Correlation and RegressionMCQMTP May 18Question 3691 of 188
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Standard Error of Correlation coefficient

Options

Afrac1−r2sqrtN\displaystyle \\frac{1-r^2}{\\sqrt{N}}
Bfrac1+r2sqrtN\displaystyle \\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 — frac1−r2sqrtN\displaystyle \\frac{1-r^2}{\\sqrt{N}}

All Options:

  • Afrac1−r2sqrtN\displaystyle \\frac{1-r^2}{\\sqrt{N}}
  • Bfrac1+r2sqrtN\displaystyle \\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

**Standard Error of the Correlation Coefficient:** The standard error (SE) of the correlation coefficient r\displaystyle r is: textSEr=frac1−r2sqrtN\\text{SE}_r = \\frac{1-r^2}{\\sqrt{N}} where N\displaystyle N is the number of pairs of observations. **Usage:** - It helps test the significance of the correlation coefficient - It is used to find confidence intervals for the population correlation - **Probable Error** =0.6745timestextSEr=0.6745timesfrac1−r2sqrtN\displaystyle = 0.6745 \\times \\text{SE}_r = 0.6745 \\times \\frac{1-r^2}{\\sqrt{N}} **Key properties:** - SE decreases as N\displaystyle N increases (larger sample Rightarrow\displaystyle \\Rightarrow more reliable estimate) - SE decreases as ∣r∣\displaystyle |r| approaches 1 Note: The given `correct_option` says 'c', but the correct formula for SE is frac1−r2sqrtN\displaystyle \\frac{1-r^2}{\\sqrt{N}} (Option A). 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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For a group of students, the sum of squares of differences in ranks for Maths and Physics marks are found to be 60, which is 120 times the value of rank correlation coefficient. How many students are there in the group?

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