Piv txwv ntawm Cov Lus Nug Sib Tham Txog Daim Duab Qhia Txog Kev Sib Tsoo
Daim duab scatterplot, tseem hu ua daim duab scatter, yog ib qho cuab yeej tseem ceeb hauv kev tshuaj xyuas cov ntaub ntawv thiab kev suav lej. Nws pab peb nkag siab txog kev sib raug zoo ntawm ob qho lej hloov pauv los ntawm kev kos cov ntsiab lus ntaub ntawv hauv lub dav hlau ob-seem. Tsab xov xwm no yuav tham txog cov piv txwv thiab kev sib tham ntawm cov duab scatterplots.
Daim Duab Qhia Txog Scatter yog dab tsi?
Ib daim duab scatterplot yog ib daim duab uas qhia txog kev sib raug zoo ntawm ob pawg ntawm cov ntaub ntawv lej. Txhua lub ntsiab lus ntawm daim duab scatterplot sawv cev rau ib khub ntawm cov nqi rau ob qho sib txawv. Piv txwv li, yog tias peb xav tshuaj xyuas kev sib raug zoo ntawm cov sijhawm kawm thiab cov qhab nia xeem, cov sijhawm kawm yuav raug sawv cev los ntawm X-axis, thaum cov qhab nia xeem los ntawm Y-axis.
Cov txiaj ntsig ntawm cov duab kos Scatter
1. Txheeb Xyuas Cov Qauv: Cov duab Scatterplots tuaj yeem pab peb txheeb xyuas cov qauv lossis cov qauv hauv cov ntaub ntawv. Cov qauv no tuaj yeem yog linear, non-linear, lossis txawm tias tsis muaj qauv hlo li.
2. Txheeb Xyuas Kev Sib Raug Zoo: Siv daim duab scatterplot, peb tuaj yeem txiav txim siab seb puas muaj kev sib raug zoo ntawm ob qho kev hloov pauv. Kev sib raug zoo tuaj yeem yog qhov zoo, qhov tsis zoo, lossis xoom (tsis muaj kev sib raug zoo).
3. Kev Tshawb Pom Qhov Tsis Zoo: Cov phiaj xwm tawg kuj ua rau nws yooj yim dua los nrhiav cov outliers, uas yog cov ntsiab lus ntaub ntawv uas nyob deb ntawm lwm cov ntaub ntawv teeb tsa.
Cov Lus Nug Piv Txwv thiab Kev Sib Tham
Piv txwv lus nug 1: Tsim daim duab qhia txog qhov sib txawv
Lo lus nug:
Muab cov ntaub ntawv hauv qab no hais txog cov sijhawm kawm (X) thiab cov qhab nia xeem (Y) ntawm tsib tus tub ntxhais kawm:
| Cov Tub Ntxhais Kawm | Cov Sijhawm Kawm (X) | Cov Qhab Nia Xeem (Y) |
|——-|———————|———————–|
| Ib | 2 | 70 |
| B | 3 | 75 |
| C | 1 | 65 |
| D | 4 | 80 |
| E | 5 | 85 |
Tsim ib daim duab scatter siv cov ntaub ntawv saum toj no.
Kev Sib Tham:
Yuav tsim ib daim duab scatter, cov kauj ruam uas ua tau yog raws li nram no:
1. Txheeb xyuas cov X thiab Y axes: Xaiv cov sijhawm kawm rau X axis thiab cov qhab nia xeem rau Y axis.
2. Kos cov ntsiab lus ntawm cov ntaub ntawv: Kos txhua khub (X, Y) rau hauv daim duab.
Nov yog ib daim duab ntawm cov ntaub ntawv:
| X-axis (Cov Sijhawm Kawm) | Y-axis (Qhab Nia Xeem) |
|————————–|—————————–|
| 2 | 70 |
| 3 | 75 |
| 1 | 65 |
| 4 | 80 |
| 5 | 85 |
Piv txwv lus nug 2: Txheeb xyuas hom kev sib raug zoo
Lo lus nug:
Raws li cov ntaub ntawv tau teeb tsa hauv Piv Txwv Lo Lus Nug 1, txiav txim siab hom kev sib raug zoo ntawm cov sijhawm kawm thiab cov qhab nia xeem.
Kev Sib Tham:
Yuav kom txiav txim siab hom kev sib raug zoo, peb yuav tsum tau them sai sai rau tus qauv uas tsim los ntawm cov ntsiab lus ntawm daim duab scatter.
