Ihe atụ nke ajụjụ mkparịta ụka gbasara oke mkpebi
Ọnụọgụ mkpebi (R²) bụ paramita dị mkpa na nyocha nlọghachi, na-egosi etu ụdị nlọghachi si akọwa mgbanwe dị n'ezie nke data ahụ. N'isiokwu a, anyị ga-akọwa echiche nke ọnụọgụgụ mkpebi site na ihe atụ na mkparịta ụka zuru ezu.
Echiche Dị Mkpa nke Ọnụọgụ Mkpebi
A na-atụ ọnụọgụ nke mkpebi ma ọ bụ \( R^2 \) na nha nke 0 ruo 1, ebe:
– \( R^2 = 0 \) na-egosi na ụdị mgbanwe enweghị ike ịkọwa mgbanwe nke data ma ọlị.
– \( R^2 = 1 \) na-egosi na ụdị mgbanwe nwere ike ịkọwa mgbanwe niile nke data ahụ nke ọma.
Usoro bụ isi maka ịgbakọ ọnụọgụ nke mkpebi bụ:
\[ R^2 = 1 – \frac{SSR}{SST} \]
Ebe:
– SSR (Nchịkọta nke ihe fọdụrụ n'akụkụ anọ) bụ mkpokọta nke akụkụ anọ nke ọdịiche dị n'etiti ụkpụrụ ndị ihe nlereanya ahụ buru n'amụma na uru ndị dị adị.
– SST (Ngụkọta nke square) bụ mkpokọta nke square nke ọdịiche dị n'etiti uru n'ezie na nkezi nke uru n'ezie.
Ihe atụ nke nsogbu
Ka anyị tụlee otu ihe atụ nsogbu iji ghọta ngụkọ nke ihe mejupụtara mkpebi n'ụzọ miri emi.
Ihe atụ nke nsogbu:
Ka anyị were ya na anyị nwere data gbasara ọnụọgụgụ awa ọmụmụ ihe (X) na akara ule (Y) nke ụmụ akwụkwọ iri:
| Ụmụ akwụkwọ | Awa ọmụmụ ihe (X) | Akara ule (Y) |
|——-|———————–|———————–|
| 1 | 2 | 58 |
| 2 | 3 | 64 |
| 3 | 4 | 70 |
| 4 | 5 | 85 |
| 5 | 2 | 57 |
| 6 | 3 | 68 |
| 7 | 4 | 72 |
| 8 | 5 | 90 |
| 9 | 3 | 62 |
| 10 | 4 | 78 |
Anyị ga-emepụta ụdị mgbanwe dị mfe nke nwere akara ule (Y) ebe a na-atụ anya akara ule (X) dabere na awa ọmụmụ ihe (X).
Mkparịta ụka
1. Ịmepụta Ụdị Nlaghachi Dị Mfe nke Linear
Ụdị nhazigharị dị mfe nwere ụdị:
\[ Y = a + bX \]
Ebe:
– \( Y \) bụ akara ule e buru amụma ya.
– \( X \) bụ ọnụọgụgụ awa ọmụmụ ihe.
– \( a \) bụ nkwụsịtụ (ebe njikọ dị na axis Y mgbe X = 0).
– \( b \) bụ mkpọda (ntụgharị nke ahịrị nlọghachi azụ).
Iji gbakọọ paramita \(a \) na \(b \), anyị na-eji usoro ndị a:
\[ b = \frac{n(\sum{XY}) – (\sum{X})(\sum{Y})}{n(\sum{X^2}) – (\sum{X})^2} \]
\[ a = \frac{\sum{Y} – b(\sum{X})}{n} \]
Ebe \(n \) bụ ọnụọgụgụ data (n = 10 n'okwu a).
