If the coefficient of correlation between x and y is 0.6 . If x and y values are multiplied by -1 , then coefficient of correlation will be

Option c: 0.6. Solution: Effect of multiplying both variables by -1 : Given: rxy = 0.6 Let U = -1 × x and V = -1 × y Using the transformation rule: If U = ax and V = by , then: rUV = /|ab| × rxy Here a = -1 and b = -1 : ab = (-1)(-1) = 1 > 0 rUV = 1/|1| × rxy = 1 × 0.6 = 0.6 Interpretation: Multiplying both variables by -1 doesn't change the correlation coefficient because both signs cancel out in the formula. The correlation remains the same. Note: The given correctoption says 'b' ( 1/0.6 ), which is incorrect. When both x and y are multiplied by -1 , r remains unchanged at 0.6 . Hence, Option C is the correct answer.

If the coefficient of correlation between $x$ and $y$ is $0.6$. If $x$ and $y$ values are multiplied by $-1$, then coefficient of correlation will be

The correct answer is Option c: 0.6. **Effect of multiplying both variables by $-1$:** Given: $r_{xy} = 0.6$ Let $U = -1 \\cdot x$ and $V = -1 \\cdot y$ **Using the transformation rule:** If $U = ax$ and $V = by$, then: $$r_{UV} = \\frac{ab}{|ab|} \\cdot r_{xy}$$ Here $a = -1$ and $b = -1$: $$ab = (-1)(-1) = 1 > 0$$ $$r_{UV} = \\frac{1}{|1|} \\cdot r_{xy} = 1 \\times 0.6 = 0.6$$ **Interpretation:** Multiplying **both** variables by $-1$ doesn't change the correlation coefficient because both signs cancel out in the formula. The correlation remains the same. Note: The given `correct_option` says 'b' ($1/0.6$), which is incorrect. When both $x$ and $y$ are multiplied by $-1$, $r$ remains unchanged at $0.6$. Hence, **Option C** is the correct answer.

Correlation and RegressionMCQMTP Nov 21Question 3658 of 188

All Questions

If the coefficient of correlation between $\displaystyle x$ and $\displaystyle y$ is $\displaystyle 0.6$ . If $\displaystyle x$ and $\displaystyle y$ values are multiplied by $\displaystyle -1$ , then coefficient of correlation will be

Options

A-0.6

\displaystyle 1/0.6

C0.6

D0.4

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

Correct Answer

✅ Option c — 0.6

All Options:

A-0.6
B $\displaystyle 1/0.6$
C0.6
D0.4

Detailed Solution & Explanation

**Effect of multiplying both variables by

\displaystyle -1

:** Given:

\displaystyle r_{xy} = 0.6

Let

\displaystyle U = -1 \\cdot x

and

\displaystyle V = -1 \\cdot y

**Using the transformation rule:** If

\displaystyle U = ax

and

\displaystyle V = by

, then:

r_{UV} = \\frac{ab}{|ab|} \\cdot r_{xy}

Here

\displaystyle a = -1

and

\displaystyle b = -1

ab = (-1)(-1) = 1 > 0

r_{UV} = \\frac{1}{|1|} \\cdot r_{xy} = 1 \\times 0.6 = 0.6

**Interpretation:** Multiplying **both** variables by

\displaystyle -1

doesn't change the correlation coefficient because both signs cancel out in the formula. The correlation remains the same. Note: The given `correct_option` says 'b' (

\displaystyle 1/0.6

), which is incorrect. When both

\displaystyle x

and

\displaystyle y

are multiplied by

\displaystyle -1

\displaystyle r

remains unchanged at

\displaystyle 0.6

. Hence, **Option C** 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.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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If the coefficient of correlation between x\displaystyle xx and y\displaystyle yy is 0.6\displaystyle 0.60.6. If x\displaystyle xx and y\displaystyle yy values are multiplied by −1\displaystyle -1−1, then coefficient of correlation will be