Te Whakarerekētanga Raina i roto i ngā Tatauranga
Ko te whakatauira rārangi tētahi o ngā tikanga tatauranga tino taketake, tino whānuitia hoki e whakamahia ana i roto i te tātari raraunga. Ka āwhina i a tātou ki te mārama me te whakatauira i te whanaungatanga i waenga i ngā taurangi motuhake (taurangi matapae rānei) me ngā taurangi whakawhirinaki (taurangi urupare rānei). He rongonui te whakatauira rārangi i roto i ngā momo mara, tae atu ki te ōhanga, te koiora, te hangarau, ngā pūtaiao pāpori, me ētahi atu, nā te mea he māmā noa iho, he ngāwari hoki te whakamārama.
Kupu Whakataki ki te Whakamuritanga Raina
Ko te whāinga o te whakatauira rārangi ko te kimi i tētahi whanaungatanga rārangi i waenga i ngā taurangi e rua, neke atu rānei. I tōna āhua māmā rawa—te whakatauira rārangi māmā—ka whakatauirahia e mātou te whanaungatanga i waenga i tētahi taurangi motuhake me tētahi taurangi whakawhirinaki hei rārangi tika. Ko te whārite pāngarau taketake mō te whakatauira rārangi māmā e kīia ana penei:
\[ Y = \beta_0 + \beta_1X + \epsilon \]
Kei hea:
– Ko \$ Y te taurangi whakawhirinaki, te taurangi urupare rānei.
– Ko \$ X te taurangi motuhake, te taurangi matapae rānei.
– Ko te \$ \beta_0 \$$ te pūwāhi e honoa ai te rārangi whakatauira ki te tuaka-Y).
– Ko te \$ \beta_1 \$$ te pikinga (te pikinga o te rārangi whakatauira).
– Ko te \$ \epsilon \$$ te hapa (toenga) e whakaahua ana i te peka o ngā raraunga mai i te rārangi taunga pai rawa atu.
I roto i te whakatautautanga rārangi maha, ka whakawhānuihia e mātou tēnei ariā ki te whakahaere i ngā taurangi motuhake neke atu i te kotahi, penei:
\[ Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + … + \beta_nX_n + \epsilon \]
I konei, ko \$ X_1, X_2, …, X_n \$$ ngā taurangi motuhake, ā, ko \$ \beta_1, \beta_2, …, \beta_n \$$ ngā taunga whakatauira e ine ana i te pānga o ia taurangi motuhake ki te taurangi whakawhirinaki.
Te Whakatau Tawhā
Ko te whakatau tata i ngā tawhā i roto i te whakatautautanga rārangi ka whakamahia mā te whakamahi i te Ordinary Least Squares (OLS). Ka whakaitihia e tēnei tikanga te tapeke o ngā tapawhā o ngā rerekētanga i waenga i ngā uara matapae me ngā uara tūturu. Mā te pāngarau, ka kitea e te tikanga OLS ngā tauwehenga e whakaiti ana i te mahi e whai ake nei:
\[ \sum_{i=1}^{n} (Y_i – (\beta_0 + \beta_1X_{i1} + \beta_2X_{i2} + … + \beta_nX_{in}))^2 \]
Mā tēnei tukanga whakaitiiti ka puta ngā tauwehenga e tino uru ana ki ngā raraunga e wātea ana, ka puta he rārangi whakatauira e whakaiti ana i te hapa tapawhā katoa.
Ngā Whakaaro Whakamuri Raina
Mō te whakamahinga tika me te pono o ngā hua, he maha ngā whakapae me tutuki i te whakatauira raina:
1. Te Raina: He raina te whanaungatanga i waenga i ngā taurangi motuhake me ngā taurangi whakawhirinaki.
2. Te Tū motuhake: He tū motuhake ngā toenga (ngā hapa) tetahi i tetahi.
3. Homoscedasticity: He pumau te rerekētanga toenga mō ngā uara katoa o te taurangi motuhake.
4. Te Auautanga: Ka whai ngā toenga i tētahi tohatoha noa.
Ki te takahia ēnei whakapae, ka kore e whai mana, ka hē hoki ngā hua whakatautau. Nō reira, he mea nui kia manatokohia ēnei whakapae mā te tātaritanga whakatautau i mua i te whakatau whakatau.
Te Whakamahinga me te Taupānga
He whānuitia te whakamahinga o te whakatauira rārangi nā tōna māmā me tōna whānui hoki. Anei ētahi tauira o ngā tono i roto i ngā mara rerekē:
1. Ōhanga: Te hono i te utu o ngā taonga ki ngā āhuatanga pēnei i ngā utu whakaputa, te tono mākete, me ētahi atu.
