Correlation and RegressionMCQMTP Nov 18Question 3659 of 188
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If the relation between two variables X\displaystyle X and Y\displaystyle Y in given by 2X+3Y+4=0\displaystyle 2X+3Y+4=0, then the Value of the correlation coefficient between X\displaystyle X and Y\displaystyle Y is

Options

A0
B1
C-1
DNegative
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Correct Answer

Option c-1

All Options:

  • A0
  • B1
  • C-1
  • DNegative

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Detailed Solution & Explanation

**Correlation when variables have a perfect linear relationship:** Given: 2X+3Y+4=0\displaystyle 2X + 3Y + 4 = 0 Rewriting as: Y=frac23Xfrac43\displaystyle Y = -\\frac{2}{3}X - \\frac{4}{3} This is a perfect linear relationship between X\displaystyle X and Y\displaystyle Y with: - Coefficient of X\displaystyle X = frac23<0\displaystyle -\\frac{2}{3} < 0 (negative) - This means as X\displaystyle X increases, Y\displaystyle Y decreases (inverse relationship) **Key theorem:** If the relationship between two variables is perfectly linear (all data points lie exactly on a line), then: - If the slope is positive: r=+1\displaystyle r = +1 - If the slope is negative: r=1\displaystyle r = -1 Since the slope is frac23<0\displaystyle -\\frac{2}{3} < 0: r=1r = -1 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

Related Comparison Tables

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