BAB 2 LANDASAN TEORI

Transkripsi

1 BAB LANDASAN TORI. Alss Rgrs Dlm bbrp mslh trdpt du tu lbh vrbl yg hubugy td dpt dpsh, d hl trsbut bsy dsld sft hubugy. Alss rgrs dlh sbuh t sttst utu mmrs d mmodl hubug dtr vrbl-vrbl. Thp rgrs trdr dr ytu rgrs sdrh d multpl rgrs. Prpy dpt djump scr lus d by bdg sprt t, oom, mjm, lmu-lmu bolog, lmu-lmu sosl, d lmu-lmu prt. Alss rgrs brgu dlm mlh hubug du vrbl tu lbh, d trutm utu mlusur pol hubug yg modly blum dthu dg smpur, shgg dlm prpy lbh brsft splortf... Rgrs Lr Rgrs lr dlh mtod sttst yg dgu utu mmbtu modl hubug tr vrbl trt dg stu tu lbh vrbl bbs. Apbl byy vrbl bbs hy d stu, dsbut sbg rgrs lr sdrh, sdg pbl trdpt lbh dr stu vrbl bbs, dsbut sbg rgrs lr brgd. Hubug tr vrbl trt dg vrbl bbs dpt drumus dlm sutu btu hubug fugsol sbg brut: Uvrsts Sumtr Utr

2 ; utu dg : = vrbl trt = vrbl bbs = trsp (tt potog urv trhdp sumbu ) = mrg (slop) urv lr. slh (rror) Alss rgrs std-tdy mml 3 gu, ytu utu tuju dsrps dr fom dt tu sus yg sdg dtlt, utu tuju otrol, srt utu tuju prds. Rgrs mmpu mdsrps fom dt mllu trbtuy sutu modl hubug yg brsfty umr. Rgrs jug dpt dgu utu mlu pgdl (otrol)trhdp sutu sus tu hl-hl yg sdg dmt mllu pggu modl rgrs yg dprolh. Sl tu, modl rgrs jug dpt dmft utu mlu prds utuvrbl trt. Nmu yg prlu dgt, prds d dlm osp rgrs hy bolh dlu ddlm rtg dt dr vrbl-vrbl bbs yg dgu utu mmbtu modl rgrs trsbut. Msl, sutu modl rgrs dprolh dg mmprgu dt vrbl bbs yg mml rtg tr 5 s.d. 5, m prds hy bolh dlu bl sutu l yg dgu sbg put utu vrbl brd d dlm rtg trsbut. osp dsbut sbg trpols. D dlm sutu modl rgrs t mmu ofs-ofs. ofs pd modl rgrs sbry dlh l dug prmtr d dlm modl rgrs utu ods yg sbry (tru codto), sm hly dg sttst m (rt-rt) pd osp sttst dsr. Hy sj, ofs-ofs utu modl rgrs mrup sutu l rt-rt yg brplug trjd pd vrbl trt bl sutu l bbs. Uvrsts Sumtr Utr

3 ofs rgrs dpt dbd mjd mcm, ytu:. Itrsp (trcpt) Itrsp, dfs scr mtmts dlh sutu tt prpotog tr sutu grs dg sumbu pd dgrm/sumbu rtsus st l. Sdg dfs scr sttst dlh l rt-rt pd vrbl pbl l pd vrbl brl. Dg t l, pbl td mmbr otrbus, m scr rt-rt, vrbl brl sbsr trsp. Prlu dgt, trsp hylh sutu ostt yg mmug muculy ofs l d dlm modl rgrs. Itrsp td sllu dpt tu prlu utu dtrprts. Apbl dt pgmt pd vrbl td mcup l tu mdt, m trsp td mml m yg brrt, shgg td prlu dtrprts.. Slop Scr mtmts, slop mrup uur mrg dr sutu grs. Slop dlh ofs rgrs utu vrbl (vrbl bbs). Dlm osp sttst, slop mrup sutu l yg muju sbrp bsr otrbus (sumbg) yg dbr sutu vrbl trhdp vrbl. Nl slop dpt pul drt sbg rt-rt prtmbh (tu pgurg) yg trjd pd vrbl utu stp pgt stu stu vrbl.. Mtod udrt Trcl (Ordry Lst Squr OLS) Mtod OLS bs dgu dlm msr l prmtr pd prsm tuggl yg brsft stu rh. Pd prsm trsbut, vrbl bbs mmpgruh vrbl t bbs. Mtod OLS lh sutu mtod utu mghtug d, sdm shgg jumlh slh udrt mml l trcl. Dg bhs mtmt, m dyt sbg brut: Uvrsts Sumtr Utr

