Muenzaniso weKudzoreredza Mutsetse Mibvunzo neKukurukurirana
Kudzoreredza mutsara inzira inoshandiswa kuona hukama huripo pakati pezvinhu zviviri kana kupfuura. Nzira iyi inoshandiswa zvakanyanya muzvikamu zvakasiyana-siyana, zvinosanganisira zvehupfumi, bhizinesi, sayenzi yemagariro evanhu, uye sayenzi yezvisikwa. Muchinyorwa chino, tichakurukura nezvekudzoka kwemutsara, maitiro ekuiverenga, uye kupa mienzaniso yakawanda yezvinetso netsananguro dzekubatsira vaverengi kunzwisisa pfungwa iyi zvakadzama.
Kunzwisisa Kudzoreredzwa Kwemutsetse
Kudzoreredza mutsara inzira yekuongorora inoshandiswa kuratidza hukama huripo pakati peimwe kana kupfuura mavariable akazvimiririra (predictors) ne dependent variable (response). Kudzoreredza mutsara kuri nyore kunosanganisira imwe independent variable ne dependent variable imwe, nepo multiple linear regression ichisanganisira zvinopfuura imwe independent variable.
Equation yemutsetse uri nyore wekudzoka kwemutsara ndeiyi:
\[ Y = a + bX \]
Di mana:
– \( Y \) ishanduro inoenderana.
– \( X \) ishanduro yakazvimiririra.
– \( a \) ndiyo intercept, inova kukosha kwaY kana X = 0.
– \( b \) ndiyo regression coefficient, kureva kuti, Y inoshanduka zvakadii kana X ikashanduka neyuniti imwe chete.
Matanho Ekudzora Mutsetse
1. Kuunganidza Data: Kutanga, unganidza data rinofanira kuongororwa.
2. Data rePlot: Gadzira pepa rekuparadzira kuti uone kana paine hukama hwakarongeka pakati pezvinhu zvinoshanduka.
3. Verenga Regression Coefficient: Shandisa nzira ye least squares kuti uone mutsetse wakanakisisa.
4. Kuedza Modeli: Edza kukosha kwema coefficients e regression uchishandisa t-test uye sarudza R-squared value kuti uone kuti moderi yacho inoenderana sei nedata.
Mibvunzo yemuenzaniso nekukurukurirana
Muenzaniso Mubvunzo 1: Kudzoreredzwa Kwemutsetse Kuri Nyore
Mubvunzo:
Muongorori anoda kuziva hukama huripo pakati pehuwandu hwemaawa ekudzidza (X) nemapoinzi ebvunzo dzevadzidzi (Y). Data rakawanikwa nderinotevera:
| Maawa Ekudzidza (X) | Chibodzwa Chebvunzo (Y) |
|———————–|——————–|
| 2 | 70 |
| 3 | 75 |
| 5 | 80 |
| 7 | 85 |
| 8 | 90 |
Gadzira equation yekudzoka kwemutsara kubva padata iri!
Kukurukurirana:
1. Kuverenga Avhareji:
\[
\bar{X} = \frac{2 + 3 + 5 + 7 + 8}{5} = 5
\]
\[
\bar{Y} = \frac{70 + 75 + 80 + 85 + 90}{5} = 80
\]
2. Kuverenga Regression Coefficient \( b \):
\[
b = \frac{\sum (X_i – \bar{X})(Y_i – \bar{Y})}{\sum (X_i – \bar{X})^2}
\]
\[
\sum (X_i – \bar{X})(Y_i – \bar{Y}) = (2 – 5)(70 – 80) + (3 – 5)(75 – 80) + (5 – 5)(80 – 80) + (7 – 5)(85 – 80) + (8 – 5)(90 – 80)
\]
\[
= (-3)(-10) + (-2)(-5) + (0)(0) + (2)(5) + (3)(10) = 30 + 10 + 0 + 10 + 30 = 80
\]
\[
\sum (X_i – \bar{X})^2 = (2 – 5)^2 + (3 – 5)^2 + (5 – 5)^2 + (7 – 5)^2 + (8 – 5)^2
\]
\[
= 9 + 4 + 0 + 4 + 9 = 26
\]
\[
b = \frac{80}{26} \inenge 3.08
\]
3. Kuverenga Intercept \( a \):
\[
a = \bha{Y} – b\bha{X}
\]
\[
a = 80 – 3.08 \kapetwa 5 = 80 – 15.4 = 64.6
\]
4. Kuenzanisa kweKudzokera shure:
\[
Y = 64.6 + 3.08X
\]
Saka, equation yemutsara wekudzoka kwedata ndeye \( Y = 64.6 + 3.08X \). Izvi zvinoreva kuti awa imwe neimwe yekudzidza inotarisirwa kuwedzera mamaki ebvunzo nemapoinzi 3.08.
