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
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
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 }. 3.3. 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. 3.4. 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 3 3 7 6 49 9 86 4 84 3496 3 3 4 8 9 4796 4 8 3 4 784 3 34 43 9 6 6 ol 8 3 88 4 7 4737 3936 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 3 3 3 697 7 9 3496 984 8 37 394 44 6 48 6
3 4 64 8 4 38 34 4 3 68 36 7 4794 466 7 8 79 86 67 949 64 89 3349837 34893976374 8 3 88 3 4 8 7 64 893 837 6 3 64 4737 33493 3489 88 89 3349 39363 3976 3 X X 3 9 3 8 34 3 86 4 3 3 3 9 86 3 4 S 8 3 3 34 8 3 88 8 7 64 89 S X X 3 64 4737 3349 88 89 3349 3936 4 7 de S 37 76 386 S 7 37 76 34 9 3783 9 9474 66983 3783 66983 4786 84374 339 339 74 7 743 74634 674 Sem wre mercl o he lef wh S 7 74634 743 674 9 9687 9687 39 S become 3 b b b b 3 84374 339 339 74 7 743 3 74634 674 7 74634 4 743 674 837 9 9687 3489 9687 39 3976 From whch 6399463 39788487 3837974 3 843 herefore Y 6399463 39788487 X 3837974 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 3 3 3837974x 396 X clcul x 6399463 39788487x x 843x 39788487 39674 39788487 888 4338 3 3x3 6
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 3837974 396 9 33 3837974 3648 448 3 3 X clcul 3 3 44 843 396 39 843 849 4447 m { 3 X clcul } m{ 888;3648;849} 849 X 3clcul he hpohe X <. 3 clcul α 3 3 3 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 8 3 34 mrxe S X X d B X Y S X X 3 3 9 3 8 38 3 9 3 8 3 34 8 3 8 7 64 3 64 4737 B X Y 3 3 9 3 8 38 7 4 8 837 4 3489 43 he deque exeded mrx A S B I 3 h 8 3 4 A 8 7 64 837 3 64 4737 3489 We ppl Gu mehod d ob A I 3 B S 744 887 346 6394 447 447 447 447 7636 346 984 84 447 447 447 447 68 6394 84 4 447 447 447 447 44 387477 343699 437674 773 469 773 436336 64876 469 64876 4963 Afer h ge he prl be regreo per Y 44 387477 X 3 43699X 7
8 4 d 44 A 8 7 837 387477x 343699x S C I3 C X Y 38398 696649 Ad A I3 C S he clculed vlue of he e re 463986 343 6749 387477 X clcul 343743 6749 37486 696649 436336 Ad 387477 79 387477 73837 X clcul 868866 37486 343699 X clcul 387477 696649 4963 4743 863 343699 884 For 847 α X 4743 348 clcul > α ;3 m{ X clcul } X clcul d. herefore we reec he hpohe X clcul 884 o he be per For α Y 44 387477 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 44 387477 X for whch 387477x 868866 he deque exeded mrx 44 REFERECES. Gber C. Sc Peroleum-G Uver Ploeş Publhg oue 7 pg. 83-8 9-34 43-4.. Ic Mu Al. Mruţ C. Voegu V. Sc Bucureş Uver Publhg oue - 3 pg. - 3-37. 3. Voegu V. Ţ E. colecv Ecoomercl heor d prcce Meeor Pre Publhg oue Bucureş 7 pg.3-47. 8