Kuwirirana uye Kuderera muZviverengero
Statistics ibazi remasvomhu rinotarisa pakuunganidza, kuongorora, kududzira, uye kuratidzwa kwedata. Pfungwa mbiri dzakakosha mustatistics icorrelation neregression. Pfungwa idzi dzinowanzoshandiswa muzvikamu zvakasiyana-siyana, zvinosanganisira economics, biology, social sciences, uye tekinoroji, kufanotaura nekunzwisisa hukama huripo pakati pezvinhu zvakasiyana-siyana.
Kubatana
Muchidimbu, hukama hunoyera simba negwara rehukama hwakatsetseka pakati pezvinhu zviviri. Hukama hunowanwa kuburikidza ne coefficient yehukama, iyo inowanzo kuratidzwa se \( r \). Kukosha kwe \( r \) kunotangira pa -1 kusvika +1. Heino dudziro ye kukosha kwe \( r \):
– \( r = +1 \): Inoratidza hukama hwakakwana hwemutsara pakati pezvinhu zviviri izvi, apo kuwedzera kwechinhu chimwe chete kunogara kuchiteverwa nekuwedzera kwechimwe chinhu.
– \( r = -1 \): Inoratidza hukama hwakakwana hwemutsara usina kunaka, uko kuwedzera kwechimwe chinoshanduka kunoteverwa nekuderera kwechimwe chinoshanduka.
– \( r = 0 \): Hapana hukama hwakatsetseka pakati pezvinhu zviviri izvi.
Pamusoro pezvo, kukosha kwe \( r \) pedyo ne +1 kana -1 kunoratidza hukama hwakasimba hwemutsara, nepo kukosha kwe \( r \) pedyo ne 0 kuchiratidza hukama husina kusimba.
Mienzaniso yeKubatana muKushanda
Semuenzaniso, ngatitii tinoda kuona kana paine hukama pakati penguva inopedzwa nevadzidzi vachidzidza nemapoinzi avo ebvunzo. Tinogona kuunganidza data kubva kuboka revadzidzi pamusoro pehuwandu hwemaawa avanoshandisa vachidzidza nemapoinzi avo ebvunzo. Tinogona kuverenga coefficient yekubatana kuti tione simba rehukama huripo pakati pezvinhu zviviri izvi.
Kana mhinduro dzekuverenga dzichiratidza kukosha kwe \(r = 0.8 \), tinogona kugumisa kuti pane hukama hwakasimba pakati penguva yekudzidza nemapoinzi ebvunzo. Izvi zvinoreva kuti nguva yakawanda inopedzwa nevadzidzi vachidzidza, ndipo panowedzera mapoinzi avo ebvunzo.
Miganhu yekubatana
Kunyange zvazvo kuwirirana kuchipa ruzivo rwakakosha nezvehukama huripo pakati pezvinhu zviviri, zvakakosha kuyeuka kuti kuwirirana hazvirevi kuti pane chikonzero. Kungoti zvinhu zviviri zvakabatana zvakanyanya hazvirevi kuti chimwe chinhu chinokonzera shanduko mune chimwe. Hukama uhwu hunogona kukonzerwa nezvimwe zvinhu zvisingaonekwe.
Kudzoreredza
Kudzoreredza, kunyanya linear regression, inzira yekuverenga inoshandiswa kutevedzera nekuongorora hukama huripo pakati peimwe kana kupfuura variables dzakazvimiririra (predictors) uye dependent variable (response). Kudzoreredza kunotibvumira kufanotaura kukosha kwedependent variable zvichibva pahunhu hwe independent variables uye kunzwisisa kuti independent variables dzinokanganisa sei dependent variable.
Kudzoreredzwa kwemutsara kuri nyore kunosanganisira imwe variable yakazvimirira uye imwe dependent variable. Muenzaniso wekudzoka kwemutsara uri nyore unoratidzwa ne equation:
\[ Y = a + bX + \epsilon \]
Di mana:
– \( Y \) ishanduro inoenderana.
– \( X \) ishanduro yakazvimiririra.
– \( a \) ndiyo intercept (kukosha kwe \( Y \) apo \( X = 0 \)).
