Correlation and RegressionMCQMTP March 21Question 3740 of 188
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If U+5x=6\displaystyle U + 5x = 6 and 3y−7v=20\displaystyle 3y - 7v = 20 and correlation coefficient between x\displaystyle x and y\displaystyle y is 0.58\displaystyle 0.58 then what be the correlation coefficient between U\displaystyle U and V\displaystyle V?

Options

A0.58\displaystyle 0.58
B−0.58\displaystyle -0.58
C−0.84\displaystyle -0.84
D0.84\displaystyle 0.84
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Correct Answer

✅ Option b — −0.58\displaystyle -0.58

All Options:

  • A0.58\displaystyle 0.58
  • B−0.58\displaystyle -0.58
  • C−0.84\displaystyle -0.84
  • D0.84\displaystyle 0.84

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Detailed Solution & Explanation

**Given Equations:** 1. U+5x=6impliesU=−5x+6\displaystyle U + 5x = 6 \\implies U = -5x + 6 2. 3y−7v=20implies7v=3y−20impliesv=frac37y−frac207\displaystyle 3y - 7v = 20 \\implies 7v = 3y - 20 \\implies v = \\frac{3}{7}y - \\frac{20}{7} - Correlation coefficient between x\displaystyle x and y\displaystyle y: rxy=0.58\displaystyle r_{xy} = 0.58 **Step 1: Identify the Signs of the Scale Changes** The relation between new variables U,V\displaystyle U, V and original variables x,y\displaystyle x, y can be written as: U=px+qquadtextwherep=−5U = p x + q \\quad \\text{where } p = -5 V=sy+tquadtextwheres=frac37V = s y + t \\quad \\text{where } s = \\frac{3}{7} The coefficients p\displaystyle p and s\displaystyle s are the scale changes for x\displaystyle x and y\displaystyle y respectively. **Step 2: Property of Change of Origin and Scale on Correlation Coefficient** The correlation coefficient is independent of change of origin, but it is affected by the sign of the scale factor: - If the signs of the scale factors p\displaystyle p and s\displaystyle s are the **same** (ps>0\displaystyle p s > 0), then ruv=rxy\displaystyle r_{uv} = r_{xy}. - If the signs of the scale factors p\displaystyle p and s\displaystyle s are **opposite** (ps<0\displaystyle p s < 0), then ruv=−rxy\displaystyle r_{uv} = -r_{xy}. Here: - p=−5\displaystyle p = -5 (negative) - s=frac37\displaystyle s = \\frac{3}{7} (positive) Since p\displaystyle p and s\displaystyle s have opposite signs (ps<0\displaystyle p s < 0): ruv=−rxy=−0.58r_{uv} = -r_{xy} = -0.58 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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