BEST PATTERN OF MULTIPLE LINEAR REGRESSION

Transcription

1 ERI COADA GERMAY GEERAL M.R. SEFAIK AIR FORCE ACADEMY ARMED FORCES ACADEMY ROMAIA SLOVAK REPUBLIC IERAIOAL COFERECE of SCIEIFIC PAPER AFASES Brov 6-8 M BES PAER OF MULIPLE LIEAR REGRESSIO Corel GABER PEROLEUM-GAS Uver of Ploeş Româ Abrc I he ecoomcl dom we ofe lze he fluece of everl cul vrble o reulg vrble ug per of mulple ler regreo. Amog he depede fcorl vrble e ll o ccou he ud we c deduce hroughou he proce h pr of hem hve gfc c fluece o he effec vrble. he rcle pree mehod of elmg gfc vrble d deermg he be per of mulple ler regreo. Mhemc Subec Clfco 6J. Keword covrce mrx Gu drbuo opmzo mehod regreo l.. IRODUCIO he coeco bewee wo or mog everl fcorl vrble d reulg vrble clled mulple coeco herefore he choce of he fcorl vrble ver mpor o h he vro of he reulg vrble hould be rel. Fcorl vrble exer greer or mller fluece o he reulg vrble coequel ome of he fcorl vrble re more mpor d mu be e o ccou he ud whch mde whle for oher vrble prove h he re o o mpor for he ud of he reulg vrble vro d mu be elmed. Fcorl or cul vrble re ordered ccordg o he mporce of her co o he effec pheomeo d oe loo for regreo equo whch he be. A be per of regreo c be obed b he rerogrde elmo mehod whch co of he ucceve elmo of he fcorl vrble e ll o he mulple regreo equo ul he per become he be crefull obervg o cll verf he emergece crero.. SAISICAL YPOESIS USED FOR E COICE OF VARIABLES WIC ARE ELIMIAED FROM E PAER We e he depede vrble Y d he depede vrble; here re X X... X coeced b mulple regreo equo Y X... X X X X... X where he coeffce mrx of he per d he mrx of he prmeer emor of he per emor obed hrough he mller qudr mehod. We ume h he emor obed re ubed hvg mml vrce d followg he orml lw. Vrble X orml m whe X m he drdzed vrble Z follow he reduced orml lw. he m dgol of he covrce mrx of he vecor formed b he 3

2 emor vrce he mrx expreo beg S X X V where herefore S. If uow he he vrble Z Follow he reduced orml lw. A uow h replced b he ubed emor he umber of obervo from whch we ob he vlue of he redul vrble re ormll drbued h whch led o he cocluo h d From whch we ob 3 From d 3 we ob 4 We clcule he emor verge M M M. h he emor d ubed. he vrble Z follow he lw Sude wh degree of freedom herefore ug he relo d 4 we ob For deermed vlue d cl clcul we e he hpohe Ad f ; clcul α > he we reec he hpohe d ccep he hpohe. For we ob clcul hee re drbued wh Sude wh degree of freedom he cl hpohee beg 4

3 ERI COADA GERMAY GEERAL M.R. SEFAIK AIR FORCE ACADEMY ARMED FORCES ACADEMY ROMAIA SLOVAK REPUBLIC IERAIOAL COFERECE of SCIEIFIC PAPER AFASES Brov 6-8 M Ad for he hpohe. we reec clcul > α ; he drbuo F α; he drbuo of he c clcul d for clcul > Fα ; hpohe. we reec he ull 3. REROGRADE ELIMIAIO MEOD O OBAI E BES REGRESSIO WE DO E FOLLOWIG 3.. We ob L b he mller qudr mehod ug ll he l fcorl vrble X X... X. 3.. he c of he e FX clcul clcul Ad we deerme m { FX } d clcul ume h he erched mml F X r clcul or we ue he c clcul d where here r o h r clcul m { clcul } We e he hpohee r r r r Ad f X clcul < Fα; F r he we r ccep he hpohe herefore he fcorl vrble X r elmed from he per we wre he ew fg equo whou X r d we ob prl be regreo per or f < r clcul α ; r we ccep he hpohe h d we ob he prl be per of he ge o he per obed 3. we ppl he ge 3. d 3.3g ul he ge where he obed reul doe o llow he elmo of oher vrble d h fl per obed he be. Exmple ble x 3 r. x x x 3 cr. x x ol Y X X 3X 3 x x 3x3 x x x x 3x x3 x x x x x 3x x3 x x3 x x3 x x3 3x3 x3 ble. Follow up x x x x3 x x3 x x x

4 X X S S X X de S S Sem wre mercl o he lef wh S S become 3 b b b b From whch herefore Y X X 843 X 3 repree he mulple ler regreo per obed fer he fg ug ll he fcorl vrble. We deerme he c X clcul 3 o h X clcul where x 396 X clcul x x x 843x x3 6

5 ERI COADA GERMAY GEERAL M.R. SEFAIK AIR FORCE ACADEMY ARMED FORCES ACADEMY ROMAIA SLOVAK REPUBLIC IERAIOAL COFERECE of SCIEIFIC PAPER AFASES Brov 6-8 M f X clcul X clcul m { 3 X clcul } m{ 888;3648;849} 849 X 3clcul he hpohe X <. 3 clcul α cceped We coder α α 97; 76 ; d deed X clcul 849 < 76 3 α 3 So we elme he 3 rd colum from he mrx X d we ob 3 9 X 3 he we deerme he mrxe S X X d B X Y S X X B X Y he deque exeded mrx A S B I 3 h A We ppl Gu mehod d ob A I 3 B S Afer h ge he prl be regreo per Y X X 7

6 8 4 d 44 A x x S C I3 C X Y Ad A I3 C S he clculed vlue of he e re X clcul Ad X clcul X clcul For 847 α X clcul > α ;3 m{ X clcul } X clcul d. herefore we reec he hpohe X clcul 884 o he be per For α Y X. 99 > α ; X clcul 884 reuled whch requre he ccepce of he hpohe herefore we elme from he per he vrble X d he equo of he be regreo per fer h ge Y X for whch x he deque exeded mrx 44 REFERECES. Gber C. Sc Peroleum-G Uver Ploeş Publhg oue 7 pg Ic Mu Al. Mruţ C. Voegu V. Sc Bucureş Uver Publhg oue - 3 pg Voegu V. Ţ E. colecv Ecoomercl heor d prcce Meeor Pre Publhg oue Bucureş 7 pg