Kuyini Ukuhlehla Okuningi
Ukuhlehla okuningi kuyindlela yokuhlaziya izibalo esetshenziswa ukuqonda ubudlelwano phakathi kwe-variable eyodwa exhomekekile kanye ne-variable ezimbili noma ngaphezulu ezizimele. Le ndlela ivame ukusetshenziswa ocwaningweni lwezenhlalo, lwezomnotho, lwebhizinisi, lwezempilo, lwezemfundo, kanye nolwesayensi yedatha ngoba ingachaza ukuthi izici eziningana zithinta kanjani umphumela.
Isibonelo, ake sithi othile ufuna ukubikezela amaphuzu okuhlolwa komfundi. Amaphuzu okuhlolwa (okuguquguqukayo okuxhomeke kukho) angathonywa amahora okufunda, ukuba khona, kanye nokufinyelela ekufundiseni (okuguquguqukayo okuzimele). Ukubuyela emuva okuningi kusiza ukuphendula imibuzo efana nalokhu: Yiziphi izici ezinethonya elikhulu? Uma amahora okufunda enyuka, amaphuzu okuhlolwa ajwayelekile azokhuphuka kangakanani, okwenza ezinye izici zingashintshi?
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Incazelo kanye nenhloso yoKuphindaphindwa Okuningi
Ngamagama alula, ukuhlehla okuningi kuhlose:
1. Qagela inani le-variable exhomeke ku-variable eziningana ezizimele.
2. Chaza ukuthi ithonya elingakanani eliyi-variable ngayinye ezimele ku-variable exhomeke kuyo.
3. Kunciphisa ukubandlulula okungase kuvele uma sisebenzisa i-variable eyodwa ezimele kuphela, yize empeleni into ethile ithonywa yizici eziningi.
4. Ukulawula ezinye iziguquguquko (ukulawula) lapho kuhlolwa ithonya lesiguquguquko esithile.
Ngokuhlehla okulula, sibheka kuphela ubudlelwano besici esisodwa nomphumela. Kodwa-ke, ezweni langempela, imiphumela ivame ukufana. Yilapho ukuhlehla okuningi kuba khona ngokoqobo: kuzama ukubona "isithombe esikhulu" ngokufaka iziguquguquko eziningi ngesikhathi esisodwa.
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Ifomu Elijwayelekile Le-Multiple Regression Equation
Ukuhlehla okuningi kuvame ukubhalwa njenge-equation:
Y = a + b1X1 + b2X2 + b3X3 + … + bnXn + e
Imininingwane:
– Y = i-variable exhomeke kuyo (okuzochazwa/okubikezelwe)
– a = okungaguquki (inani lika-Y uma wonke ama-X engu-0)
– b1, b2, … bn = ama-coefficient okubuyela emuva kwe-variable ngayinye ezimele
– X1, X2, … Xn = iziguquguquko ezizimele
– e = iphutha/insalela (ingxenye yokwehluka ku-Y engenakuchazeka ngemodeli)
I-coefficient b iyisakhi esivame ukuhunyushwa kakhulu. Isibonelo, uma i-b1 = 2,5, khona-ke ukwanda ngakunye kweyunithi eli-1 ku-X1 kuzokhulisa u-Y ngo-2,5, uma kucatshangelwa ukuthi ezinye iziguquguquko ezizimele zihlala zingaguquki. Ibinzana elithi "konke okunye kuhlala kungaguquki" libalulekile ngoba limelela isici esiyinhloko sokuphindaphinda okuningi: lilinganisa umphumela "ongaphelele" weguquguquko.
