Whakarerekētanga Raina: Te Pūtake o te Tātari Raraunga me te Matapae
Ko te whakatauira rārangi tētahi o ngā tikanga tatauranga e whakamahia whānuitia ana i roto i te rangahau pūtaiao me te tātari raraunga. Nā te pūtake o ngā tatauranga me te pāngarau, ka āwhina te whakatauira rārangi i a tātou ki te mārama me te matapae i te whanaungatanga i waenga i ngā taurangi e rua, neke atu rānei. Ka matapakihia e tēnei tuhinga ngā kaupapa matua o te whakatauira rārangi, ōna tono, me pēhea te hanga, me ōna painga me ōna herenga.
Kupu Whakataki: He aha te Whakamuritanga Raina?
Ka whakamahia te whakatauira raina hei whakatauira i te whanaungatanga i waenga i ngā taurangi motuhake me ngā taurangi whakawhirinaki. E whakaarohia ana he tauira raina tēnei, arā, ko te huringa kotahi-wae i roto i te taurangi motuhake ka hua ake he huringa pumau i roto i te taurangi whakawhirinaki. Hei tauira, ka taea e tātou te whakamahi i te whakatauira raina hei matapae i ngā kaute whakamātautau i runga i te maha o ngā hāora ako, i ngā utu whare rānei i runga i te horahanga whenua.
Tauira Whakamuri Raina Māmā
Kotahi anake te taurangi motuhake me te taurangi whakawhirinaki kotahi kei roto i tētahi tauira whakatauira rārangi māmā. He maha ngā wā ka hangaia tēnei tauira pēnei \( y = b_0 + b_1x \), arā:
– Ko \( y \) te taurangi whakawhirinaki.
– Ko te taurangi motuhake ko \( x \).
– Ko te haukoti te \( b_0 \).
– Ko te \( b_1 \) te tauwehenga whakatauira e tohu ana i te pari o te rārangi.
Tauira Whakamuri Raina Maha
He nui atu i te kotahi te taurangi motuhake e pā ana ki te whakatauira rārangi maha. Ko te tauira nei kua hangaia penei \( y = b_0 + b_1x_1 + b_2x_2 + … + b_nx_n \). Mā tēnei ka taea e tātou te whakaaro ki ngā āhuatanga maha i roto i te matapae i te taurangi whakawhirinaki.
Tikanga Whakatau Tatau: Ngā Tapawhā Iti Rawa
Ko tētahi o ngā tikanga matua e whakamahia ana hei whakatau tata i ngā tawhā i roto i te whakatautau rārangi ko te tikanga tapawhā iti rawa. Ko te whāinga o tēnei tikanga he whakaiti i te tapeke o ngā tapawhā o ngā rerekētanga i waenga i ngā uara i kitea me ngā uara i whakatau tatahia. Arā, kei te rapu mātou i ngā uara o \( b_0 \) me \( b_1 \) e whakaiti ana i te mahi utu:
\[ J(b_0, b_1) = \tapeke_{i=1}^{n} (y_i – (b_0 + b_1x_i))^2 \]
Te Haukoti (\(b_0\)) me te Pikinga (\(b_1\))
Ko te pūwāhi haukoti ko te wāhi e whiti ai te rārangi whakatauira i te tuaka \( y \) ina kore te \( x \). Ko te pikinga e tohu ana i te huringa o \( y \) nā te huringa o \( x \). Hei tauira, mēnā ka puta he pikinga o te 2 i te whakatauira i waenga i ngā hāora ako me ngā kaute whakamātautau, ko te tikanga mō ia hāora ako tāpiri, ka piki ake te kaute whakamātautau mā te rua ngā tohu.
Me pēhea te tatau i ngā whārite whakahōunga
Hei tatau i ngā tawhā \( b_0 \) me \( b_1 \) i roto i te whakatauira rārangi māmā, ka taea e tātou te whakamahi i te tātai e whai ake nei:
\[ b_1 = \frac{n(\tapeke xy) – (\tapeke x)(\tapeke y)}{n(\tapeke x^2) – (\tapeke x)^2} \]
\[ b_0 = \frac{(\tapeke y)(\tapeke x^2) – (\tapeke x)(\tapeke xy)}{n(\tapeke x^2) – (\tapeke x)^2} \]
Ko \( n \) te maha o ngā kitenga, ko \( \sum \) te āhua tāpiritanga (tāpiri).
Taupānga Whakamuri Raina
He whānuitia ngā whakamahinga o te whakatauira rārangi i roto i ngā momo mara pūtaiao, tae atu ki:
Ōhanga me te Pūtea
I roto i te ōhanga me te pūtea, ka whakamahia te whakatauira raina hei whakatauira i te whanaungatanga i waenga i ngā tohu ōhanga. Hei tauira, te whanaungatanga i waenga i te moni whiwhi me te kai, ngā utu hea me te rahinga hokohoko, te kore mahi me te pikinga utu rānei.
