Correlation and RegressionMCQMTP March 22Question 3695 of 188
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If the coefficient of correlation between two variables is 0.9\displaystyle -0.9, then the coefficient of determination is

Options

A0.9\displaystyle 0.9
B0.81\displaystyle 0.81
C0.1\displaystyle 0.1
D0.19\displaystyle 0.19
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Correct Answer

Option b0.81\displaystyle 0.81

All Options:

  • A0.9\displaystyle 0.9
  • B0.81\displaystyle 0.81
  • C0.1\displaystyle 0.1
  • D0.19\displaystyle 0.19

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Detailed Solution & Explanation

The relationship between the coefficient of correlation (r\displaystyle r) and the coefficient of determination is given by: Coefficient of Determination=r2\text{Coefficient of Determination} = r^2 Given: - Coefficient of correlation, r=0.9\displaystyle r = -0.9 Substituting the value of r\displaystyle r into the formula: Coefficient of Determination=(0.9)2=0.81\text{Coefficient of Determination} = (-0.9)^2 = 0.81 Therefore, the coefficient of determination is 0.81\displaystyle 0.81. *Note: The textbook/source file incorrectly lists the correct option as Option A (0.9\displaystyle 0.9). However, the coefficient of determination must be the square of the correlation coefficient, which is mathematically 0.81\displaystyle 0.81 (Option B).* 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

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