4 ; Jd mtod udrt trcl dlh mtod utu mghtug d sdm rup shgg trcl (mmum). Cry lh dg mmbut turu prsl (prtl dffrtl) dr mul-mul trhdp mud trhdp d mymy dg ol. (.) (.) Prsm (.) dbg dg Shgg Msu dlm prsm (.) Uvrsts Sumtr Utr

5 Shgg..3 Rgrs udrt Trcl Mtod ddsr pd pmlh d shgg mmml jumlh udrt dvs tt-tt dt dr grs yg dcoco. Jumlh dr udrt dvs (JD) dr grs dlh: (.3) JD Gmbr.3 Sutu pgmt (dt) yg td tpt pd grs rgrs mud dtsr d shgg j tsr dsubsttus dlm prsm (.3) m jumlh dvs udrt mjd mmum. Dg mdfrsl prsm (.3) trhdp d d mtp drvtf prsl yg dhsl sm dg ol, dprolh Uvrsts Sumtr Utr

6 SSD SSD (.4) D ry (.5) dr prsm (.5), dprolh (.6) prsm (.6) dsbut dg prsm orml. Dr prsm (.6) dprolh, d, dm d dlh d. d yg dprolh dg cr dsbut tsr udrt trcl msg-msg dr d. Dg dm, tsr prsm rgrs dpt dtuls sbg,, yg dsbut prsm prds udrt trcl.. Dtrm Mtrs Uvrsts Sumtr Utr

7 Dfs. Dtrm dr sutu mtrs bujur sgr A, dots dg A tu dt(a) dlh fugs slr yg ddfs sdm rup shgg mrup jumlh hsl l usur- usur yg sjjr dgol utm durg jumlh usur- usur yg sjjr dgol l. Cotoh. () A ; m () A ; m.. Mghtug Dtrm dg Rdus Brs D bg dprlht bhw dtrm sbuh mtrs dpt dhtug dg mrdus mtrs trsbut pd btu slo brs. Mtod ptg r mtod mghdr prhtug yg pjg yg trlbt d dlm pm dfs dtrm scr lgsug. Mul-mul dtju du golog mtrs yg dtrmy dpt dhtug dg mudh, t prdul brppu bsry uur mtrs trsbut. Torm. J A dlh sbrg mtrs udrt yg mgdug sbrs blg ol, m dt(a) =. Sbuh mtrs udrt dm sgtg ts (uppr trgulr) j smu tr d bwh dgol utm dlh sgtg bwh (lowr trgulr) j smu tr d ts dgol utm dlh ol. Sbuh mtrs b yg mrup sgtg bwh dm sgtg (trgulr). Cotoh. Sbuh mtrs sgtg ts 4 x 4 yg umum mmpuy btu Uvrsts Sumtr Utr

8 A Sbuh mtrs sgtg bwh 4 x 4 yg umum mmpuy btu A Torm. J A dlh sbuh mtrs sgtg yg bruur x, m dt(a) dlh hsl prl tr-tr pd dgol utm y A Cotoh.3 dt. A m A ()( 3)(6)(9)(4) 96 Torm 3. Aggp A dlh sbrg mtrs x. () J A dlh mtrs yg dhsl bl sbuh brs tuggl dr A dl olh sbuh ostt, m dta dta Uvrsts Sumtr Utr

