cu tkrk gSA fo{ksi fp=k ij vafdr fcUnqvksa osQ eè;
ls xqtjus okyh nks loksZi;qDr js[kk,a (lines of best fit) [khaph tk ldrh gSa] bUgha dks izrhixeu js[kk,¡
dgrs gSaA tc ;s js[kk,a ljy (straight) gksrh gSa rks bUgsa js[kh; izrhixeu dh laKk nh tkrh gSA ;fn
fcUnq&fp=k ij [khaph tkus okyh js[kk,a oØ osQ :i esa gksrh gSa rks izrhixeu oØjs[kh; (curvilinear)

dgykrk gSA
(ii) ljy o cgqxq.kh izrhixeu (Simple and Multiple Regression)μtc nks pjksa (x vkSj y) osQ eè;

izrhixeu dk vè;;u fd;k tkrk gS rks ljy (Simple) izrhixeu dgykrk gSA bu nks pjksa esa ls ,d
pj Lora=k gksrk gS] vkSj nwljk vkfJrA tc nks ls vf/d pjksa esa izrhixeu fo'ys"k.k dk vè;;u fd;k
tkrk gS rc ogka cgqxq.kh (Multiple) izrhixeu fo'ys"k.k dk vè;;u djuk gksrk gSA ;gka nks ;k nks
ls vf/d Lora=k pj gksrs gSa vkSj osQoy ,d vkfJrA ge ;gka ij js[kh; izrhixeu dk vè;;u djsaxsA

izrhixeu dh mi;ksfxrk (Utility of Regression)

1. “It is often more important to find out what the relation actually is, in order to estimate or
predict one variable (the dependent variable); and the statistical technique appropriate to
such a case is called Regression Analysis.” —Wallis and Roberts

190 LOVELY PROFESSIONAL UNIVERSITY