Correlation and RegressionMCQPYQ May 18Question 3635 of 188
All Questions

Correlation coefficient is _________ of the units of measurements.

Options

Adependent
Bindependent
Cboth
Dnone of these
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Correct Answer

✅ Option b — independent

All Options:

  • Adependent
  • Bindependent
  • Cboth
  • Dnone of these

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Detailed Solution & Explanation

**Property of Correlation Coefficient — Unit Independence:** Karl Pearson's correlation coefficient r\displaystyle r is defined as: r=fractextCov(X,Y)sigmaXcdotsigmaY=fracsum(X−barX)(Y−barY)sqrtsum(X−barX)2cdotsum(Y−barY)2r = \\frac{\\text{Cov}(X, Y)}{\\sigma_X \\cdot \\sigma_Y} = \\frac{\\sum(X-\\bar{X})(Y-\\bar{Y})}{\\sqrt{\\sum(X-\\bar{X})^2 \\cdot \\sum(Y-\\bar{Y})^2}} **Why it is unit-free (independent of units):** - 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 also has units = (unit of X\displaystyle X) × (unit of Y\displaystyle Y) - These units cancel out, making r\displaystyle r a **pure/dimensionless number** **Example:** If X\displaystyle X is in kg and Y\displaystyle Y is in cm, then r\displaystyle r has no units. Changing X from kg to grams doesn't change r\displaystyle r. This is one of the key advantages of the correlation coefficient over covariance. 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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