Ukunquma i-Correlation Coefficient: Isingeniso, Izindlela, kanye Nezicelo
I-coefficient yokuxhumana iyisilinganiso sezibalo esinquma amandla obudlelwano phakathi kwezinguquko ezimbili kusethi yedatha. Ubudlelwano busukela ku--1 kuya ku-1. Inani le-coefficient eliseduze no-1 noma u--1 libonisa ubudlelwano obuqinile phakathi kwezinguquko ezimbili. Inani le-coefficient eliseduze no-0 alibonisi ubudlelwano obuqinile phakathi kwezinguquko ezimbili. Lesi sihloko sizoxoxa nge-coefficient yokuxhumana, izindlela zokuyibala, ukuchazwa kwayo, kanye nokusetshenziswa kwayo emikhakheni eyahlukahlukene.
Isingeniso ku-Correlation Coefficient
I-coefficient yokuxhumana isinika umbono wezinombolo wokuthi iziguquguquko ezimbili zihlobene kangakanani. Ama-coefficient okuxhumana ahlukaniswe ngezinhlobo ezimbili eziyinhloko ngokusekelwe endleleni ubuhlobo obuqondiswa ngayo:
1. I-Positive Correlation Coefficient: Ibonisa ukuthi lapho i-variable eyodwa ikhula, enye i-variable nayo iyanda.
2. I-Negative Correlation Coefficient: Ibonisa ukuthi lapho i-variable eyodwa ikhula, enye i-variable iyancipha.
Ubudlelwano phakathi kweziguquguquko ezimbili bungahlukaniswa ngezinhlobo ezintathu ngokusekelwe emandleni obudlelwano:
1. Ubudlelwano Obuqinile: I-coefficient iseduze no--1 noma u-1.
2. Ubudlelwano Obumaphakathi: I-coefficient iphakathi kuka--0.5 kuya ku--1 noma u-0.5 kuya ku-1.
3. Ubudlelwano Obubuthakathaka: I-coefficient iseduze no-0.
Indlela Yokubala I-Coefficient Yokuxhumana
Izindlela eziningana ezivamile zisetshenziswa ukubala i-coefficient yokuxhumana, okuhlanganisa ukuhlangana kukaPearson, ukuhlangana kukaSpearman, kanye nokuhlangana kukaKendall. Ake sixoxe ngenye yalezi zindlela ngokuningiliziwe.
1. Ubudlelwano bukaPearson
I-Pearson correlation coefficient ivame ukusetshenziswa lapho zombili iziguquguquko ziqhubeka futhi zinokusatshalaliswa okuvamile. Ifomula ye-Pearson coefficient coefficient ithi:
\[ r = \frac {n(\Sigma xy) – (\Sigma x)(\Sigma y)}{ \sqrt{ [n \Sigma x^2 – (\Sigma x)^2] [n \Sigma y^2 – (\Sigma y)^2 ] } } \]
Di mana:
– \( r \) = i-coefficient yokuxhumana,
– \( n \) = inani lama-data pairs,
– \( \Sigma xy \) = isamba semikhiqizo yamabhangqa edatha \( x \) kanye \( y \),
– \( \Sigma x \) = isamba samanani \( x \),
– \( \Sigma y \) = isamba samanani \( y \),
– \( \Sigma x^2 \) = isamba sezikwele ze \( x \),
– \( \Sigma y^2 \) = isamba sezikwele zika \( y \).
2. Ubudlelwano Besikhundla SikaSpearman
I-Spearman correlation coefficient isetshenziselwa idatha ye-ordinal noma lapho ukucabanga kokujwayelekile kungenakufinyelelwa. I-Spearman correlation isekelwe ekulinganisweni kwamanani edatha kunenani lawo langempela. Ifomula ye-Spearman coefficient coefficient yile:
\[ \rho = 1 – \frac {6\Sigma d_i^2}{n(n^2-1)} \]
Di mana:
– \( \rho \) = I-coefficient yokuxhumana kukaSpearman,
– \( d_i \) = umehluko phakathi kokuhlelwa kwama-data pairs \( x \) kanye \( y \),
– \( n \) = inani lama-data pairs.