Daim duab qhia tau hais tias thaum cov sijhawm kawm ntawv nce ntxiv, cov qhab nia xeem kuj nce ntxiv. Qhov no qhia tau hais tias muaj kev sib raug zoo ntawm cov sijhawm kawm ntawv thiab cov qhab nia xeem. Qhov kev sib raug zoo no suav tias yog qhov zoo vim tias ob qho tib si txav mus rau tib qho kev taw qhia.
Piv txwv 3: Xam tus lej sib raug zoo ntawm Pearson
Lo lus nug:
Xam tus lej sib raug zoo ntawm Pearson los ntawm cov ntaub ntawv hauv Piv Txwv Qhov Teeb Meem 1.
Kev Sib Tham:
Tus lej sib raug zoo ntawm Pearson (r) ntsuas lub zog thiab kev coj ntawm txoj kev sib raug zoo ntawm ob qho kev hloov pauv. Cov mis rau r yog:
\[ r = \frac{n(\sum XY) - (\sum X)(\sum Y)}{\sqrt{[n\sum X^2 - (\sum
Qhov twg:
- \( n \) yog tus naj npawb ntawm cov khub ntaub ntawv.
- \( \sum XY \) yog qhov sib ntxiv ntawm cov khoom ntawm X thiab Y.
- \( \sum X \) yog qhov sib sau ua ke ntawm tag nrho cov nqi ntawm X.
- \( \sum Y \) yog qhov sib sau ua ke ntawm tag nrho cov nqi Y.
- \( \sum X^2 \) yog qhov sib npaug ntawm cov plaub fab ntawm tag nrho cov nqi ntawm X.
- \( \sum Y^2 \) yog qhov sib npaug ntawm cov squares ntawm tag nrho cov nqi Y.
Ua ntej, cia peb xam cov nqi uas yuav tsum tau muaj:
\[ \sum X = 2 + 3 + 1 + 4 + 5 = 15 \]
\[ \sum Y = 70 + 75 + 65 + 80 + 85 = 375 \]
\[ \sum
\[ \sum
\[ \sum Y^2 = 70^2 + 75^2 + 65^2 + 80^2 + 85^2 = 4900 + 5625 + 4225 + 6400 + 7225 = 28375 \]
Tom qab ntawd, hloov rau hauv cov mis:
\[ r = \frac{5(1175) – (15)(375)}{\sqrt{[5(55) – (15)^2][5(28375) – (375)^2]}} \]
\[ r = \frac{5875 – 5625}{\sqrt{[275 – 225][141875 – 140625]}} \]
\[ r = \frac{250}{\sqrt{50 1250}} \]
\[ r = \frac{250}{\sqrt{62500}} \]
\[ r = \frac{250}{250} \]
\[ r = 1 \]
Yog li, tus lej sib raug zoo ntawm Pearson ntawm cov ntaub ntawv saum toj no yog 1, uas qhia txog kev sib raug zoo zoo meej.
Piv txwv lus nug 4: Nrhiav cov Outliers
Lo lus nug:
Los ntawm cov ntaub ntawv hauv Piv txwv Lo Lus Nug 1, txiav txim siab seb puas muaj cov outliers hauv daim scatterplot.
Kev Sib Tham:
Tus outlier yog ib qho chaw khaws ntaub ntawv uas nyob deb ntawm lwm cov ntaub ntawv. Los ntawm cov ntaub ntawv:
| X-axis (Cov Sijhawm Kawm) | Y-axis (Qhab Nia Xeem) |
|————————–|—————————–|
| 2 | 70 |
| 3 | 75 |
| 1 | 65 |
| 4 | 80 |
| 5 | 85 |
Tag nrho cov ntaub ntawv zoo li sib sau ua ke, thiab tsis muaj ib qho txawv ntawm lwm tus. Yog li ntawd, peb tuaj yeem xaus lus tias cov ntaub ntawv no tsis muaj qhov tsis zoo.
Xaus
Ib daim duab scatterplot yog ib qho cuab yeej siv tau zoo heev hauv kev tshuaj xyuas cov ntaub ntawv los txiav txim siab txog kev sib raug zoo ntawm ob qho lej hloov pauv. Los ntawm cov piv txwv saum toj no, peb tuaj yeem nkag siab yuav ua li cas los tsim ib daim duab scatterplot, txiav txim siab hom kev sib raug zoo, xam tus lej sib raug zoo Pearson, thiab nrhiav pom cov outliers. Kev nkag siab txog cov ntsiab lus no yog qhov tseem ceeb rau kev tshuaj xyuas cov ntaub ntawv thiab txiav txim siab raws li qhov kev tshuaj xyuas ntawd.
Yog li ntawd, cov phiaj xwm tawg tsis yog tsuas yog pab nkag siab cov ntaub ntawv kom tob dua xwb tab sis kuj tseem ua rau muaj kev tshuaj xyuas ntxiv.
