nyq.=k m%;smdhkh úyaf,aikh€¦ · mse = fodai j¾.hkaf.a uohkh j¾.hkaf.a tl;=j iqp,k wxlh ssr k...

nyq.=K m%;smdhkh úYaf,aIKh


• ir, m%;smdhkh úYaf,aIKh : tla iajdh;a; úp,Hhla (X) uÕska mrdh;a; úp,Hfhys (Y) w.h mqfrdal;kh lsrSu i|ydfhdod .kS.

• nyq.=K m%;smdhk úYaf,aIKh : • mrdh;a; úp,Hfhys (Y) w.h mqfrdal;kh lsrSu i|yd iajdh;a;

úp,Hh tllg jeä m%udKhla fhdod .kS.

• nyq.=K m%;smdhkh úYaf,aIKh ixLHdkuh fuj,uls . tuÕskaiajdh;a; úp,Hhka flfia mrdh;a; úp,H yd iïnkaO jkafkaohkak ms<sn| yeoErSula l< yels w;r tu l%shdj,sh nyq.=Km%;smdhkh úYaf,aIKh fõ.


ix.yk nyq.=K m%;smdhk wdlD;sh𝑦𝑖 = α + β1𝑋𝑖1 + β2𝑋𝑖2 + β3𝑋𝑖3 + …………+ β𝑚𝑋𝑖𝑚 + Ɛ𝑖

ix.yk nyq.=K f¾Çh m%;smdhkh iólrKhμ𝑦.𝑋1.𝑋2….𝑋𝑚= α + β1𝑋1 + β2𝑋2 + β3𝑋3 + …………+ β𝑚𝑋𝑚

β1, β2,β3, ….. β𝑚 - md¾Yaùh m%;smdhkh ix.=Kl

kshos nyq.=K fraÇh m%;smdhkh iólrKh

𝑦𝑐= a + b1𝑋𝑖1 + b2𝑋𝑖2 + b3𝑋𝑖3 + …………+ b𝑚𝑋𝑖𝑚

𝑦𝑐= μ𝑦.𝑋1.𝑋2….𝑋𝑚 ys weia;fïka;=

a = α wka;(lKav weia;fïka;=j (Y wka;(lKavh )

b1, b2, b3,…..b𝑚 = β1, β2,β3, ….. β𝑚 mdraYaùh m%;smdhkh ix.=Kl weia;fïka;=

𝑏𝑖 = wfkl=;a úp,Hhka ksh;j ;nd 𝑋𝑖 úp,Hh iuÕ .;a úg Y ys wkql%uKh

iajdh;a; úp,Hhka folla we;s úg nyq.=K m%;smdhk wdlD;sh

𝑦𝑖 = α + β1𝑋1𝑖 + β2𝑋2𝑖 + Ɛ𝑖

α = Y wka;(lKavhβ1= 𝑋2 úp,Hh ksh;j ;nd 𝑋1 úp,Hh iuÕ .;a úg Y

ys wkql%uKhβ2= 𝑋1 úp,Hh ksh;j ;nd 𝑋2 úp,Hh iuÕ .;a úg Y

ys wkql%uKhƐ𝑖 = i ksrSlaIKh i|yd Y ys iiïNdú fodaYh


• m%;smdhk ixÕ=Kl w¾:ksrEmkh

• m%;smdhk ixÕ=Kl j, ixLdkuh fjfiishdj

• weia;fïka;= l< iólrKfha iuia; wdlD;sh úia;r lsrSfï n,h

• iuia; wdlD;sh úia;r lsrSfï n,fhys ixLdkuh fjfiishdj

• m%;smdhk ixÕ=Kl w¾:ksrEmkh

• a = ishÆ iajdh;a; úp,Hhka Y=kH jk úg Y (𝑦𝑐) ysweia;fïka;= w.h

• 𝑋1 = 𝑋2 = ⋯𝑋𝑚 = 0 úg 𝑦𝑐= a

m%;smdhk ixÕ=Klh 𝑏𝑖 w¾:ksrEmkh

• wfkl=;a ishÆ iajdh;a; úp,Hhka ksh;j we;s úg 𝑋𝑖 ys tallhla fjkia jk úg 𝑦𝑐 ys fjkia ùu 𝑏𝑖 uÕska fmkajhs