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Isibonelo Sohlelo Lokusebenza Lokuhlushwa Okuningi
Ukuze kube lula, nansi isibonelo sebhizinisi esilula. Ake sithi inkampani ifuna ukwazi izici ezithonya ukuthengiswa komkhiqizo (Y). Inkampani iqoqa idatha:
– X1 = izindleko zokukhangisa (ngezigidi zama-rupiah)
– X2 = intengo yomkhiqizo (ngezinkulungwane zama-rupiah)
– X3 = inani labathengisi abasebenzayo
Imiphumela yokuhlaziywa iveza i-equation:
Ukuthengisa = 100 + 8X1 – 5X2 + 12X3
Incazelo:
– I-Constant 100: lapho izindleko zokukhangisa, amanani, kanye nabathengisi bezitolo kubhekwa njengo-0, ukuthengisa kulinganiselwa ukuthi kungamayunithi ayi-100 (lokhu kumane kuyincazelo yezibalo, ngezinye izikhathi akunangqondo empeleni).
– 8X1: zonke izindleko zokukhangisa ezengeziwe eziyisigidi esingu-1 kulinganiselwa ukuthi zizokhulisa ukuthengisa ngamayunithi angu-8, uma intengo kanye nomthengisi kabusha kuhlala kufana.
– -5X2: njalo ukwenyuka kwentengo okungu-1 000 rupiah kulinganiselwa ukuthi kuzonciphisa ukuthengiswa ngamayunithi ama-5, uma ezinye izinto eziguquguqukayo zihlala zingaguquguquki.
– 12X3: wonke umthengisi oyedwa osebenzayo ukhulisa ukuthengisa ngamayunithi ayi-12, uma ezinye izinto eziguquguqukayo zihlala zingaguquguquki.
Ngale modeli, izinkampani zingakha izinqubomgomo: isibonelo, ukunquma inhlanganisela yokukhangisa, amanani, kanye nenani labathengisi ukuze kufezwe imigomo yokuthengisa.
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Kunini Lapho Kufaneleka Ukuhlehliswa Okuningi?
Ukuhlehla okuningi kufanelekile ukusetshenziswa uma:
1. Unomphumela owodwa oyinhloko ofuna ukuwubikezela (Y).
2. Kunezinto ezingaphezu kweyodwa okusolwa ukuthi zithonya umphumela (X).
3. Idatha isezingeni lezinombolo noma ingashintshwa ibe yifomu lezinombolo (isibonelo, izigaba zishintshwa zibe ama-dummies).
Le ndlela ingasetshenziswa futhi "ukuhlola imibono" ocwaningweni, isibonelo ukuthi umphumela wemfundo emholweni usabalulekile yini ngemva kokulawula ulwazi lomsebenzi kanye nendawo yokuhlala.
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Imibono Ebalulekile Ekubuyeleni Okuningi
Ukuze imiphumela ibe semthethweni, ukuhlehla okuningi kunezinkolelo eziningana okudingeka zicatshangelwe:
1. Ukulingana
Ubudlelwano phakathi kweziguquguquko ezizimele nezixhomeke kuzo bucatshangwa ukuthi buqondile. Uma ubudlelwano bangempela bugobile (bungewona oqondile), imodeli eqondile ingase ingabi nembambo kangako.
2. Akukho ukuhlangana okuningi okuphezulu
Iziguquguquko ezizimele akufanele zihlobane kakhulu. Uma i-X1 ne-X2 zicishe zifane, kuzoba nzima ukuhlukanisa imiphumela yazo.
3. Ukuthandana Kwabantu Abashadile
Ukwehluka okusele kulindeleke ukuthi kuhlale njalo kuzo zonke izilinganiso ezibikezelwe. Uma okusele kuba kukhulu ngenani elithile (i-heteroscedasticity), ukulinganisa kungase kungasebenzi kahle.
4. Ukujwayelekile kwezinsalela (okuvame ukufiseleka)
Izinsalela kufanele zisakazwe cishe ngokujwayelekile, ikakhulukazi ngezinjongo zokuhlola ukubaluleka.
5. Ukuzimela kwamaphutha
Amaphutha phakathi kokubonwa akufanele ahlotshaniswe. Le nkinga ivame ukuvela kudatha yochungechunge lwesikhathi.
Ukuhlola izibikezelo kuvame ukwenziwa ngamagrafu asele, izivivinyo zezibalo (isb., i-VIF ye-multicollinearity), kanye nokunye ukuhlaziya kokuxilonga.