Muenzaniso Mubvunzo 2: Bvunzo yeModeli uye Dudziro
Mubvunzo:
Uchienderera mberi nedata rimwe chete, verenga kukosha kweR-squared (R²) kuti uone kuti modhi yacho inoenderana sei nedata racho. Zvakare, edza kukosha kwe regression coefficient \( b \).
Kukurukurirana:
1. Verenga Huwandu Hwese hweMakwere (SST), Huwandu HweRegression hweMakwere (SSR), uye Huwandu HweError hweMakwere (SSE):
\[
SST = \sum (Y_i – \bar{Y})^2
\]
\[
SST = (70 – 80)^2 + (75 – 80)^2 + (80 – 80)^2 + (85 – 80)^2 + (90 – 80)^2 = 100 + 25 + 0 + 25 + 100 = 250
\]
\[
SSR = \sum (\hat{Y}_i – \bar{Y})^2
\]
Apo \( \hat{Y}_i \) iri kukosha kwakafanotaurwa kwe regression equation:
\[
\hat{Y}_i = 64.6 + 3.08X_i
\]
\[
\hat{Y} = [67.76, 70.84, 76.0, 82.16, 85.24]
\]
\[
\bar{Y} = 80
\]
\[
SSR = (67.76 – 80)^2 + (70.84 – 80)^2 + (76.0 – 80)^2 + (82.16 – 80)^2 + (85.24 – 80)^2
\]
\[
SSR = (-12.24)^2 + (-9.16)^2 + (-4.0)^2 + 2.16^2 + 5.24^2 = 149.8
\]
2. Kuverenga SSE:
\[
SSE = SST – SSR = 250 – 149.8 = 100.2
\]
3. Kuverenga R-squared:
\[
R^2 = \frac{SSR}{SST} = \frac{149.8}{250} \inenge 0.6
\]
Kukosha kweR-squared kwe0.6 kunoratidza kuti modhi iyi inotsanangura inenge 60% yemusiyano uri mudata. Izvi zvinoratidza kuti mutsetse wekudzoka unoenderana nedata zvakanaka.
4. t-Test yekuona kukosha kweCoefficient \( b \):
\[
t = \frac{b}{SE(b)}
\]
\[
SE(b) = \sqrt{\frac{SSE}{n-2}} / \sqrt{\sum (X_i – \bar{X})^2}
\]
\[
SE(b) = \sqrt{\frac{100.2}{5-2}} / \sqrt{26}
\]
\[
SE(b) = \sqrt{33.4} / \sqrt{26} \inenge 1.13
\]
\[
t = \frac{3.08}{1.13} \inenge 2.73
\]
Ne \( t-statistic \approx 2.73 \), kana tikashandisa common threshold pakukosha (α = 0.05), tinoienzanisa ne t-table. Semuenzaniso, kune \( df = 3 \), critical \( t \) inenge iri 2.353. Zvadaro \( t-yakaonekwa > t-critical \), zvichiratidza kuti coefficient inokosha.
Mhedziso
Muchinyorwa chino, takurukura nezvekutanga kwemutsara wekuregera, maitiro ekuverenga chiyero chekuregera uye kupindira, uye maitiro ekududzira mhedzisiro uchishandisa matambudziko emuenzaniso. Kudzidzira nguva dzose nedata rakasiyana-siyana kwakakosha kuti uve nyanzvi mukushandisa nzira iyi. Kuregera mutsara chishandiso chakakosha mukuongorora data uye kunogona kupa ruzivo rwakadzama muhukama huripo pakati pezvimiro.
