Correlation and RegressionMCQMTP Nov 18Question 3657 of 188
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If the correlation coefficient between u\displaystyle u and v\displaystyle v are 2u+40\displaystyle 2u + 4 - 0 and 4v+16u+11=0\displaystyle 4v + 16u + 11 = 0

Options

Ar=0.8\displaystyle r = 0.8
Br=0.8\displaystyle r = -0.8
Cr=0\displaystyle r = 0
Dr=pm1\displaystyle r = \\pm 1
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Correct Answer

Option dr=pm1\displaystyle r = \\pm 1

All Options:

  • Ar=0.8\displaystyle r = 0.8
  • Br=0.8\displaystyle r = -0.8
  • Cr=0\displaystyle r = 0
  • Dr=pm1\displaystyle r = \\pm 1

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Detailed Solution & Explanation

**Analyzing the relationship between u\displaystyle u and v\displaystyle v:** Note: The question text appears to have a typo/OCR issue. The equations seem to define a direct linear relationship between u\displaystyle u and v\displaystyle v. From 4v+16u+11=0\displaystyle 4v + 16u + 11 = 0: 4v=16u114v = -16u - 11 v=4ufrac114v = -4u - \\frac{11}{4} This is a **perfect linear relationship** between v\displaystyle v and u\displaystyle u (with a negative coefficient 4\displaystyle -4). When two variables have a **perfect linear relationship**, the correlation coefficient is either +1\displaystyle +1 or 1\displaystyle -1: r=pm1r = \\pm 1 Since the coefficient of u\displaystyle u in the expression for v\displaystyle v is 4<0\displaystyle -4 < 0, we have r=1\displaystyle r = -1. But the option pm1\displaystyle \\pm 1 covers both cases, and indeed the answer is: r=pm1r = \\pm 1 Hence, **Option D** 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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