SSC CGL Statistics – Correlation & Regression – Level 2 · Exam Level · Paper II Sprint
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R lies between 0 and 1 and is at least |r₁₂|; a partial coefficient can reverse sign (r₁₂ = 0.5, r₁₃ = r₂₃ = 0.8 gives −0.39).
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SSC CGL Statistics – Correlation & Regression – Level 2 · Exam Level · Paper II Sprint – 15 questions, subject: Statistics (Tier II Paper II). Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.
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1.
A bivariate data set has regression coefficient −0.5 for y on x and −0.32 for x on y. Find r.
Correct Answer: B [−0.4]
Explanation:
r² = 0.16; both coefficients negative → r = −0.4.
2.
r = 0.5, σₓ = 4 and σᵧ = 10. The regression coefficient of y on x is:
Correct Answer: D [1.25]
Explanation:
byx = rσᵧ/σₓ = 0.5 × 10/4 = 1.25.
3.
The two regression lines are x + 4y = 28 and x + y = 10. The means x̄ and ȳ are:
Correct Answer: A [x̄ = 4, ȳ = 6]
Explanation:
Subtracting: 3y = 18 → y = 6, x = 4.
4.
For 6 pairs of ranks Σd² = 14. Spearman's coefficient is:
Correct Answer: C [0.6]
Explanation:
ρ = 1 − 84/210 = 1 − 0.4 = 0.6.
5.
For 8 pairs of ranks ρ = 0.5. What is Σd²?
Correct Answer: A [42]
Explanation:
Answer: 42. Σd² = (1 − 0.5) × 504/6 = 42.
6.
r = 0.6 is computed from 64 pairs. The probable error of r is approximately:
Correct Answer: C [0.054]
Explanation:
PE = 0.6745 × (1 − 0.36)/√64 = 0.6745 × 0.08 ≈ 0.054.
7.
Two-quantity comparisonGiven u = 2x + 3 and v = 5y − 1:
Quantity I: r between x and y
Quantity II: r between u and v
Quantity I: r between x and y
Quantity II: r between u and v
Correct Answer: C [Quantity I = Quantity II]
Explanation:
r is unchanged by change of origin and scale when both scale factors are positive.
8.
Assertion–Reason
A: Both regression coefficients cannot be numerically greater than 1 at the same time.
R: The product of the two regression coefficients equals r², which is at most 1.
A: Both regression coefficients cannot be numerically greater than 1 at the same time.
R: The product of the two regression coefficients equals r², which is at most 1.
Correct Answer: B [Both A and R are true and R explains A]
Explanation:
byx × bxy = r² ≤ 1, so if one exceeds 1 the other must be below 1.
9.
Odd one outwhich of these is NOT a measure of relationship between two variables or attributes?
Correct Answer: D [Coefficient of variation]
Explanation:
CV measures relative dispersion of one variable.
10.
r = 0.8, byx = 1.6 and σₓ = 2. What is σᵧ?
Correct Answer: B [4]
Explanation:
Answer: 4. σᵧ = byx σₓ/r = 3.2/0.8 = 4.
11.
N = 200, (A) = 100, (B) = 80 and (AB) = 50. Yule's coefficient of association is:
Correct Answer: D [0.4]
Explanation:
(Aβ) = 50, (αB) = 30, (αβ) = 70; Q = (3500 − 1500)/(3500 + 1500) = 0.4.
12.
For 10 pairs of ranks Σd² was found to be 34, but one difference was taken as 2 instead of 6. The correct ρ is:
Correct Answer: C [0.6]
Explanation:
Correct Σd² = 34 − 4 + 36 = 66; ρ = 1 − 6 × 66/990 = 0.6.
13.
Spot My Mistake“n = 6 and Σd² = 35, so ρ = 1 − 6 × 35/(6 × 5) = −6.” What is the correct ρ?
Correct Answer: A [0]
Explanation:
The denominator is n(n² − 1) = 210, not n(n − 1): ρ = 1 − 210/210 = 0.
14.
u = (x − 10)/3 and v = (y − 20)/4. If the regression coefficient of v on u is 0.6, then byx equals:
Correct Answer: B [0.8]
Explanation:
byx = (k/h) × bvu = (4/3) × 0.6 = 0.8.
15.
Statement-basedWhich of the following is/are correct?
I. The multiple correlation coefficient R₁.₂₃ can be negative.
II. R₁.₂₃ is never less than |r₁₂|.
III. r₁₂.₃ can be negative even when r₁₂ is positive.
I. The multiple correlation coefficient R₁.₂₃ can be negative.
II. R₁.₂₃ is never less than |r₁₂|.
III. r₁₂.₃ can be negative even when r₁₂ is positive.
Correct Answer: A [Only II and III]
Explanation:
R lies between 0 and 1 and is at least |r₁₂|; a partial coefficient can reverse sign (r₁₂ = 0.5, r₁₃ = r₂₃ = 0.8 gives −0.39).
➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Statistics (Tier II Paper II) book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-statistics
📘 SSC CGL 2026 – Statistics (Tier II Paper II)
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