2. Pūtea: Te whakatauira i ngā hokinga mai o ngā hea i runga i te mōrearea, i ngā āhuatanga ōhanga rānei.
3. Koiora: Ka tirotiro i te whanaungatanga i waenga i te horopeta o tētahi rongoā me tōna taumata whai huatanga.
4. Hapori: Te tātari i te whanaungatanga i waenga i te mātauranga me te moni whiwhi.
Hei tāpiritanga, he maha ngā wā ka whakamahia te whakatauira rārangi i roto i te matapae raraunga, i te matapae rānei. Mā te tātari i ngā au o ngā raraunga o mua, ka taea te whakamahi i te whakatauira rārangi hei matapae i ngā uara ā muri ake nei.
Aromatawai Tauira
Ka whakahaerehia te aromatawai tauira whakatauira rārangi hei whakarite kia rawaka te tauira, kia mārama hoki te whakamārama i ngā raraunga. He maha ngā inenga e whakamahia pinepinetia ana i roto i tēnei aromatawai tauira, tae atu ki:
– R-tapawhā (R^2): E ine ana i te ōwehenga o te rerekētanga katoa i roto i te taurangi whakawhirinaki e whakamāramahia ana e te tauira whakatauira. Ko ngā uara R^2 kei waenga i te 0 me te 1, ā, ko ngā uara teitei ake e tohu ana i tētahi tauira pai ake.
– R-tapawhā kua Whakatikatikahia: Ka whakatika i te R-tapawhā i runga i te maha o ngā taurangi motuhake e whakamahia ana, ka whakamahia pinepinetia ngā tatauranga-F hei whakatau i te hiranga whānui o te tauira.
– Hapa Tapawhā Toharite (MSE): Ko te toharite o ngā rerekētanga tapawhā i waenga i ngā uara tūturu me ngā uara i matapaetia.
Tātaritanga me te Whakamana
I mua i te whakamahinga o te tauira whakatautau mō te matapae, mō te whakatau kaupapa rānei, he mea nui kia whakahaerehia he tātaritanga whakatautau. Ko ētahi o ngā tikanga tātaritanga noa ko:
1. Kauwhata toenga: Aromatawai i te rārangitanga me te ōritetanga.
2. Kauwhata QQ: Aromatawaihia te āhua noa o ngā toenga.
3. Whakamātautau Durbin-Watson: Ka whakamātau i te hononga ā-roto toenga.
4. Tauwehenga Pikinga Rerekētanga (VIF): Te tautuhi i te maha-whakapiripiri i waenga i ngā taurangi motuhake.
Mā te whakamahinga o ēnei tātaritanga ka āwhina i te tautuhi i ngā raruraru pea, ā, ka taea hoki e ngā kaiwhakamahi te mahi i ngā whakarerekētanga e tika ana, te whakawhiti raraunga rānei.
Ngā Raru me ngā Here
Ahakoa he taputapu kaha te whakatauira raina, he iti anō ōna herenga. Ko ētahi o ngā take noa ko:
– Te maha-whakapiripiri: Ka puta ina he hononga nui ngā taurangi motuhake tetahi ki tetahi. Ka taea e tēnei te arahi ki ngā whakatau tauwehenga kore pumau me ngā whakamaoritanga whakapoauau.
– Ngā mea o waho: Ka taea e ngā uara raraunga tino nui te whakapohehe i ngā hua whakatauira.
– Kore-rārangi: Mena he kore-rārangi te whanaungatanga i waenga i ngā taurangi, kāore pea i te tino tika te whakatauira rārangi. Tērā pea he pai ake te tauira kore-rārangi i ētahi wā.
– Heteroscedasticity: Mā te huri i te rerekētanga toenga ka hua ake he whakatau tauwehenga koretake.
Whakamutunga
He tikanga tatauranga nui te whakatauira rārangi i roto i te tātari raraunga. Mā te whakamahi i te whakatauira rārangi, ka taea e tātou te mārama me te whakatauira i te whanaungatanga i waenga i tētahi, neke atu rānei o ngā taurangi motuhake me tētahi taurangi whakawhirinaki. Ahakoa he taputapu māmā te whakatauira rārangi, he mea nui kia tirohia tonutia ngā whakaaro matua me te mahi i ngā tātaritanga whakatauira kia tika ai ngā hua. Ahakoa ētahi herenga, me te huarahi tika me ngā whakarerekētanga, he tikanga tino whai hua tonu te whakatauira rārangi i roto i ngā tono mahi maha puta noa i te whānuitanga o ngā mara.
