Kusarudza Coefficient yekubatana: Nhanganyaya, Nzira, uye Mashandisirwo
Coefficient yekubatana inzira yekuongorora nhamba inoratidza simba rehukama huripo pakati pezvinhu zviviri zviri mudataset. Correlations dzinotangira pa -1 kusvika pa 1. Coefficient value iri pedyo ne 1 kana -1 inoratidza hukama hwakasimba pakati pezvinhu zviviri izvi. Coefficient value iri pedyo ne 0 inoratidza kuti hapana hukama hwakasimba pakati pezvinhu zviviri izvi. Chinyorwa chino chichakurukura coefficient yekubatana, nzira dzekuiverenga, dudziro yayo, uye mashandisirwo ayo muminda yakasiyana-siyana.
Nhanganyaya yeCorrelation Coefficient
Coefficient yekubatana inotipa maonero enhamba ekuti mavariable maviri akabatana zvakadii. Coefficient yekubatana yakakamurwa kuita mhando mbiri huru zvichienderana nekwakatangira hukama:
1. Positive Correlation Coefficient: Inoratidza kuti kana chimwe chinhu chichiwedzera, chimwe chinowedzerawo.
2. Negative Correlation Coefficient: Inoratidza kuti kana chimwe chinhu chichiwedzera, chimwe chinoderera.
Hukama huripo pakati pezvinhu zviviri zvinogonawo kukamurwa kuita mhando nhatu zvichienderana nekusimba kwehukama:
1. Kubatana Kwakasimba: Chiyero chiri pedyo ne -1 kana 1.
2. Kubatana kuri pakati nepakati: Chiyero chiri pakati pe -0.5 kusvika -1 kana 0.5 kusvika 1.
3. Kubatana Kusina Simba: Chiyero chiri pedyo ne0.
Nzira yekuverenga Coefficient yekubatana
Nzira dzakawanda dzinoshandiswa kuverenga coefficient yekubatana, kusanganisira Pearson's correlation, Spearman's correlation, uye Kendall's correlation. Ngatikurukurei imwe neimwe yenzira idzi zvakadzama.
1. Kubatana kwaPearson
Pearson correlation coefficient inowanzo shandiswa kana mavariable ese ari maviri ari continuous uye aine normal distribution. Fomura yePearson coefficient coefficient ndeiyi:
\[ r = \frac {n(\Sigma xy) – (\Sigma x)(\Sigma y)}{ \sqrt{ [n \Sigma x^2 – (\Sigma x)^2] [n \Sigma y^2 – (\Sigma y)^2 ] } } \]
Di mana:
– \( r \) = coefficient yekubatana,
– \( n \) = nhamba yemapeya edata,
– \( \Sigma xy \) = huwandu hwezvigadzirwa zvemapeya edata \( x \) uye \( y \),
– \( \Sigma x \) = huwandu hwezviyero \( x \),
– \( \Sigma y \) = huwandu hwezviyero \( y \),
– \( \Sigma x^2 \) = huwandu hwezvikwere zve \( x \),
– \( \Sigma y^2 \) = huwandu hwezvikwere zve \( y \).
2. Kubatana kweSpearman's Rank
Chiyero cheSpearman chinoshandiswa padata re ordinal kana kuti kana fungidziro yekuti zvinhu zvakajairwa haigone kuzadzikiswa. Chiyero cheSpearman chinoenderana nerongero re data kwete kukosha kwaro chaiko. Fomura yeSpearman inoenderana ne coefficient ndeiyi:
\[ \rho = 1 – \frac {6\Sigma d_i^2}{n(n^2-1)} \]
Di mana:
– \( \rho \) = Kuenzana kwehukama hwaSpearman,
– \( d_i \) = musiyano uripo pakati pemapeya edata \( x \) uye \( y \),
– \( n \) = nhamba yemapeya edata.
