Correlation and RegressionMCQMTP May 18Question 3692 of 188
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Probable Error can be obtained using Correlation coefficient as

Options

A0.675timesfrac1−r2sqrtN\displaystyle 0.675 \\times \\frac{1-r^2}{\\sqrt{N}}
B2timesfrac1+r2sqrtN\displaystyle 2 \\times \\frac{1+r^2}{\\sqrt{N}}
Cfrac1+r2N\displaystyle \\frac{1+r^2}{N}
Dfrac1−r2N\displaystyle \\frac{1-r^2}{N}
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Correct Answer

✅ Option a — 0.675timesfrac1−r2sqrtN\displaystyle 0.675 \\times \\frac{1-r^2}{\\sqrt{N}}

All Options:

  • A0.675timesfrac1−r2sqrtN\displaystyle 0.675 \\times \\frac{1-r^2}{\\sqrt{N}}
  • B2timesfrac1+r2sqrtN\displaystyle 2 \\times \\frac{1+r^2}{\\sqrt{N}}
  • Cfrac1+r2N\displaystyle \\frac{1+r^2}{N}
  • Dfrac1−r2N\displaystyle \\frac{1-r^2}{N}

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Detailed Solution & Explanation

**Probable Error of the Correlation Coefficient:** Probable Error (PE) of r\displaystyle r is defined as: textPE(r)=0.6745timesfrac1−r2sqrtN\\text{PE}(r) = 0.6745 \\times \\frac{1-r^2}{\\sqrt{N}} where N\displaystyle N = number of pairs of observations. **Derivation:** If the correlation coefficient follows a normal distribution, the probable error is 0.6745times\displaystyle 0.6745 \\times Standard Error: textPE(r)=0.6745timestextSE(r)=0.6745timesfrac1−r2sqrtN\\text{PE}(r) = 0.6745 \\times \\text{SE}(r) = 0.6745 \\times \\frac{1-r^2}{\\sqrt{N}} **Usage of PE:** - If ∣r∣>6timestextPE\displaystyle |r| > 6 \\times \\text{PE}: correlation is definitely significant - If ∣r∣<textPE\displaystyle |r| < \\text{PE}: correlation is not significant - rpmtextPE\displaystyle r \\pm \\text{PE} gives the range within which population correlation lies Note: Option (a) uses 0.675 which is approximately 0.6745 ✓ Hence, **Option A** 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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