Te akuaku
I roto i te hauora, ka taea te whakamahi i te whakatauira rārangi hei matapae i ngā putanga haumanu pēnei i te toto totoka i runga i te taupū papatipu tinana (BMI), i te whanaungatanga rānei i waenga i te horopeta rongoā me te tere whakaora o te tūroro.
Hokohoko
Ka whakamahia hoki te whakatauira rārangi i roto i te hokohoko hei tātari i ngā raraunga hoko, hei matapae i te tono hua, me te whakatau i te whai huatanga o ngā kaupapa pānuitanga.
Te Hangarau me te Pūtaiao
I roto i te hangarau me te pūtaiao, he maha ngā wā ka whakamahia te whakatauira raina hei whakatauira i ngā whanaungatanga i waenga i ngā taurangi ā-tinana. Hei tauira, te whanaungatanga i waenga i te ahotea me te taumahatanga i roto i tētahi rauemi, i waenga rānei i te pāmahana me te kawe wera.
Ngā Painga o te Whakamuritanga Raina
He māmā noa iho, he ngāwari hoki te mārama
Ko tētahi o ngā painga matua o te whakatauira rārangi ko tōna māmā noa iho. He ngāwari te mārama me te whakamārama i tēnei tauira, ā, he taputapu pai rawa atu tēnei mō ngā whakaaturanga me te whakawhitiwhiti kōrero.
Te Pūtake mō Ētahi Atu Tikanga
Mā te whakatauira rārangi ka whakaratohia he tūāpapa pakari mō ngā tikanga tatauranga me te ako mīhini uaua ake. He maha ngā tauira matatau, pērā i te whakatauira logistic me ngā whatunga io, e hangai ana ki ngā mātāpono o te whakatauira rārangi.
Te Tāutuhi Hononga
Mā te whakatautautanga rārangi ka taea e ngā kaiwhakamahi te tautuhi me te ine i ngā whanaungatanga i waenga i ngā taurangi, ka taea hoki te whakamahi hei hanga matapae whai kōrero me te whakatau whakatau pai ake.
Ngā Here o te Whakamuritanga Raina
Te Whakaaro Raina
E whakaarohia ana e te whakatauira rārangi he whanaungatanga rārangi i waenga i ngā taurangi, kāore pea e pēnei tonu i ngā raraunga o te ao tūturu. Mō ngā raraunga kore-rārangi, he pai ake pea ētahi atu tikanga pēnei i te whakatauira pūronomial, ngā tauira kore-tawhā rānei.
Tairongo ki ngā Mea o Waho
He tino tairongo ngā tauira whakatauira rārangi ki ngā uara tino nui (ngā uara tino nui) ka taea te whakapohehe i ngā hua. Nō reira, he mea nui kia tirohia ngā raraunga me te aro atu ki ngā raraunga tino nui i mua i te whakahaere i te tātari whakatauira.
Te maha-whakapiripiri
I roto i te whakatautautanga rārangi maha, ka puta te maha-whakapiripiri ina he hononga nui ngā taurangi motuhake tetahi ki tetahi, ā, ka uaua pea te whakatau tika i ngā taunga. Ka taea te whakatika i tēnei mā te whakamahi i ngā tikanga pēnei i te tātaritanga wāhanga matua (PCA) me te whakatauritenga rānei.
Kāore e hopu ana i te uauatanga
Kāore e taea e te whakatauira rārangi te hopu i ngā whanaungatanga uaua ake i waenga i ngā taurangi. I roto i te nuinga o ngā wā, me whakamahi pea i ngā tauira uaua ake pēnei i te whakatauira kore-rārangi, te ako mīhini rānei kia tika ake ai ngā hua.
Whakamutunga
He taputapu kaha, he taputapu maha hoki te whakatauira rārangi i roto i te tātari raraunga me te matapae. Ahakoa tōna māmā noa iho, he tūāpapa pakari tēnei tauira mō te mārama ki ngā whanaungatanga i waenga i ngā taurangi me te whakatakoto matapae i runga i ngā raraunga o mua. Mā te mārama ki ōna painga me ōna herenga, ka taea e ngā kairangahau me ngā kaitātari te whakamahi i te whakatauira rārangi kia whai hua ake, kia tika hoki i roto i ngā momo tono.
Hei whakamutunga, ahakoa he ākonga koe, he kairangahau, he tohunga rānei e mahi ana ki ngā raraunga, mā te mōhio ki te ariā o te whakatauira raina ka tino whakarei ake i ō pūkenga tātari raraunga me te whakatau kaupapa. Whakauruhia te whakatauira raina ki roto i ō taputapu tātari, ā, ka kitea e koe ka hohonu ake tō māramatanga ki ngā raraunga me ngā whanaungatanga i waenga i ngā taurangi.
