If byx = 1.6 and bxy = 0.4 , then rxy will be:

Option b: 0.8. Solution: The relationship between the correlation coefficient ( rxy ) and the regression coefficients ( byx and bxy ) is given by: rxy2 = byx × bxy Taking the square root on both sides: rxy = ± sqrt(byx) × bxy Given: - byx = 1.6 - bxy = 0.4 Substitute these values into the formula: rxy = ± sqrt(1.6 × 0.4) rxy = ± sqrt(0.64) rxy = ± 0.8 Since both regression coefficients byx and bxy are positive, the correlation coefficient rxy must also be positive. Therefore: rxy = 0.8 Hence, Option B is the correct answer.

If $b_{yx} = 1.6$ and $b_{xy} = 0.4$, then $r_{xy}$ will be:

The correct answer is Option b: 0.8. The relationship between the correlation coefficient ($r_{xy}$) and the regression coefficients ($b_{yx}$ and $b_{xy}$) is given by: $$r_{xy}^2 = b_{yx} \times b_{xy}$$ Taking the square root on both sides: $$r_{xy} = \pm \sqrt{b_{yx} \times b_{xy}}$$ Given: - $b_{yx} = 1.6$ - $b_{xy} = 0.4$ Substitute these values into the formula: $$r_{xy} = \pm \sqrt{1.6 \times 0.4}$$ $$r_{xy} = \pm \sqrt{0.64}$$ $$r_{xy} = \pm 0.8$$ Since both regression coefficients $b_{yx}$ and $b_{xy}$ are positive, the correlation coefficient $r_{xy}$ must also be positive. Therefore: $$r_{xy} = 0.8$$ Hence, **Option B** is the correct answer.

Correlation and RegressionPYQ Jan 26Question 4544 of 188

All Questions

If $\displaystyle b_{yx} = 1.6$ and $\displaystyle b_{xy} = 0.4$ , then $\displaystyle r_{xy}$ will be:

Options

A0.4

B0.8

C0.64

D-0.8

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — 0.8

All Options:

A0.4
B0.8
C0.64
D-0.8

Detailed Solution & Explanation

The relationship between the correlation coefficient (

\displaystyle r_{xy}

) and the regression coefficients (

\displaystyle b_{yx}

and

\displaystyle b_{xy}

) is given by:

r_{xy}^2 = b_{yx} \times b_{xy}

Taking the square root on both sides:

r_{xy} = \pm \sqrt{b_{yx} \times b_{xy}}

Given:
-

\displaystyle b_{yx} = 1.6

\displaystyle b_{xy} = 0.4

Substitute these values into the formula:

r_{xy} = \pm \sqrt{1.6 \times 0.4}

r_{xy} = \pm \sqrt{0.64}

r_{xy} = \pm 0.8

Since both regression coefficients

\displaystyle b_{yx}

and

\displaystyle b_{xy}

are positive, the correlation coefficient

\displaystyle r_{xy}

must also be positive. Therefore:

r_{xy} = 0.8

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.

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If byx=1.6\displaystyle b_{yx} = 1.6byx​=1.6 and bxy=0.4\displaystyle b_{xy} = 0.4bxy​=0.4, then rxy\displaystyle r_{xy}rxy​ will be: