Correlation and RegressionMCQMTP June 24 Series IIQuestion 3669 of 188
All Questions

Correlation Co-efficient is _________ of the units of measurements.

Options

ADependent
BIndependent
CBoth
DNone of these
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Correct Answer

Option bIndependent

All Options:

  • ADependent
  • BIndependent
  • CBoth
  • DNone of these

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Detailed Solution & Explanation

**Unit independence of the correlation coefficient:** Karl Pearson's correlation coefficient: r=fractextCov(X,Y)sigmaXcdotsigmaYr = \\frac{\\text{Cov}(X,Y)}{\\sigma_X \\cdot \\sigma_Y} - Numerator textCov(X,Y)\displaystyle \\text{Cov}(X,Y) has units: (unit of X\displaystyle X) × (unit of Y\displaystyle Y) - Denominator sigmaXcdotsigmaY\displaystyle \\sigma_X \\cdot \\sigma_Y has units: (unit of X\displaystyle X) × (unit of Y\displaystyle Y) - These cancel, making r\displaystyle r a **pure number** (dimensionless) Therefore, r\displaystyle r is **independent** of the units of measurement. This is a key advantage — changing measurement units (kg to g, cm to m, etc.) does not affect r\displaystyle r. 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

Related Comparison Tables

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