– \( b \) ndiyo regression coefficient (kutsveyama kwemutsara we regression).
– \( \epsilon \) chikanganiso kana kuti chisara, chinova musiyano uripo pakati pehuwandu hwakaonekwa nehuwandu hwakafanotaurwa.
Mienzaniso yeKudzokera Kumashure Mukuita
Semuenzaniso, mumuenzaniso mumwe chete wenguva yekudzidza nemapoinzi ebvunzo, tinoda kufanotaura mamakisi ebvunzo zvichienderana nehuwandu hwemaawa ekudzidza. Tinounganidza data kubva kuvadzidzi vakati wandei tobva tashandisa linear regression analysis kuti tiwane equation yemutsetse weregression.
Semuenzaniso, mhedzisiro yekuongorora inopa equation yekudzoka:
\[ \text{Bvunzo dzeChibodzwa} = 50 + 5 \times (\text{Maawa ekudzidza}) \]
Izvi zvinoreva kuti awa imwe neimwe inopedzerwa pakudzidza inofungidzirwa kuwedzera mamaki ebvunzo nemapoinzi mashanu, nechikamu chekutanga (kupindira) chemapoinzi makumi mashanu.
Kushandiswa Pamwe Chete Kwehukama uye Kudzoreredza
Kuwirirana uye kudzoreredza (correlation) zvinowanzo shandiswa pamwe chete kuti pave nemufananidzo wakakwana wehukama huripo pakati pezvinhu zviviri. Kutanga, tinogona kushandisa kuenderana kuti tione kana paine hukama hwakakosha pakati pezvinhu zviviri. Kana zviripo, tinogona kushandisa kudzoreredza (regression) kuti tiite muenzaniso wehukama ihwohwo uye tiite fungidziro.
Kuongorora Kubatana uye Kudzokorora muKutsvagurudza
Mukutsvaga kwesainzi, kuongorora kuwirirana uye kudzokorora kunowanzova matanho akakosha. Vaongorori vanogona kushandisa kuwirirana kuti vaongorore data ravo uye vaone mapatani ekutanga kana hukama. Kana vangowana hukama hwakakosha, vanogona kushandisa kudzokorora kuhuenzanisa zvakadzama uye kuyedza fungidziro dzavo.
Semuenzaniso, mukudzidza kwezvinhu zvinokanganisa hutano hwepfungwa, muongorori angaona kuti pane hukama hwakaipa pakati pehuwandu hwekushushikana nehunhu hwekurara. Danho rinotevera nderekushandisa regression kuratidza hukama uhwu uye kuona kuti kushushikana kunokanganisa sei hunhu hwekurara. Vaongorori vanogona kushandisa regression model inobuda kuti vafanotaura uye kugadzira nzira dzinoshanda dzekuvandudza hunhu hwekurara kwevanhu vane huwandu hwekushushikana kwakanyanya.
Mhedziso
Kubatana uye kudzoka shure inzira mbiri dzinobatsira zvikuru dzekuverenga dzinoshandiswa kakawanda mukuongorora data. Kubatana kunotibatsira kunzwisisa simba negwara rehukama huripo pakati pezvinhu zviviri, nepo kudzoka shure kuchitibvumira kutevedzera hukama ihwohwo uye kufanotaura.
Zvisinei, zvakakosha kuyeuka kuti kuwirirana hakurevi chikonzero, uye chero mhedzisiro yekuongorora kwekudzoka inofanira kududzirwa nekungwarira, tichifunga nezve mukana wekuvhiringidza kana kusabvisa mavariable. Kushandisa matekiniki aya maviri nemazvo kunogona kupa ruzivo rwakadzama uye kutibatsira kuita sarudzo dziri nani zvichibva padata.
Mukupedzisa, kuwirirana nekudzokorora zvinhu zvakakosha mukuongorora data zvinogona kupa nhungamiro inokosha uye ruzivo muminda yakasiyana-siyana yekutsvagisa uye mashandisirwo anoshanda. Nekunzwisisa kwakakwana uye kushandiswa kwakakodzera, tinogona kugadzirisa nekududzira data zviri nani uye nemazvo.
