Indlela eSebenzayo yokuBaliswa kweeNkcukacha zokuHlola iNgcaciso yolwazi
Iimodeli zokuhlukumeza eziqhelekileyo zisetyenziselwa ukubonisa okanye ukuqikelela ubudlelwane phakathi kweenguqu ezimbini okanye izinto . Umbandela ochazwayo (into ebanjwe ngayo i-equation) ezixhomekeke kuyo. Iimeko ezisetyenziselwa ukuqikelela ixabiso lentengo exhomekeke kuyo zibizwa ngokuba ziimpendulo ezizimeleyo.
Idatha efanelekileyo ayisoloko ixelela ibali elipheleleyo. Uhlalutyo lwenkohlakalo luqhelekileyo kusetyenziswa uphando njengoko lubeka ukuba kukho ukulungiswa phakathi kwezinto eziguqukayo.
Kodwa ukulungiswa akufani noko kubangelwa . Nangona umgca kwi-regression elula engqinelanayo ehambelana neenkcukacha zeenkcukacha ngokufanelekileyo akunako ukusho into ecacileyo malunga nobudlelwane bangela kunye nentsingiselo.
Ngendlela elula yokulungiswa, umboniso ngamnye unamaxabiso amabini. Ixabiso elilodwa liyintlukwano exhomekeke kuyo kwaye inenani elilodwa liyi-variable variable.
- Uluhlu olulula oluqhelekileyo lokuhlalutya uhlalutyo Oluhlobo olulula kakhulu lokuhlalutya ngokutsha lusebenzisa kwizinto ezixhomekeke kuzo kunye nomlinganiselo omnye ozimeleyo. Kulo mzekelo olula , umgca ochanekileyo ulingana nobudlelwane phakathi kwezinto ezixhomekeke kuyo kunye nezimo ezizimeleyo.
- Uhlalutyo Oluninzi Lokunciphisa Ukusetyenziswa Xa kuhlaziywa ezimbini okanye ngaphezulu ezizimeleyo ukuhlalutya, umzekelo awusekho enye elula.
Umzekelo oqhelekileyo wokuLawula
Imodeli elula yokulungiswa komzimba imelwe njengale: y = ( β 0 + β 1 + Ε
Ngendibano yeemathematika, ezimbini izinto ezibandakanyeka kuhlalutyo oluqhelekileyo lwe-regression zikhethwe x kunye y .
I-equation echaza indlela y ihambelana ngayo x iyaziwa njengemodeli yokulawula . Imodeli yolawulo lodidi iqulethe iiposenti zexesha elimelelwa yi- Ε , okanye i-Greek letter epsilon. Ixesha lesiphene lisetyenziselwa ukuphendula i-akhawunti malunga nokuhluka kwinto engakwazi ukuchazwa ngobudlelwane obufanelekileyo phakathi kwe- x no- y .
Kukho iiparameter ezimela uluntu olufundiswayo. Ezi parameters zemizekelo ezimele ( β 0+ β 1 x ).
Umzekelo oqhelekileyo wokuLawula
I-equation equarry regression equation imelwe njengale: Ε ( y ) = ( β 0 + β 1 x ).
I-equation elula yokuguqulwa kwe-equation i-graphed njengomgca ochanekileyo.
( β 0 yiyo y inqamulelo yomgca wokulawula.
β 1 yi-slope.
I- y ( y ) yinani elithethiweyo okanye elindelekileyo y yenani elinikeziweyo le x .
Umgca wokuguqulwa ungabonisa ulwalamano oluhle, ulwalamano olubi, okanye ulwalamano oluhle. Ukuba umgca we graphed kwi-regression elula (flat-down) i-flat (ayikho i-slope), akukho buhlobo phakathi kweenguqu ezimbini. Ukuba umgca wokugqithisa uphuphukela phezulu kunye nomgca osezantsi kumgca kwinqanaba le- y (i-axis) yesigrafu, kunye nomgca wokugqibela womgca okhuphukela phezulu kwinqanaba legrafu, kude no x xhaxha (i-axis) ubudlelwane obuhle obudibeneyo bukhona . Ukuba umgca wokugqithisa wehla ukuya kumgca ophezulu womgca kwinqanaba le- y (i-axis) yesigrafu, kwaye umgca wezantsi we-line uphahla ukuya kwinqanaba legrafu, kwinqanaba le-graph (axis).
Uqikelelo lweNkcazo yokuLungiswa koNgcono
Ukuba iiparameters zoluntu zaziwa, ukulingana okulula kokulungelelanisa (kuboniswe ngezantsi) kunokusetyenziswa ukulinganisa ixabiso lentengo ye- y yexabiso elichanekileyo lika- x .
Σ ( y ) = ( β 0 + β 1 x ).
Nangona kunjalo, ngokusebenza, ixabiso leparameter alingaziwa ke ngoko kufuneka liqikelelwe ngokusebenzisa idatha ukusuka kwisampula yabemi. Imilinganiselo yamanani iqikelelwa ngokusebenzisa iisampuli zamanani . Isampuli zamanqaku zimelelwe ngu- b 0 + b 1. Xa inani leesampula zithatyathwa endaweni yamaritha omlinganiselo, i-equation regression equation yenziwa.
Uqikelelo olulinganisiweyo lokulinganisa luboniswe ngezantsi.
( ▸ ) = ( β 0 + β 1 x
()) libizwa ngokuba yinto.
Igrafu ye-equation equance regression equation ibizwa ngokuba ngumgca wokunciphisa umgca.
I- b 0 yiyo y yithatha.
I- b 1 yi-slope.
I- ❑ ixabiso eliqikelelwa y yenani elinikeziweyo le x .
Inqaku elibalulekileyo: Uhlalutyo lokunciphisa ingasetyenziswanga ukuchazela ubudlelwane obangela-kunye-effect phakathi kwezinto eziguqukayo. Uhlalutyo lokunciphisa unokwenza, nangona kunjalo, lubonisa indlela iimeko ezinxulumene ngayo kunye nokuba zingakanani iindlela ezichaphazelekayo .
Ngokwenza njalo, ukuhlalutya ukuhlaziywa kwenza ukuba ubudlelwane obunamalungelo obuvumela umphandi onolwazi ukuba athathele .
Eyaziwayo Njengaye: ukuguqulwa kwamanzi, ukuhlaziywa kwemigudu
Imizekelo: Iindlela eziphambili zeNgcaciso zendlela yenkqubo yokubala ngokusebenzisa idatha yesampuli ukufumana ixabiso lokulinganiswa kokulinganisa. Indlela eLahlukileyo yeziGqeba zacetyiswa nguCarl Friedrich Gauss, owazalwa ngonyaka ka-1777 waza wafa ngo-1855.
Imithombo:
Anderson, DR, Sweeney, DJ, kunye noWilliams, TA (2003). Izinto ezibalulekileyo zeStatisti zoShishino kunye nezoQoqosho (3rd ed.) Mason, Ohio: kusezantsi-ntshona, Thompson Learning.
______. (2010). Uchazwe: Uhlalutyo lokuLawula. Iindaba zeMIT.
McIntyre, uL. (1994). Ukusebenzisa iCigarette Data for Introduction to Multiple Regression. I-Journal ye-Statistics Education, 2 (1).
IMendenhall, W., noSincich, T. (1992). Izibalo zobunjineli kunye neSayensi (3rd ed.), ENew York, NY: iDellen Publishing Co.
Panchenko, D. 18.443 Izibalo zeZicelo, Ukuwa kwe-2006, iSigaba 14, Ukunyanzeliswa okulula. (I-Massachusetts Institute of Technology: iMIT OpenCourseWare)