Correlation and RegressionMCQMTP June 24 Series IIQuestion 3668 of 188
All Questions

The correlation between two variables x and y is found to be 0.4\displaystyle 0.4. What is the correlation between 2x\displaystyle 2x and (−y)\displaystyle (-y)?

Options

A0.4\displaystyle 0.4
B−0.4\displaystyle -0.4
C0.6\displaystyle 0.6
DNone of these
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Correct Answer

✅ Option b — −0.4\displaystyle -0.4

All Options:

  • A0.4\displaystyle 0.4
  • B−0.4\displaystyle -0.4
  • C0.6\displaystyle 0.6
  • DNone of these

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Detailed Solution & Explanation

**Effect of scaling on correlation:** Given: rxy=0.4\displaystyle r_{xy} = 0.4 Let U=2x\displaystyle U = 2x and V=−y\displaystyle V = -y - Coefficient of x\displaystyle x in U\displaystyle U: a=2>0\displaystyle a = 2 > 0 - Coefficient of y\displaystyle y in V\displaystyle V: b=−1<0\displaystyle b = -1 < 0 **Rule:** rUV=fracab∣ab∣cdotrxy=frac(2)(−1)∣(2)(−1)∣times0.4=frac−22times0.4=−1times0.4=−0.4r_{UV} = \\frac{ab}{|ab|} \\cdot r_{xy} = \\frac{(2)(-1)}{|(2)(-1)|} \\times 0.4 = \\frac{-2}{2} \\times 0.4 = -1 \\times 0.4 = -0.4 **Explanation:** Multiplying x\displaystyle x by 2 (positive) doesn't change the sign of r\displaystyle r. But multiplying y\displaystyle y by −1\displaystyle -1 (negative) **reverses** the sign of r\displaystyle r. So r(2x,−y)=−r(x,y)=−0.4\displaystyle r(2x, -y) = -r(x,y) = -0.4. 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.

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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