Correlation and RegressionMCQMTP May 18Question 3654 of 188
All Questions

Correlation Co-efficient is ______ of the units of measurements

Options

AIndependent
BDependent
CBoth
DNone of these
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Correct Answer

✅ Option a — Independent

All Options:

  • AIndependent
  • BDependent
  • CBoth
  • DNone of these

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Detailed Solution & Explanation

**Unit independence of Correlation Coefficient:** Karl Pearson's correlation coefficient: r=fractextCov(X,Y)sigmaXcdotsigmaYr = \\frac{\\text{Cov}(X,Y)}{\\sigma_X \\cdot \\sigma_Y} **Proof of unit independence:** - textCov(X,Y)\displaystyle \\text{Cov}(X,Y) has units = (unit of X\displaystyle X) times\displaystyle \\times (unit of Y\displaystyle Y) - sigmaX\displaystyle \\sigma_X has units = unit of X\displaystyle X - sigmaY\displaystyle \\sigma_Y has units = unit of Y\displaystyle Y - sigmaXcdotsigmaY\displaystyle \\sigma_X \\cdot \\sigma_Y has units = (unit of X\displaystyle X) times\displaystyle \\times (unit of Y\displaystyle Y) The units in numerator and denominator cancel: r=fractextCov(X,Y)sigmaXcdotsigmaY=textpurenumber(dimensionless)r = \\frac{\\text{Cov}(X,Y)}{\\sigma_X \\cdot \\sigma_Y} = \\text{pure number (dimensionless)} So r\displaystyle r is **independent** of the units of measurement. Changing units (e.g., from kg to lbs, from cm to inches) doesn't affect the value of r\displaystyle r. Note: The given `correct_option` says 'd' (None of these), but the correct answer is clearly (a) Independent. Hence, **Option A** 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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