Correlation and RegressionMCQMTP May 20Question 3651 of 188
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If the relation between x\displaystyle x and u\displaystyle u is 3x+4u+7=0\displaystyle 3x + 4u + 7 = 0 and the correlation coefficient between x\displaystyle x and y\displaystyle y is 0.6\displaystyle -0.6, then what is the correlation coefficient between u\displaystyle u and y\displaystyle y?

Options

A-0.6
B-0.8
C0.6
D0.8
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Correct Answer

Option c0.6

All Options:

  • A-0.6
  • B-0.8
  • C0.6
  • D0.8

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Detailed Solution & Explanation

**Effect of transformation on correlation coefficient:** Given: - 3x+4u+7=0Rightarrow4u=3x7Rightarrowu=frac34xfrac74\displaystyle 3x + 4u + 7 = 0 \\Rightarrow 4u = -3x - 7 \\Rightarrow u = -\\frac{3}{4}x - \\frac{7}{4} - rxy=0.6\displaystyle r_{xy} = -0.6 **Analysis:** u\displaystyle u is a linear function of x\displaystyle x with coefficient a=frac34<0\displaystyle a = -\\frac{3}{4} < 0 (negative) Since u=ax+b\displaystyle u = ax + b where a<0\displaystyle a < 0: ruy=fracaacdotrxy=(1)times(0.6)=0.6r_{uy} = \\frac{a}{|a|} \\cdot r_{xy} = (-1) \\times (-0.6) = 0.6 **Explanation:** When x\displaystyle x is multiplied by a negative constant to get u\displaystyle u, the correlation changes sign. So: ruy=rxy=(0.6)=0.6r_{uy} = -r_{xy} = -(-0.6) = 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

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