SSC CGL Statistics – Correlation & Regression – Level 3 · Challenge
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(i), (iii), (iv) true; r is the geometric mean, not the arithmetic mean.
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SSC CGL Statistics – Correlation & Regression – Level 3 · Challenge – 8 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.
The regression lines are x + 4y = 28 and x + y = 10. The coefficient of correlation is:
Correct Answer: D [−0.5]
Explanation:
If x + 4y = 28 is y on x: byx = −1/4; then x + y = 10 is x on y: bxy = −1.
2.
For the lines of the previous question, the variance of x is 16. What is the standard deviation of y?
Correct Answer: C [2]
Explanation:
byx = rσᵧ/σₓ → −1/4 = −0.5 × σᵧ/4 → σᵧ = 2.
3.
Diagram-basedThe scatter diagram shows a fictional survey of 18 people.
The value of r for these data is most likely close to:
The value of r for these data is most likely close to:
Correct Answer: A [−0.95]
Explanation:
The points fall steadily along a narrow downward band – a strong negative correlation (r ≈ −0.97).
4.
r₁₂ = 0.6, r₁₃ = 0.6 and r₂₃ = 0.8. The partial correlation coefficient r₁₂.₃ is:
Correct Answer: C [0.25]
Explanation:
(0.6 − 0.48)/√(0.36 × 0.64) = 0.12/0.48 = 0.25.
5.
Given r₁₂ = 0.5, r₁₃ = 0.8 and r₂₃ = 0.8, how well do x₂ and x₃ together predict x₁? Find R₁.₂₃.
Correct Answer: B [5/6 ≈ 0.833]
Explanation:
R² = (0.25 + 0.64 − 0.64)/0.36 = 0.25/0.36 = 25/36 → R = 5/6.
6.
Marks of six students: Test 1 – 52, 47, 47, 60, 38, 70; Test 2 – 40, 35, 42, 42, 30, 42. Using tie corrections, Spearman's ρ is:
Correct Answer: D [24/35 ≈ 0.69]
Explanation:
Ranks 3, 4.5, 4.5, 2, 6, 1 and 4, 5, 2, 2, 6, 2; d = −1, −0.5, 2.5, 0, 0, −1; Σd² = 8.5; corrections 0.5 + 2 = 2.5; ρ = 1 − 6 × 11/210 = 24/35 ≈ 0.686.
7.
Two-quantity comparisonGiven r = 0.6, σₓ = 2 and σᵧ = 3:
Quantity I: byx
Quantity II: bxy
Quantity I: byx
Quantity II: bxy
Correct Answer: A [Quantity I > Quantity II]
Explanation:
byx = 0.6 × 3/2 = 0.9; bxy = 0.6 × 2/3 = 0.4.
8.
True/False countHow many of the following statements are true?
(i) If byx > 1, then bxy < 1.
(ii) r is the arithmetic mean of byx and bxy.
(iii) When r = 0 the two regression lines are perpendicular.
(iv) Yule's Q is zero when ad = bc.
(i) If byx > 1, then bxy < 1.
(ii) r is the arithmetic mean of byx and bxy.
(iii) When r = 0 the two regression lines are perpendicular.
(iv) Yule's Q is zero when ad = bc.
Correct Answer: A [Three]
Explanation:
(i), (iii), (iv) true; r is the geometric mean, not the arithmetic mean.
➤ 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)
Here you get the answer with a one-line explanation. 657 original questions with worked answers · notes, formulas, figures and statistical tables (z, t, χ², F) · practice sets + 3 mock tests
Get the book – ₹149 More quizzes
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