• m%;smdhk ixÕ=Kl j, ixLdkuh fjfiishdj

wNsY=kH l,ams;h (Ho) yd fjl,ams;h (H1) f.dvk.kak.• wNsY=kH l,ams;h u.ska mrSlaIdjg ,lal, hq;= mrdñ;sfhys w.h kshu

lrhs.

Ho : 𝐵1 = 0H1 : 𝐵1 ≠ 0 (oaú md¾Yaj mrSlaIdj)

Or Ho : 𝐵1 = 0H1 : 𝐵1 < 0 (tal md¾Yaj mrSlaIdj)

Or Ho : 𝐵1 = 0H1 : 𝐵1 > 0 (tal md¾Yaj mrSlaIdj)

fjfiishdj mrSlaIdj t mrSlaIdjla u.ska l<yel.

mrSlaIK ixLHdk :

𝑡 =𝑏𝑖 − 𝐵𝑖

𝑆𝑏𝑖𝑆𝑏𝑖= 𝑏𝑖 ys iïu; fodaIh

wNsY=kH l,ams;h u.ska

𝑡 =𝑏𝑖 −0

𝑆𝑏𝑖=

𝑏𝑖

𝑆𝑏𝑖

iqp,k wxlh : n – k – 1 n= ksrSlaIK ixLHdjk = iajdh;a; úp,Hhka ixLHdj

weia;fïka;= l< iólrKfha iuia; úia;r lsrSfï n,h

nyq ks¾Kk ix.=Klh (R2)

𝑅2 = SSR

SST= 1-

SSE

SST

nyq iyiïnkaO;d ix.=Klh (R)

iuia; wdlD;sh úia;r lsrSfï n,fhys ixLdkuh fjfiishdj

• mrdh;a; úp,Hfhys yd iajdh;a; úp,Hhka w;r we;s iïnkaO;djixLdkuh jYfhka fjfiis jkafkao mrSlaIdj.

H0: 𝛽1= 𝛽2= ……..=𝛽𝑘 = 0 (mrdh;a; úp,Hfhys yd iajdh;a; úp,Hhka w;r

fraÇh iïnkaO;djla ke; )H1:wvqjYfhka tla 𝛽𝑖≠ 0 (mrdh;a; úp,Hfhys yd iajdh;a; úp,Hhka w;r

fraÇh iïnkaO;djla we;)

F mrSlaIdj fhdod .ksñka wNsY=kH l,ams;h mrSlaId lrkak.


• F ixLHdk

F = MSR

MSE=

SSR 𝐾

SSE (𝑛 −𝑘 −1)SST = SSR + SSE

MSR = j¾. m%;smdhkfha uOHkhMSE = fodaI j¾.hkaf.a uOHkh

j¾.hkaf.a tl;=j iqp,k wxlhSSR kSSE n – k - 1SST n – 1

;SrK rS;sh: H0 m%;slafIam ù H1 ms<s.kS.F >𝐹𝑈(𝑘,𝑛−𝑘−1) úg α fjfiishd uÜgfïoS H0 m%;slafIam fõ.

Wod: udi 12 l ld,hla ;=, wdh;khl wf,ú jk oyk bkaOk

m%udKh^ ,Sgr&, ,Sgrhla i|yd uiloS we;s ñf,ys idudkH ^re. ish

.Kkska&, udihloS orK m%pdrK úhou ^re. oyia .Kkska& iy

ffoksl WIaK;ajfhys idudkH (°C) ms<sn| o;a; my; olajd we;.

fuu o;a; fhdod .ksñka mrdh;a; úp,Hfhys yeisrSu flfrys l=uk

iajdh;a; úp,Hhka n,mdkq ,nkafkaoehs fiùu i|yd .e,fmk

m%;smdhk wdlD;sh f.dvk.kak.

úiÿï újrKh lrkak.

udih wf,úh ,Sgrhl ñ,udihl m%pdrK

úhoï WIaK;ajh

(,Sg¾) (re ish .Kkska) (re oyia .Kkska) (°C)ckjdrs 450 0.60 25 27.50fmnrjdrs 380 1.20 17 25.00ud¾;= 298 1.80 14 29.00wfm%a,a 350 1.50 18 30.00uehs 201 3.00 10 31.00cQks 215 2.70 11 35.00cQ,s 220 2.70 12 32.00wf.daia;= 240 2.10 11 30.00iema;eïn¾ 192 3.00 7 29.00Tlaf;dan¾ 201 2.40 7 24.00fkdjeïn¾ 202 2.40 8 22.00Foieïn¾ 235 2.30 10 20.00

Regression Analysis – Computer Output

m%;smdhkh iólrKh :wf,úh = a + 𝑏1(ñ,) + 𝑏2 (m%pdrK úhoï ) + 𝑏3 (WIaK;ajh)

m%;smdhkh iólrKh :wf,úh = 281.357 - 53.344(ñ,) + 8.853(m%pdrK úhoï ) -0.446(WIaK;ajh)

újrKh ( mrs.Kl m%;sodkh uÕska)

1. ixÕ=Kl j, ,l=K iy m%udKh

• wf,úh iy ñ, w;r m%;sf,dau iïnkaO;djla mj;S.

• wf,úh iy m%pdrK úhoï w;r wkqf,dau iïnkaO;djla mj;S.

• wf,úh iy WIaK;ajh w;r m%;sf,dau iïnkaO;djla mj;S.

újrKh …..

m%;smdhkh iólrKh :

wf,úh = 281.357 - 53.344(ñ,) + 8.853(m%pdrK úhoï ) -0.446(WIaK;ajh)

ñ, tallhlska ^re. 100& jeäjk úg wf,úh ,Sg¾ 53.344 my< niskw;r m%pdrK úhoï tallhlska ^re. 1000& jeäjk úg wf,úh ,Sg¾ 8.853 ka jeä fõ. WIaK;ajh tallhlska jeäjk úg wf,úh ,Sg¾ 0.446 my< niS.

m%;smdhk ixÕ=Kl j, ixLdkuh fjfiishdj

• ñ, i|yd t w.h -2.842 jk w;r tys iïNdú;d w.h .022 fõ fuhska ksrEmKh jkafka α = 0.05 fjfiishd uÜgfïoS ñf,ys ixÕ=KlhixLdkuh jYfhka fjfiis jk njhs. (H0 m%;slafIam fõ&

• m%pdrK úhoï i|yd t w.h -3.410 jk w;r tys iïNdú;d w.h .009 fõ. fuhska ksrEmKh jkafka α = 0.05 fjfiishd uÜgfïoS m%pdrK úhoïixÕ=Klh ixLdkuh jYfhka fjfiis fõ. (H0 m%;slafIam fõ &

• WIaK;ajh i|yd t w.h -.307 jk w;r tys iïNdú;d w.h .767 fõ.fuhska ksrEmKh jkafka α = 0.05 fjfiishd uÜgfïoS ñf,ysixÕ=Klh ixLdkuh jYfhka fjfiis fkdjk njhs.(H0 ms<s.kS&


• F w.h( 131.704) ,eîfï iïNdú;dj .000 ls. tuÕska iuia; m%;smdhk wdlD;sh ixLdkuh jYfhka fjfiis fõ.

iuia; wdlD;sh úia;r ùfï yelshdj

• iuia; wdlD;sh uÕska wf,úfhys úp,kfhka 98 % la úia;r jk nj 𝑅2 w.fhka fmkajhs.

nyq.=k m%;smdhkh úyaf,aikh€¦ · mse = fodai j¾.hkaf.a uohkh j¾.hkaf.a tl;=j iqp,k wxlh ssr k...

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