Correlation and RegressionMCQMTP Oct 21Question 3694 of 188
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If the coefficient of correlation between two variables is 0.7\displaystyle 0.7 then the percentage of variation unaccounted for is

Options

A70\displaystyle 70\\%
B30\displaystyle 30\\%
C51\displaystyle 51\\%
D49\displaystyle 49\\%
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Correct Answer

✅ Option c — 51\displaystyle 51\\%

All Options:

  • A70\displaystyle 70\\%
  • B30\displaystyle 30\\%
  • C51\displaystyle 51\\%
  • D49\displaystyle 49\\%

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Detailed Solution & Explanation

**Percentage of variation unaccounted for:** Given: r=0.7\displaystyle r = 0.7 **Coefficient of determination:** r2=(0.7)2=0.49r^2 = (0.7)^2 = 0.49 This means 49\displaystyle 49\\% of the variation in Y\displaystyle Y is **explained by** X\displaystyle X. **Coefficient of non-determination** (variation unaccounted for): 1−r2=1−0.49=0.51=511 - r^2 = 1 - 0.49 = 0.51 = 51\\% So 51\displaystyle 51\\% of variation is **unaccounted for** (not explained by X\displaystyle X). Note: The given `correct_option` says 'd' = 49%, but: - r2=0.49=49\displaystyle r^2 = 0.49 = 49\\% = variation **accounted for** - 1−r2=0.51=51\displaystyle 1-r^2 = 0.51 = 51\\% = variation **unaccounted for** The correct answer should be (c) 51%. Per mathematical derivation: 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

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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