3. Ubudlelwano bukaKendall neTau
I-coefficient kaKendall yokuxhumana ilinganisa amandla obudlelwano phakathi kweziguquguquko ezimbili ze-ordinal. Ngokungafani nekaSpearman, i-coefficient kaKendall igxile kakhulu enanini lama-pair avumelanayo nalawo angaboni ngaso linye. Ifomula ye-coefficient kaKendall yokuxhumana yile:
\[ \tau = \frac{ (C – D)} { \sqrt{(C + D + T) (C + D + U) } } \]
Di mana:
– \( \tau \) = I-coefficient yokuxhumana kukaKendall,
– \( C \) = inani lamapheya avumelanayo,
– \( D \) = inani lamapheya angavumelani,
– \( T \) = inani lamapheya ochungechunge ku-variable \( x \),
– \( U \) = inani lamapheya ochungechunge ku-variable \( y \).
Ukuhunyushwa kwe-Correlation Coefficient
Ukuchazwa kwe-coefficient yokuhlobana kuncike enanini le-coefficient etholiwe:
– Isilinganiso +1: Ubudlelwano obuhle obuphelele.
– Isilinganiso esiphakathi kuka-0.7 no-0.9: Ubudlelwano obuhle obuqinile.
– Isilinganiso 0.4 kuya ku-0.6: Ubudlelwano obuhle obumaphakathi.
– Isilinganiso 0.1 kuya ku-0.3: Ubudlelwano obuhle obubuthakathaka.
– Isilinganiso 0: Akukho buhlobo.
– I-Coefficient -0.1 kuya ku-0.3: Ubudlelwano obungebuhle obubi.
– Isilinganiso -0.4 kuya ku-0.6: Ubudlelwano obuphakathi obungebuhle.
– I-Coefficient -0.7 kuya ku-0.9: Ubudlelwano obuqinile obubi.
– I-Coefficient -1: Ubudlelwano obuphelele obungalungile.
Isicelo se-Coefficient sokuhlobana
I-coefficient yokuxhumana inezinhlobo eziningi zezicelo emikhakheni eyahlukene, okuhlanganisa ezomnotho, ezesayensi yezenhlalo, ezempilo, ezemfundo, nokuningi. Nazi ezinye izibonelo:
1. Ezomnotho: Ukunquma ubudlelwano phakathi kokukhuphuka kwamanani kanye nokungasebenzi, noma phakathi kokusetshenziswa kwemali ngabathengi kanye nemali engenayo.
2. Isayensi Yezenhlalo: Ukunquma ubudlelwano phakathi kwemfundo nemali engenayo, noma phakathi kwezokuxhumana kanye nenhlalakahle yengqondo.
3. Impilo: Ukuqhathanisa ubudlelwano phakathi kwemikhuba yokubhema kanye namacala omdlavuza wamaphaphu, noma phakathi kwendlela yokuphila esebenzayo kanye nempilo yenhliziyo.
4. Imfundo: Ukuhlola ubudlelwano phakathi kwesikhathi sokufunda nemiphumela yezivivinyo, noma phakathi kobukhulu bekilasi kanye nempumelelo yabafundi.
Izibonelo Eziwusizo Ezisebenzisa Amasethi Edatha
Ake sithi sinesethi yedatha ehlanganisa amaphuzu okuhlolwa kwezibalo kanye nesikhathi sokufunda emahoreni abafundi abayi-10 kanje:
``
Amahora Okufunda Abafundi Amabanga Ezibalo
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
``
Singabala i-Pearson coefficient yokuxhumana phakathi kwama-Study_Hours kanye ne-Math_Score. Sisebenzisa ifomula kaPearson, sibala kuqala i-\( \Sigma x \), \( \Sigma y \), \( \Sigma xy \), \( \Sigma x^2 \), kanye ne-\( \Sigma y^2 \) bese sifaka lawa manani esikhundleni sefomula ukuze sithole inani le-\( r \).
Isiphetho
I-coefficient yokuxhumana iyithuluzi elinamandla ekuhlaziyweni kwedatha lokunquma amandla kanye nesiqondiso sobudlelwano phakathi kweziguquguquko ezimbili. Ukuqonda umqondo, izindlela zokubala, kanye nokuchazwa kwe-coefficient yokuxhumana kubalulekile ekuhlaziyweni kwedatha okuphumelelayo. Ngokuqonda okufanele, singanquma kangcono ubudlelwano phakathi kweziguquguquko emikhakheni eyahlukene futhi senze izinqumo ezinolwazi oluthe xaxa, eziqhutshwa idatha.
