Match plots P–S to attributes I: x> y, 0 x, =1; III: y> x, 0<<1; IV: x= y, =1. Here σ denotes standard deviation and ρ the Pearson correlation.

GATE 2022 MN – Question 37

Engineering Mathematics · Probability and Statistics · 2 marks · Multiple choice

Match plots P–S to attributes I: $\sigma_x>\sigma_y$, $0<\rho<1$; II: $\sigma_y>\sigma_x$, $\rho=1$; III: $\sigma_y>\sigma_x$, $0<\rho<1$; IV: $\sigma_x=\sigma_y$, $\rho=1$. Here σ denotes standard deviation and ρ the Pearson correlation.

P–I; Q–II; R–III; S–IV
P–II; Q–I; R–IV; S–III
P–III; Q–IV; R–I; S–II
P–IV; Q–II; R–III; S–I

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Correct answer: (D) P–IV; Q–II; R–III; S–I

Explanation

P lies exactly on the equal-scale 45° line, giving equal spreads and perfect correlation (IV). Q lies on a steeper straight line, so Y has larger spread and correlation one (II). R is a scattered steep positive trend, giving larger Y spread and correlation below one (III). S is a curved positive trend with larger X spread and non-perfect Pearson correlation (I). Thus D.

GATE 2022 MN – Question 37

Explanation

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