Correlation and RegressionMCQPYQ June 24Question 3649 of 188
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The range of the coefficient of correlation is

Options

Abetween −1\displaystyle -1 and 1\displaystyle 1
Bbetween −1\displaystyle -1 and 1\displaystyle 1 including 1\displaystyle 1
Cbetween −1\displaystyle -1 and 1\displaystyle 1 including −1\displaystyle -1
Dbetween −1\displaystyle -1 and 1\displaystyle 1 including −1,1\displaystyle -1, 1
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Correct Answer

✅ Option d — between −1\displaystyle -1 and 1\displaystyle 1 including −1,1\displaystyle -1, 1

All Options:

  • Abetween −1\displaystyle -1 and 1\displaystyle 1
  • Bbetween −1\displaystyle -1 and 1\displaystyle 1 including 1\displaystyle 1
  • Cbetween −1\displaystyle -1 and 1\displaystyle 1 including −1\displaystyle -1
  • Dbetween −1\displaystyle -1 and 1\displaystyle 1 including −1,1\displaystyle -1, 1

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Detailed Solution & Explanation

**Range of Karl Pearson's Correlation Coefficient:** The correlation coefficient r\displaystyle r is defined such that: −1leqrleq1-1 \\leq r \\leq 1 **Explanation:** - r=−1\displaystyle r = -1: Perfect negative linear correlation (achievable — e.g., Y=−X\displaystyle Y = -X) - r=+1\displaystyle r = +1: Perfect positive linear correlation (achievable — e.g., Y=2X+3\displaystyle Y = 2X + 3) - −1<r<1\displaystyle -1 < r < 1: Imperfect correlation - r=0\displaystyle r = 0: No linear correlation Both extreme values −1\displaystyle -1 and +1\displaystyle +1 are **included** in the range since they correspond to perfect linear relationships (data lying exactly on a straight line). Therefore, the correct range is: −1leqrleq1\displaystyle -1 \\leq r \\leq 1, i.e., **between −1\displaystyle -1 and 1\displaystyle 1, including both −1\displaystyle -1 and 1\displaystyle 1**. Hence, **Option D** 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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