SSC CGL Statistics – Correlation & Regression – Level 1 · Warm-up

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SSC CGL Statistics – Correlation & Regression – Level 1 · Warm-up – 12 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.  
Karl Pearson's coefficient of correlation always lies between:

Correct Answer: C [−1 and +1]

Explanation:

r = Cov/(σₓσᵧ) and |Cov| ≤ σₓσᵧ.

2.  
If r = 0 for two variables, then:

Correct Answer: D [there is no linear relationship between them]

Explanation:

r measures only linear association; a curved relationship can still give r = 0.

3.  
Cov(x, y) = 15, σₓ = 5 and σᵧ = 4. The coefficient of correlation is:

Correct Answer: A [0.75]

Explanation:

Answer: 0.75. r = 15/(5 × 4) = 0.75.

4.  
byx = 0.8 and bxy = 0.2. The coefficient of correlation r is:

Correct Answer: B [0.4]

Explanation:

r = √(0.8 × 0.2) = √0.16 = 0.4.

5.  
The two lines of regression intersect at the point:

Correct Answer: C [(x̄, ȳ)]

Explanation:

Both lines pass through the point of means.

6.  
For 5 pairs of ranks Σd² = 10. Spearman's rank correlation coefficient is:

Correct Answer: A [0.5]

Explanation:

ρ = 1 − 6 × 10/120 = 1 − 0.5 = 0.5.

7.  
If r = −1, the two regression lines:

Correct Answer: B [coincide]

Explanation:

With r = ±1 all points lie on one line, so both lines are the same.

8.  
In a 2 × 2 table, a = 40, b = 10, c = 20 and d = 30. Yule's coefficient of association Q is:

Correct Answer: D [5/7]

Explanation:

Q = (1200 − 200)/(1200 + 200) = 1000/1400 = 5/7.

9.  
Statement-basedWhich of the following is/are correct?
I. r is independent of change of origin.
II. The regression coefficient byx is independent of change of scale.

Correct Answer: C [Only I]

Explanation:

r is free of origin and scale; byx changes with scale (byx = (k/h)bvu).

10.  
If r = 0.9, the percentage of variation in y explained by the linear relation with x is:

Correct Answer: A [81%]

Explanation:

Answer: 81%. r² = 0.81 → 81%.

11.  
Match the followingMatch the measure with what it describes:
P. Karl Pearson's r Q. Spearman's ρ R. Yule's Q S. R₁.₂₃
1. agreement of two rankings 2. association of two attributes 3. linear correlation of two variables 4. multiple correlation

Correct Answer: B [P-3, Q-1, R-2, S-4]

Explanation:

r – linear correlation; ρ – ranks; Q – attributes; R₁.₂₃ – multiple correlation.

12.  
Fill in the blankIn Spearman's method the sum of the rank differences Σd is always ______.

Correct Answer: D [zero]

Explanation:

Both rank sets add to n(n + 1)/2, so their differences add to 0.

➤ 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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