Correlation and RegressionMCQMTP Dec 22 Series IIQuestion 3753 of 188
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AM of regression coefficient is:

Options

AEqual to r\displaystyle r
BGreater than or equal to r\displaystyle r
Chalf of r\displaystyle r
DNone of these
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Correct Answer

✅ Option b — Greater than or equal to r\displaystyle r

All Options:

  • AEqual to r\displaystyle r
  • BGreater than or equal to r\displaystyle r
  • Chalf of r\displaystyle r
  • DNone of these

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Detailed Solution & Explanation

Let the two regression coefficients be byx\displaystyle b_{yx} and bxy\displaystyle b_{xy}.\nTheir Arithmetic Mean (AM) is:\ntextAM=fracbyx+bxy2\\text{AM} = \\frac{b_{yx} + b_{xy}}{2}\n\nTheir Geometric Mean (GM) is related to the correlation coefficient r\displaystyle r by:\ntextGM=sqrtbyxcdotbxy=∣r∣\\text{GM} = \\sqrt{b_{yx} \\cdot b_{xy}} = |r|\n\nBy the Arithmetic Mean-Geometric Mean inequality (textAMgetextGM\displaystyle \\text{AM} \\ge \\text{GM}):\nfracbyx+bxy2gesqrtbyxcdotbxy=∣r∣ger\\frac{b_{yx} + b_{xy}}{2} \\ge \\sqrt{b_{yx} \\cdot b_{xy}} = |r| \\ge r\n\nThus, the Arithmetic Mean of the regression coefficients is greater than or equal to the correlation coefficient r\displaystyle r.\n\nHence, **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

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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