Correlation and RegressionMCQMTP Apr 21Question 3770 of 188
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If the coefficient of correlation between two variables is 0.8\displaystyle 0.8 then the percentage of variation unaccounted for is

Options

A70\displaystyle 70\\%
B30\displaystyle 30\\%
C51\displaystyle 51\\%
D36\displaystyle 36\\%
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Correct Answer

✅ Option d — 36\displaystyle 36\\%

All Options:

  • A70\displaystyle 70\\%
  • B30\displaystyle 30\\%
  • C51\displaystyle 51\\%
  • D36\displaystyle 36\\%

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Detailed Solution & Explanation

We are given the coefficient of correlation, r=0.8\displaystyle r = 0.8. 1. The coefficient of determination, r2\displaystyle r^2, represents the proportion of variation in the dependent variable explained by the regression line: r2=(0.8)2=0.64textor64r^2 = (0.8)^2 = 0.64 \\text{ or } 64\\% 2. The percentage of variation unaccounted for (unexplained variation) is given by the coefficient of non-determination (1−r2\displaystyle 1 - r^2): textUnexplainedvariation=1−r2\\text{Unexplained variation} = 1 - r^2 textUnexplainedvariation=1−0.64=0.36textor36\\text{Unexplained variation} = 1 - 0.64 = 0.36 \\text{ or } 36\\% Therefore, the percentage of variation unaccounted for is 36\displaystyle 36\\%. 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

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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