3. Kubatana kwaKendall neTau
Kendall's correlation coefficient inoyera simba rehukama huripo pakati pezvinhu zviviri zve ordinal. Kusiyana neSpearman's, Kendall's correlation inonyanya kutarisisa huwandu hwema concordant ne discordant pairs. Fomura ye correlation coefficient yaKendall ndeiyi:
\[ \tau = \frac{ (C – D)} { \sqrt{(C + D + T) (C + D + U) } } \]
Di mana:
– \( \tau \) = Kuenzana kweKendall,
– \( C \) = nhamba yemapeya akabatana,
– \( D \) = nhamba yemapeya asina kuenzana,
– \( T \) = nhamba yemapeya akatevedzana mu variable \( x \),
– \( U \) = nhamba yemapeya akatevedzana mu variable \( y \).
Dudziro yeCoefficient yekubatana
Kududzirwa kwe coefficient yekubatana kunoenderana nekukosha kwe coefficient yakawanikwa:
– Coefficient +1: Hukama hwakanaka hwakakwana.
– Coefficient 0.7 kusvika 0.9: Hukama hwakanaka hwakasimba.
– Koefficient 0.4 kusvika 0.6: Hukama hwakanaka huri pakati nepakati.
– Koefficient 0.1 kusvika 0.3: Hukama hwakanaka husina kusimba.
– Koefficient 0: Hapana hukama.
– Koefficient -0.1 kusvika -0.3: Hukama husina kusimba.
– Koefficient -0.4 kusvika -0.6: Hukama huri pakati nepakati husina kunaka.
– Koefficient -0.7 kusvika -0.9: Hukama hwakasimba husina kunaka.
– Chiyero -1: Hukama hwakakwana husina kunaka.
Kushandiswa kweCoefficient yekubatana
Iyo correlation coefficient ine mashandisirwo akasiyana-siyana muzvikamu zvakasiyana-siyana, zvinosanganisira economics, social sciences, health, education, nezvimwewo. Heano mimwe mienzaniso:
1. Zvehupfumi: Kuona hukama huripo pakati pekukwira kwemitengo nekushaikwa kwemabasa, kana pakati pekushandisa mari nezvinobuda mubhizinesi.
2. Sainzi Yemagariro Evanhu: Kuona hukama huripo pakati pedzidzo nemari inowanikwa, kana pakati pesocial media nekugara zvakanaka kwepfungwa.
3. Hutano: Kuenzanisa hukama huripo pakati petsika dzekusvuta nevanhu vane kenza yemapapu, kana pakati pemararamiro anoshanda uye hutano hwemwoyo.
4. Dzidzo: Kuongorora hukama huripo pakati penguva yekudzidza nemigumisiro yebvunzo, kana pakati pehukuru hwekirasi nekubudirira kwevadzidzi.
Mienzaniso Inoshanda Inoshandisa Datasets
Ngatitii tine data rine mamakisi ebvunzo yemasvomhu uye nguva yekudzidza mumaawa evadzidzi gumi seizvi:
``
Vadzidzi Maawa Ekudzidza Magiredhi Emasvomhu
1 5 85
2 3 78
3 6 90
4 2 76
5 4 80
6 6 88
7 5 85
8 3 82
9 7 91
10 5 87
``
Tinogona kuverenga coefficient yePearson correlation pakati peStudy_Hours neMath_Score. Tichishandisa fomura yaPearson, tinoverenga \( \Sigma x \), \( \Sigma y \), \( \Sigma xy \), \( \Sigma x^2 \), uye \( \Sigma y^2 \) kutanga, tobva tatsiva ma values aya mufomura kuti tiwane kukosha kwe \( r \).
Mhedziso
Chiyero chekubatana chishandiso chine simba mukuongorora data rekuona simba negwara rehukama huripo pakati pezvinhu zviviri. Kunzwisisa pfungwa, nzira dzekuverenga, uye kududzirwa kwechiyero chekubatana kwakakosha pakuongorora data zvinobudirira. Nekunzwisisa kwakakodzera, tinogona kuona zviri nani hukama huripo pakati pezvinhu zvakasiyana-siyana uye kuita sarudzo dzine ruzivo rwakawanda, dzinotungamirirwa nedata.
