Page 198 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV izÑfr dk irk pyrk gSA blosQ }kjk bl ckr dk irk pyrk gS fd ,d pj osQ vkSlr ewY; osQ vk/kj
ij mlls lEcfU/r nwljs pj dk vkSlr ewY; fdruk gksxk\

Lo&ewY;kadu (Self Assessment)

1- fjDr LFkkuksa dh iw£r djsa (Fill in the blanks)μ
1. --------- us loZizFke izrhixeu dk fo'ys"k.kkRed vè;;u fd;kA
2. izrhixeu rduhd }kjk --------- osQ vk/kj ij vkfJr pj dk vuqeku yxk;k tkrk gSA
3. tc nks pjksa osQ eè; --------- dk vè;;u fd;k tkrk gS] rks ;g ljy izrhixeu dgykrk gSA
4. izrhixeu fo'ys"k.k dk iz;ksx izcU/ vf/dkfj;ksa }kjk O;olk; osQ fu;U=k.k --------- osQ :i esa fd;k

tkrk gSA

12-2 js[kh; izrhixeu (Linear Regression)

nks lEcfUèkr vk¡dM+ksa esa izrhixeu dk fo'ys"k.k vfèkdrj fcUnqjs[kh; jhfr }kjk fd;k tkrk gSA X rFkk Y Js.kh
osQ pj&ewY;ksa dks fcUnqjs[kk ij vafdr djus ls ,d fo{ksi fp=k cu tkrk gSA bl fp=k ij vafdr fofHkUu fcUnqvksa
osQ chp ls xqtjrh gqbZ nks loksZi;qDr js[kk,¡ [khaph tkrh gSaA ;s js[kk,¡ gh izrhixeu js[kk,¡ dgykrh gSaA tc ;s
js[kk,¡ ljy gksrh gSa rks izrhixeu js[kh; dgykrh gSaA bl ljy izrhixeu js[kkvksa osQ lehdj.k ,d&?kkrh;
izo`fÙk osQ gksrs gSaA x dk y ij izrhixeu js[kk dk lehdj.k x = a + by gksrk gS rFkk y dk x ij izrhixeu js[kk
dk lehdj.k y = a + bx gksrk gSA
nks ljy pj&ewY;ksa x vkSj y osQ chp js[kh; izrhixeu dk vè;;u ljyjs[kh; izrhixeu dgykrk gSA nksuksa pjksa
esa ls ml pj dks LorU=k ekuk tkrk gS tks Kkr gksrk gS vkSj nwljs pj osQ vuqeku dk vkèkkj gksrk gS vkSj og
pj vkfJr dgykrk gS ftlosQ ewY; dk vuqeku yxkuk gksrk gSA izrhixeu dh fofèk dk iz;ksx nks ls vfèkd
pjksa osQ ikjLifjd lEcU/ dk fo'ys"k.k djus esa Hkh fd;k tk ldrk gSA rhu ;k rhu ls vf/d pjksa osQ fy,
iz;qDr js[kh; izrhixeu cgqeq[kh js[kh; izrhixeu dgykrk gSA
izrhixeu js[kk,¡ (Regression Lines)

vFkZμdky&Jsf.k;ksa osQ fo'ys"k.k ls Kkr gksrk gS fd loksZi;qDr js[kk (Line of best fit) }kjk bl ckr dk irk
pyrk gS fd le; dh bdkbZ esa ifjorZu gksus ij vkfJr Js.kh esa D;k ifjorZu visf{kr gSA nks Jsf.k;ksa osQ
ikjLifjd ekè; lEcU/ dks izdV djus okyh loksZi;qDr js[kk,a bu nksuksa Jsf.k;ksa esa Øe'k% gksus okys
ifjorZuksa dks izdV djrh gSaA bUgsa ge izrhixeu js[kk,a (Regression Lines) dgrs gSaA
nks izrhixeu js[kk,a D;ksa gksrh gSa\ nks izrhixeu js[kk,a gksus dk izFke dkj.k rks ;g gS fd nks lEcfU/r Jsf.k;ksa
osQ fy, nks izrhixeu js[kk,a gksrh gSaA ,d js[kk y dk x ij izrhixeu izdV djrh gS ftldh jpuk x dks Lora=k
py&ewY; (Subject or Independent Series) vkSj y dks vkfJr ekudj dh tkrh gSA bldh lgk;rk ls x osQ
fn, gq, ewY; osQ led{k y dk ewY; vuqekfur fd;k tk ldrk gSA nwljh js[kk x dk y ij izrhixeu O;Dr
djrh gS ftldh jpuk esa y dks Lora=k rFkk x dks vkfJr ekuk tkrk gS rFkk blosQ vk/kj ij y osQ fn, gq,
ewY;ksa osQ led{k x osQ ewY; Kkr fd, tkrs gSaA nks izrhixeu js[kk,a gksus dk nwljk dkj.k ;g gS fd izrhixeu
js[kk,a os loksZi;qDr js[kk,a gksrh gSa ftudh jpuk U;wure oxZ dh ekU;rk (Least Squares Assumptions) osQ
vk/kj ij gksrh gSA U;wure oxZ jhfr osQ vuqlkj [khaph tkus okyh js[kk ,slh gksuh pkfg, ftlls fofHkUu fcUnqvksa
osQ fopyuksa osQ oxks± dk ;ksx U;wure gksA fcUnqvksa ls js[kk rd osQ fopyuksa dks eki nks izdkj ls fd;k tk ldrk
gSμ,d rks {kSfrt :i ls (Horizontally) vFkkZr~ Hkqtk{k osQ lekukUrj rFkk nwljs yEcor~ (Vertically) vFkkZr~
dksfV&v{k osQ lekukUrjA nksuksa izdkj osQ fopyuksa osQ oxks± osQ vyx&vyx ;ksx U;wure ;ksx U;wure djus osQ

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