Isibonelo Sombuzo Wengxoxo Yomdwebo Wokuhlakaza
I-scatterplot, eyaziwa nangokuthi i-scatter diagram, iyithuluzi elibalulekile ekuhlaziyweni kwedatha kanye nezibalo. Isisiza ukuqonda ubudlelwano phakathi kweziguquguquko ezimbili zezinombolo ngokuhlela amaphuzu edatha endizeni enezinhlangothi ezimbili. Lesi sihloko sizomboza izibonelo kanye nengxoxo ngama-scatterplot.
Iyini i-Scatter Plot?
I-scatterplot iwukubonakaliswa okubonakalayo kobudlelwano phakathi kwamasethi amabili edatha yezinombolo. Iphuzu ngalinye ku-scatterplot limelela amanani amabili eziguquguquko ezimbili ezahlukene. Isibonelo, uma sifuna ukuhlaziya ubudlelwano phakathi kwamahora okufunda namaphuzu okuhlolwa, amahora okufunda angamelwa yi-X-axis, kuyilapho amaphuzu okuhlolwa emelwa yi-Y-axis.
Izinzuzo ze-Scatter Diagrams
1. Ukuhlonza Amaphethini: Ama-Scatterplot angasisiza ukuthi sibone amaphethini noma izitayela kudatha. Lawa maphethini angaba aqondile, angaqondile, noma angabi naphethini nhlobo.
2. Ukunquma Ubudlelwano: Sisebenzisa i-scatterplot, singanquma ukuthi kukhona yini ubudlelwano phakathi kweziguquguquko ezimbili. Ubudlelwano bungaba buhle, bube bubi, noma bube zero (akukho ubudlelwano).
3. Ukutholwa Kwangaphandle: Ama-Scatter plots enza kube lula ukubona ama-outliers, okungamaphuzu edatha aqhelelene kakhulu neqoqo lonke ledatha.
Imibuzo Eyisibonelo Nengxoxo
Isibonelo Umbuzo 1: Ukudala Umdwebo Wokuhlakaza
Umbuzo:
Njengoba kunikezwe idatha elandelayo mayelana namahora okufunda (X) kanye namaphuzu okuhlolwa (Y) abafundi abahlanu:
| Abafundi | Amahora Okufunda (X) | Amaphuzu Okuhlolwa (Y) |
|——-|———————|——————–|
| A | 2 | 70 |
| B | 3 | 75 |
| C | 1 | 65 |
| D | 4 | 80 |
| E | 5 | 85 |
Dala umdwebo wokuhlakaza usebenzisa idatha engenhla.
Ingxoxo:
Ukuze udale umdwebo wokuhlakaza, izinyathelo ezingathathwa yilezi ezilandelayo:
1. Thola ama-axis ka-X no-Y: Khetha i-variable yamahora okufunda ye-axis ka-X kanye namaphuzu okuhlolwa kwe-axis ka-Y.
2. Beka amaphuzu edatha: Beka i-pair ngayinye (X, Y) kugrafu.
Nasi isiqephu sedatha:
| I-X-axis (Amahora Okufunda) | I-Y-axis (Amaphuzu Okuhlolwa) |
|————————–|————————–|
| 2 | 70 |
| 3 | 75 |
| 1 | 65 |
| 4 | 80 |
| 5 | 85 |
Isibonelo Umbuzo 2: Ukunquma Uhlobo Lokuxhumana
Umbuzo:
Ngokusekelwe kudatha edwetshwe kuMbuzo Wesibonelo 1, nquma uhlobo lokuhlobana phakathi kwamahora okufunda kanye namaphuzu okuhlolwa.
Ingxoxo:
Ukuze sinqume uhlobo lokuhlobana, sidinga ukunaka iphethini eyakhiwe amaphuzu edatha kumdwebo wokuhlakaza.
Umdwebo ukhombisa ukuthi njengoba amahora okufunda enyuka, amaphuzu okuhlolwa nawo ayanda. Lokhu kubonisa ubudlelwano obuhle phakathi kwamahora okufunda namaphuzu okuhlolwa. Lokhu kuxhumana kubhekwa njengokuhle ngoba zombili iziguquguquko zihamba ngendlela efanayo.
