Correlation and RegressionMCQMTP Apr 21Question 3656 of 188
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The coefficient of correlation between x\displaystyle x and y\displaystyle y is the ______ of the two regression coefficients

Options

AAM
BGM
CHM
DMedian
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Correct Answer

✅ Option b — GM

All Options:

  • AAM
  • BGM
  • CHM
  • DMedian

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Detailed Solution & Explanation

**Relationship between r\displaystyle r and regression coefficients:** Given regression coefficients: byx=rcdotfracsigmaysigmax,quadbxy=rcdotfracsigmaxsigmayb_{yx} = r \\cdot \\frac{\\sigma_y}{\\sigma_x}, \\quad b_{xy} = r \\cdot \\frac{\\sigma_x}{\\sigma_y} **Product of regression coefficients:** byxcdotbxy=left(rcdotfracsigmaysigmaxright)cdotleft(rcdotfracsigmaxsigmayright)=r2b_{yx} \\cdot b_{xy} = \\left(r \\cdot \\frac{\\sigma_y}{\\sigma_x}\\right) \\cdot \\left(r \\cdot \\frac{\\sigma_x}{\\sigma_y}\\right) = r^2 Therefore: r=pmsqrtbyxcdotbxy=textGMofbyxtextandbxyr = \\pm\\sqrt{b_{yx} \\cdot b_{xy}} = \\text{GM of } b_{yx} \\text{ and } b_{xy} The correlation coefficient r\displaystyle r is the **Geometric Mean (GM)** of the two regression coefficients byx\displaystyle b_{yx} and bxy\displaystyle b_{xy} (with the same sign as both regression coefficients). Note: The given `correct_option` says 'a' (AM), which is incorrect. The correct relationship is GM. 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.

Regression

A statistical method used for estimating the relationships between a dependent variable and one or more independent variables.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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