Covariance i.e. Cov (X,Y) and standard deviations of different datasets are…
2024
Covariance i.e. Cov (X,Y) and standard deviations of different datasets are given. Estimate the correlation coefficients and arrange in increasing order:
A. Cov(X,Y) = 32, σₓ = 8, σᵧ = 7
B. Cov(X,Y) = 36, σₓ = 12, σᵧ = 5
C. Cov(X,Y) = 35, σₓ = 7, σᵧ = 8
D. Cov(X,Y) = 39, σₓ = 6, σᵧ = 13
Choose the correct answer:
- A.
A, B, C, D
- B.
B, C, D, A
- C.
C, D, A, B
- D.
D, A, B, C
Attempted by 6 students.
Show answer & explanation
Correct answer: D
Correlation formula:
r=Cov(X,Y)σxσyr = \frac{\text{Cov}(X,Y)}{\sigma_x \sigma_y}r=σxσyCov(X,Y)
Now calculate:
A: 32 / (8×7) = 32/56 ≈ 0.57
B: 36 / (12×5) = 36/60 = 0.60
C: 35 / (7×8) = 35/56 ≈ 0.625
D: 39 / (6×13) = 39/78 = 0.50
Increasing order:
D (0.50) < A (0.57) < B (0.60) < C (0.625)
Answer: D, A, B, C