Isibonelo 3: Ukubala i-Pearson Correlation Coefficient
Umbuzo:
Bala i-Pearson coefficient yokuxhumana kusukela kudatha eku-Isibonelo Senkinga 1.
Ingxoxo:
I-Pearson correlation coefficient (r) ilinganisa amandla kanye nesiqondiso sobudlelwano obuqondile phakathi kweziguquguquko ezimbili. Ifomula ka-r ithi:
\[ r = \frac{n(\sum XY) – (\sum X)(\sum Y)}{\sqrt{[n\sum X^2 – (\sum
Di mana:
– \( n \) inani lama-data pairs.
– \( \sum XY \) yisamba semikhiqizo ka-X no-Y.
– \( \sum X \) yisamba sawo wonke amanani ka-X.
– \( \sum Y \) yisamba sawo wonke amanani ka-Y.
– \( \sum X^2 \) yisamba sezikwele zawo wonke amanani ka-X.
– \( \sum Y^2 \) yisamba sezikwele zawo wonke amanani ka-Y.
Okokuqala, ake sibale amanani adingekayo:
\[ \isamba X = 2 + 3 + 1 + 4 + 5 = 15 \]
\[ \isamba Y = 70 + 75 + 65 + 80 + 85 = 375 \]
\[ \isamba
\[ \isamba
\[ \isamba Y^2 = 70^2 + 75^2 + 65^2 + 80^2 + 85^2 = 4900 + 5625 + 4225 + 6400 + 7225 = 28375 \]
Bese, faka ifomula esikhundleni sayo:
\[ r = \frac{5(1175) – (15)(375)}{\sqrt{[5(55) – (15)^2][5(28375) – (375)^2]}} \]
\[r = \frac{5875 – 5625}{\sqrt{[275 – 225][141875 – 140625]}} \]
\[r = \frac{250}{\sqrt{50 1250}} \]
\[r = \frac{250}{\sqrt{62500}} \]
\[r = \frac{250}{250} \]
\[r = 1 \]
Ngakho-ke, i-Pearson correlation coefficient yedatha engenhla ingu-1, okubonisa ubudlelwano obuhle obuphelele obuqondile.
Isibonelo Umbuzo 4: Ukuthola Izinto Ezingaphandle
Umbuzo:
Kusukela kudatha eku-Isibonelo Umbuzo 1, nquma ukuthi kukhona yini izinto ezingaphandle ku-scatterplot.
Ingxoxo:
I-outlier yiphuzu ledatha elikude kakhulu neqoqo lonke ledatha. Kusukela kudatha:
| I-X-axis (Amahora Okufunda) | I-Y-axis (Amaphuzu Okuhlolwa) |
|————————–|————————–|
| 2 | 70 |
| 3 | 75 |
| 1 | 65 |
| 4 | 80 |
| 5 | 85 |
Zonke izindawo zedatha zibonakala zihlangana, futhi azikho ezihluke kakhulu kwezinye. Ngakho-ke, singaphetha ngokuthi leli sethi ledatha alinazo izinto ezingaphandle.
Isiphetho
I-scatterplot iyithuluzi elibonakalayo eliwusizo kakhulu ekuhlaziyweni kwedatha ekunqumeni ubudlelwano phakathi kweziguquguquko ezimbili zezinombolo. Ngezibonelo ezingenhla, singaqonda ukuthi singakha kanjani i-scatterplot, sinqume uhlobo lokuxhumana, sibale i-Pearson correlation coefficient, futhi sithole izinto ezingaphandle. Ukuqonda le mibono kubalulekile ekuhlaziyeni idatha nokwenza izinqumo ezinolwazi ngokusekelwe kulokho kuhlaziya.
Ngakho-ke, ama-scatter plot awasizi nje kuphela ekuqondeni idatha ngokujulile kodwa futhi avula indlela yokuhlaziywa okwengeziwe kwezibalo.