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Ukulinganisa Ikhwalithi Yemodeli: Ukuhlolwa kwe-R² kanye Nokubaluleka
Ekubuyiseleni emuva okuningi, kusetshenziswa izinkomba eziningana ezivamile:
– R² (Isilinganiso Sokunquma)
Ibonisa isilinganiso sokwehluka ku-Y esingachazwa ngemodeli. Amanani e-R² aqala ku-0–1. Uma i-R² inkulu, kulapho i-variable ezimele ichaza khona ukwehluka okukhulu. Kodwa-ke, i-R² enkulu ayisho ngokuzenzakalelayo ukuthi imodeli "ilungile"; ukulingana ngokweqile kungenzeka.
– I-R² Elungisiwe
Inguqulo ye-R² ecabangela inani lezinto eziguquguqukayo ezizimele. Lokhu kusiza ukuqhathanisa amamodeli nezinombolo ezahlukene zezinto eziguquguqukayo.
– Ukuhlolwa kwe-F (okuyenzeka ngesikhathi esisodwa)
Ukuhlola ukuthi iziguquguquko ezizimele ndawonye zinomthelela omkhulu ku-Y.
– ukuhlolwa kwe-t (okungaphelele)
Hlola ukuthi i-coefficient ngayinye (b1, b2, njll.) ibalulekile ngokwezibalo.
Ngalesi sivivinyo, abacwaningi bangahlola ukuthi imodeli iwusizo yini nokuthi yiziphi iziguquguquko ezifaka isandla ngempela.
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Izinzuzo kanye nemikhawulo yoKuphindaphindwa Okuningi
Ngokweqile
- Kunengqondo kakhulu ngoba kucatshangelwa izinto eziningi ngesikhathi esisodwa.
- Ingasetshenziswa ukubikezela kanye nokuchazwa.
– Ivumela ukuhlaziywa komphumela ongaphelele (ukulawulwa kwezinye izinto eziguquguqukayo).
- Kuyisisekelo sezindlela eziningi ezithuthukisiwe zezibalo kanye nokufunda komshini.
Ukulinganiselwa
– Ithinteka yi-multicollinearity.
– Imiphumela ingaba yiphutha uma izibikezelo zingahlangatshezwanga.
– Akubonisi ngokuzenzakalelayo ubudlelwano obuyimbangela; ukuhlehla kubonisa ukuhlangana, kanti ukuba yimbangela kudinga umklamo oqinile wocwaningo.
– Ukufaka idatha ngokweqile kungenzeka uma kuneziguquguquko eziningi kakhulu uma kuqhathaniswa nenani ledatha.
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I-Penutup
Ukuhlehla okuningi kuyithuluzi elibalulekile lezibalo lokuhlaziya ubudlelwano phakathi kwe-variable eyodwa exhomekekile kanye ne-variable eziningi ezizimele. Isebenzisa i-equation elula, le ndlela isiza abacwaningi kanye nochwepheshe ukuqonda izici ezinethonya, ukukala amandla ethonya le-variable ngayinye, nokwenza izibikezelo ezinembile kakhulu kunokusebenzisa i-factor eyodwa kuphela.
Kodwa-ke, ukuhlehla okuningi akuyona "ithuluzi lomlingo." Kudinga ikhwalithi enhle yedatha, ukukhetha okuguquguqukayo okunengqondo, kanye nokuhlola okucatshangwayo ukuqinisekisa ukuhumusha okunembile. Uma kusetshenziswa ngendlela efanele, ukuhlehla okuningi kunganikeza isisekelo esiqinile sokwenza izinqumo eziqhutshwa idatha emikhakheni eyahlukahlukene.
Uma ungathanda, ngingakusiza ukuthi udale inguqulo yalesi sihloko yomongo othize (isb., yethisisi, yebhizinisi, noma yabafundi besikole samabanga aphezulu) egcwele izibonelo ezilula zokubala kanye nendlela yokufunda umphumela we-SPSS/Excel/R.
