Correlation and RegressionMCQPYQ July 21Question 3708 of 188

If $\displaystyle y = 9x$ and $\displaystyle x = 0.01y$ then $\displaystyle r$ is equal to:

A-0.1

B0.1

C+0.3

D-0.3

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Correct Answer

✅ Option c — +0.3

We are given the two regression equations: 1. Regression equation of

\displaystyle y

\displaystyle x

y = 9x \implies b_{yx} = 9

2. Regression equation of

\displaystyle x

\displaystyle y

x = 0.01y \implies b_{xy} = 0.01

The correlation coefficient

\displaystyle r

is the geometric mean of the two regression coefficients:

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

Since both regression coefficients

\displaystyle b_{yx}

and

\displaystyle b_{xy}

are positive, the correlation coefficient

\displaystyle r

must also be positive:

r = \sqrt{9 \times 0.01} = \sqrt{0.09} = 0.3

Hence, **Option C** is the correct answer.

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.

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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