9 (b) J A dlh mtrs yg dhsl bl du brs dr A dprtur, m dt A dt A (c) J A dlh mtrs yg dhsl bl sbuh lpt dr stu brs dr A dtmbh pd brs l, m dta dta Sft-sft Fugs Dtrm J A dlh sbrg mtrs m x, m trsposs dr A (trspos of A) t dyt olh A d ddfs sbg mtrs x m yg olom prtmy dlh brs prtm dr A, yg olom duy dlh brs du dr A, yg olom tgy dlh brs tg dr A, d strusy. Sft-sft Oprs Trsposs ( ) A ( ) ( ) t t A t t t A B A B t t A A ; d m dlh sbrg slr..3. sps oftor dg dh Crmr Dfs. J A dlh sbuh mtrs udrt, m mor tr j dyt olh M j d ddfs sbg dtrm dr submtrs yg tggl stlh brs d olom j dcort dr A. Blg dm oftor tr. j j M j dyt olh j Cotoh.4 Ad Mor tr 3 A dlh M oftor M dlh Uvrsts Sumtr Utr

10 M M 6 Dfs 3. J A dlh sbrg mtrs x d dlh oftor, m mtrs j j dm mtrs oftor dr A. Trsposs mtrs dm djo dr A d dyt dg dj(a). Torm 4. J A dlh sbuh mtrs yg dpt dbl, m A dt A dj A But. Mul-mul dprlht bhw A dja dtai A dj A j j j tr d dlm brs d olom j dr A dj (A) dlh (.7) j j j J = j, m (.7) dlh sps oftor dr dt(a) spjg brs dr A. Sbly, j j, m ofs-ofs d oftor-oftor brsl dr brs-brs A yg brbd, shgg l dr (.7) sm dg ol. M Uvrsts Sumtr Utr

11 A dj A dt A dt A dt A dtai (.8) r A dpt dbl, m dta, m prsm (.8) dpt dtuls mbl sbg tu dt A dja I A A dt A dj A I Dg mgl du rus dr r dg A m mghsl (.9) A dt A dj A.3 Multpl Rgrs Multpl rgrs dlh lss rgrs yg mrml pgruh du vrbl bbs tu lbh trhdp stu vrbl trt. Dpt jug dgu utu mmbut d tu tdy hubug fugsol tr du buh vrbl bbs tu lbh dg sbuh vrbl trt. Btu prsm umum multpl rgrs dlh (.) Apbl dyt dlm btu mtrs, dprolh rumus brut dg Uvrsts Sumtr Utr

12 ofs hrus dstms brdsr dt hsl plt smpl c. Prosdur stms trgtug pd sums mg vrbl d slh pggggu ε. Bbrp sums yg ptg dlh sbg brut:. l hrp stp slh pggggu sm dg ol ) (, utu smu. ) ( ) ( ) ( ) (. slh pggggu yg stu (ε ) td brorls (bbs) trhdp slh pggggu ly (ε j ), ttp mmpuy vrs yg sm. utu smu. ) (,, ) ( j j Apbl dyt dlm btu mtrs, m sums trsbut mjd sbg brut: I ' Uvrsts Sumtr Utr

13 ' = trspos dr vtor olom ε, tu dg t l, ' mrup vtor brs ' = ( ε ε ε ε ). I = mtrs dtts, r stp slh pggggu mmpuy vrs yg sm. 3.,,, mrup blg rl, tp mgdug slh. Dg prt l, mtrs mrup hmpu g-g ost (fxd umbrs). 4. Mtrs mmpuy r (d olom dr mtrs yg bbs lr). Jumlh obsrvs hrus lbh by dr jumlh vrbl, tu lbh by dr ofs rgrs lr yg dstms. (.) Apbl,,,, sudh dhtug sbg pdug prmtr,,,, brdsr dt dr smpl, m dpt dgu utu mrml, stlh,,, dthu ly..3. Tsr tu Pdug pd ofs Multpl Rgrs Msl sbg pdug mrup vtor olom dg brs sbg brut: = + = Uvrsts Sumtr Utr

14 _ (.) stms vtor dg mggu udrt trcl, lh vtor sdm rup shgg jumlh udrt slh pggggu, = mmum. Cry lh dg mlu puru prsl trhdp stp ompo vtor d mymy dg. (.3) Prsm dts, stlh dsdrh mjd Uvrsts Sumtr Utr

15 (.4) Prsm d ts dsbut prsm orml. Dg mmmum ' m dhsl : ' dg turu prsl dr prsm, m ddpt : tu (.5) (.6) Uvrsts Sumtr Utr