Correlation and RegressionMCQPYQ May 18Question 3674 of 188
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Rank correlation coefficient lies between

Options

A0\displaystyle 0 to 1\displaystyle 1
B−1\displaystyle -1 to 1\displaystyle 1 inclusive of these value
C−1\displaystyle -1 to 0\displaystyle 0
DBoth
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Correct Answer

✅ Option b — −1\displaystyle -1 to 1\displaystyle 1 inclusive of these value

All Options:

  • A0\displaystyle 0 to 1\displaystyle 1
  • B−1\displaystyle -1 to 1\displaystyle 1 inclusive of these value
  • C−1\displaystyle -1 to 0\displaystyle 0
  • DBoth

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Detailed Solution & Explanation

**Range of Spearman's Rank Correlation Coefficient:** Spearman's rank correlation coefficient rs\displaystyle r_s is defined as: rs=1−frac6sumd2n(n2−1)r_s = 1 - \\frac{6\\sum d^2}{n(n^2-1)} where d\displaystyle d = difference in ranks of corresponding observations. **Range:** Like Karl Pearson's r\displaystyle r, Spearman's rs\displaystyle r_s also satisfies: −1leqrsleq1-1 \\leq r_s \\leq 1 - rs=+1\displaystyle r_s = +1: Perfect agreement in rankings (both variables ranked identically) - rs=−1\displaystyle r_s = -1: Complete disagreement in rankings (one ranking is the reverse of the other) - rs=0\displaystyle r_s = 0: No correlation between rankings Both extreme values −1\displaystyle -1 and +1\displaystyle +1 are **included** (hence "inclusive of these values"). Hence, **Option B** is the correct answer.

About This Chapter: Correlation and Regression

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Correlation Coefficient, Regression Equations

This chapter covers Correlation Coefficient, Regression Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

Key Concepts to Understand

Correlation

A statistical measure that expresses the extent to which two variables are linearly related.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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