SSC CGL Statistics – Correlation & Regression – Exam-Level Drill

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SSC CGL Statistics – Correlation & Regression – Exam-Level Drill – 10 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.  

Directions (Q 36–39): Weekly advertising spend x (₹ thousand) and sales y (₹ lakh) of a fictional shop over five weeks: x = 2, 4, 6, 8, 10; y = 4, 12, 20, 18, 16.

What is Karl Pearson's coefficient of correlation?

Correct Answer: D [0.75]

Explanation:

dₓ = −4, −2, 0, 2, 4; dᵧ = −10, −2, 6, 4, 2; Σdₓdᵧ = 60, Σdₓ² = 40, Σdᵧ² = 160; r = 60/√6400 = 0.75.

2.  
(Use the directions above – Q 36–39)
What is the regression line of y on x?

Correct Answer: B [y = 1.5x + 5]

Explanation:

byx = 60/40 = 1.5; y − 14 = 1.5(x − 6) → y = 1.5x + 5.

3.  
(Use the directions above – Q 36–39)
Estimate the advertising spend x for a week with sales y = 22.

Correct Answer: C [9]

Explanation:

Use x on y: bxy = 60/160 = 0.375; x = 6 + 0.375 × (22 − 14) = 9.

4.  
(Use the directions above – Q 36–39)
What percentage of the variation in sales is NOT explained by the linear relation with advertising?

Correct Answer: D [43.75%]

Explanation:

Answer: 43.75%. 1 − r² = 1 − 0.5625 = 0.4375.

5.  
Given r₁₂ = 0.7, r₁₃ = 0.5, r₂₃ = 0.5, σ₁ = 6 and σ₂ = 4, the partial regression coefficient b₁₂.₃ is:

Correct Answer: C [0.9]

Explanation:

b₁₂.₃ = (σ₁/σ₂)(r₁₂ − r₁₃r₂₃)/(1 − r₂₃²) = 1.5 × 0.45/0.75 = 0.9.

6.  
r₁₂ = 0.6, r₁₃ = 0.6 and r₂₃ = 0.8. The multiple correlation coefficient R₁.₂₃ is approximately:

Correct Answer: B [0.63]

Explanation:

R² = (0.36 + 0.36 − 2 × 0.6 × 0.6 × 0.8)/(1 − 0.64) = (0.72 − 0.576)/0.36 = 0.4 → R ≈ 0.632.

7.  
A survey reports N = 100, (A) = 60, (B) = 50 and (AB) = 5. Which conclusion is correct?

Correct Answer: A [The data are inconsistent because (αβ) would be −5]

Explanation:

(αβ) = N − (A) − (B) + (AB) = 100 − 60 − 50 + 5 = −5 < 0 – impossible, so the data are inconsistent.

8.  
byx = 0.9 and bxy = 0.1. Which statement is correct?

Correct Answer: B [r = 0.3 and (byx + bxy)/2 = 0.5 ≥ r]

Explanation:

r = √(0.9 × 0.1) = √0.09 = 0.3; the AM of the coefficients is 0.5, never less than r.

9.  
In the concurrent deviation method, 12 pairs of deviations have only 3 concurrent signs. The coefficient of concurrent deviation is about:

Correct Answer: D [−0.71]

Explanation:

(2c − m)/m = (6 − 12)/12 = −0.5; rc = −√0.5 ≈ −0.707.

10.  
u = (x − 20)/5 and v = (y − 40)/2. The regression coefficients are bvu = 0.32 and buv = 0.5. Then byx and bxy are:

Correct Answer: A [0.128 and 1.25]

Explanation:

byx = (2/5)(0.32) = 0.128; bxy = (5/2)(0.5) = 1.25; check: product 0.16 = r² with r = 0.4.

➤ 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
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