Match List-I with List-II: Choose the correct answer:
2024
Match List-I with List-II:
Choose the correct answer:
- A.
A–I, B–II, C–III, D–IV
- B.
A–II, B–III, C–IV, D–I
- C.
A–III, B–IV, C–I, D–II
- D.
A–IV, B–III, C–II, D–I
Show answer & explanation
Correct answer: D
The coefficient of determination, R2, of a regression model measures the proportion of variation in the dependent variable explained by the model. It is calculated as R2 = 1 − (RSS / TSS), where RSS is the Residual Sum of Squares (the unexplained variation left over after fitting the model) and TSS is the Total Sum of Squares (the total variation in the data). A value closer to 1 indicates a better model fit.
Compute R2 for each List-I entry using its own RSS and TSS values:
For A: RSS = 25, TSS = 60, so R2 = 1 − (25/60) = 1 − 0.417 ≈ 0.58.
For B: RSS = 35, TSS = 75, so R2 = 1 − (35/75) = 1 − 0.467 ≈ 0.53.
For C: RSS = 30, TSS = 70, so R2 = 1 − (30/70) = 1 − 0.429 ≈ 0.57.
For D: RSS = 40, TSS = 75, so R2 = 1 − (40/75) = 1 − 0.533 ≈ 0.467. List-II records this pair as 0.46 — a minor truncation rather than an exact round-off — and it remains the only plausible match since the other three List-II values (0.57, 0.53, 0.58) are all far from 0.467.
Matching each computed value to List-II:
List-I item | Computed R² | Matches List-II |
|---|---|---|
A | ≈ 0.58 | IV (0.58) |
B | ≈ 0.53 | III (0.53) |
C | ≈ 0.57 | II (0.57) |
D | ≈ 0.467 | I (0.46, truncated) |
All four computed values are distinct, so each pairs with exactly one List-II entry — confirming the match is unambiguous.
Therefore, the correct matching is A–IV, B–III, C–II, D–I.