Correlation and RegressionPYQ May 25Question 4391 of 188
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When both the regression co-efficients are bxy=0.7\displaystyle b_{xy} = 0.7 and byx=0.8\displaystyle b_{yx} = 0.8, respectively, then correlation co-efficient between x and y is

Options

A0.75
B0.56
C0.28
D0.87
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Correct Answer

✅ Option a — 0.75

All Options:

  • A0.75
  • B0.56
  • C0.28
  • D0.87

Detailed Solution & Explanation

The relationship between the regression coefficients (bxy\displaystyle b_{xy} and byx\displaystyle b_{yx}) and the correlation coefficient (r\displaystyle r) is given by the geometric mean of the regression coefficients:
r=±bxy×byxr = \pm \sqrt{b_{xy} \times b_{yx}} Since both regression coefficients are positive (bxy=0.7\displaystyle b_{xy} = 0.7 and byx=0.8\displaystyle b_{yx} = 0.8), the correlation coefficient must also be positive.
Substituting the values:
r=0.7×0.8=0.56≈0.74833r = \sqrt{0.7 \times 0.8} = \sqrt{0.56} \approx 0.74833 Rounding to two decimal places:
r≈0.75r \approx 0.75
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.

Regression

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

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