Site na tebụl anyị nwere ike ịgbakọ:
– \(\sum{X} = 36\)
– \(\sum{Y} = 704\)
– \(\sum{X^2} = 140\)
– \(\sum{Y^2} = 50428\)
– \(\sum{XY} = 2576\)
Ka anyị gbakọọ b mbụ:
\[ b = \frac{10(2576) – (36)(704)}{10(140) – (36)^2} \]
\[ b = \frac{25760 – 25344}{1400 – 1296} \]
\[ b = \frac{416}{104} \]
\[ b = 4 \]
Mgbe ahụ, anyị na-agbakọ otu:
\[ a = \frac{704 – 4(36)}{10} \]
\[ a = \frac{704 – 144}{10} \]
\[a = \frac{560}{10} \]
\[a = 56 \]
Ya mere, ụdị nhazigharị ahịrị anyị na-enweta bụ:
\[ Y = 56 + 4X \]
2. Gbakọọ Uru E Buru n'Amụma (Y')
Na-esote, anyị na-agbakọ uru e buru amụma \( Y' \) maka nke ọ bụla \( X \):
| Ụmụ akwụkwọ | Awa Ọmụmụ Ihe (X) | Akara Ule (Y) | Akara Amụma (Y') |
|——-|———————–|————————–|—————————-|
| 1 | 2 | 58 | \( 56 + 4(2) = 64 \) |
| 2 | 3 | 64 | \( 56 + 4(3) = 68 \) |
| 3 | 4 | 70 | \( 56 + 4(4) = 72 \) |
| 4 | 5 | 85 | \( 56 + 4(5) = 76 \) |
| 5 | 2 | 57 | \( 56 + 4(2) = 64 \) |
| 6 | 3 | 68 | \( 56 + 4(3) = 68 \) |
| 7 | 4 | 72 | \( 56 + 4(4) = 72 \) |
| 8 | 5 | 90 | \( 56 + 4(5) = 76 \) |
| 9 | 3 | 62 | \( 56 + 4(3) = 68 \) |
| 10 | 4 | 78 | \( 56 + 4(4) = 72 \) |
3. Ịgbakọ SSR na SST
Na-esote, anyị na-agbakọ SSR na SST iji nweta \( R^2 \).
SSR:
\[ SSR = \mkpokọta{(Y – Y')^2} \]
\[ SSR = (58 – 64)^2 + (64 – 68)^2 + (70 – 72)^2 + (85 – 76)^2 + (57 – 64)^2 + (68 – 68)^2 + (72 – 72)^2 + (90 – 76)^2 + (62 – 68)^2 + (78 – 72)^2 \]
\[ SSR = 36 + 16 + 4 + 81 + 49 + 0 + 0 + 196 + 36 + 36 \]
\[ SSR = 454 \]
SST:
\[ SST = \ nchikota {(Y - \bar{Y})^2} \]
Ebe:
\[ \bar{Y} = \frac{\sum{Y}}{n} = \frac{704}{10} = 70.4 \]
\[ SST = (58 – 70.4)^2 + (64 – 70.4)^2 + (70 – 70.4)^2 + (85 – 70.4)^2 + (57 – 70.4)^2 + (68 – 70.4)^2 + (72 – 70.4)^2 + (90 – 70.4)^2 + (62 – 70.4)^2 + (78 – 70.4)^2 \]
\[ SST = 153.76 + 40.96 + 0.16 + 213.16 + 178.56 + 5.76 + 2.56 + 384.16 + 70.56 + 57.76 \]
\[ SST = 1107.44 \]
4. Ịgbakọ ọnụọgụ nke mkpebi \( R^2 \):
\[ R^2 = 1 – \frac{SSR}{SST} \]
\[ R^2 = 1 – \frac{454}{1107.44} \]
\[ R^2 = 1 – 0.41 \]
\[ R^2 = 0.59 \]
Mmechi
Site na ngụkọ dị n'elu, anyị nwetara ihe dị ka mkpebi (R2 = 0.59). Nke a na-egosi na ụdị mgbanwe ahịrị anyị mepụtara nwere ike ịkọwa ihe dị ka 59% nke mgbanwe dị na akara ule dabere na awa ọmụmụ. 41% fọdụrụ nke mgbanwe nwere ike ịbụ n'ihi ihe ndị ọzọ na-adịghị na ihe nlereanya ahụ.
Site n'ịghọta usoro na mgbakọ na mwepụ dị n'elu, anyị nwere ike ịhụ mkpa nke oke mkpebi n'ịtụle etu ụdị nhazi anyị si arụ ọrụ si kọwaa mgbanwe dị n'ezie nke data ahụ. Ọ bụ ngwa bara uru nke ukwuu na nyocha ọnụọgụgụ na nhazi data.
