Correlation and RegressionMCQMTP June 22Question 3696 of 188
All Questions

For 10\displaystyle 10 pairs of observations, number of concurrent deviations was found to be 4\displaystyle 4. What is the value of the coefficient of concurrent deviation?

Options

A0.2\displaystyle \sqrt{0.2}
B1/3\displaystyle 1/3
C−1/3\displaystyle -1/3
D−0.2\displaystyle -\sqrt{0.2}
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Correct Answer

✅ Option c — −1/3\displaystyle -1/3

All Options:

  • A0.2\displaystyle \sqrt{0.2}
  • B1/3\displaystyle 1/3
  • C−1/3\displaystyle -1/3
  • D−0.2\displaystyle -\sqrt{0.2}

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Detailed Solution & Explanation

The coefficient of concurrent deviation (rc\displaystyle r_c) is calculated using the formula: rc=±±2c−mmr_c = \pm \sqrt{\pm \frac{2c - m}{m}} where: - n=10\displaystyle n = 10 is the number of pairs of observations. - m=n−1=10−1=9\displaystyle m = n - 1 = 10 - 1 = 9 is the number of deviations. - c=4\displaystyle c = 4 is the number of concurrent deviations. First, let's calculate the value of 2c−m\displaystyle 2c - m: 2c−m=2(4)−9=8−9=−12c - m = 2(4) - 9 = 8 - 9 = -1 Since 2c−m<0\displaystyle 2c - m < 0 (negative), we use the negative sign both inside and outside the square root to keep the value real and preserve the sign: rc=−−2c−mmr_c = - \sqrt{- \frac{2c - m}{m}} rc=−−−19=−19=−13r_c = - \sqrt{- \frac{-1}{9}} = - \sqrt{\frac{1}{9}} = -\frac{1}{3} *Note: The source file incorrectly lists Option B (1/3\displaystyle 1/3) as the correct answer. However, because 2c−m=−1\displaystyle 2c - m = -1 is negative, the coefficient of concurrent deviation must also be negative, which is -\frac{1}{3} (Option C).* 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.

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Correlation vs Regression: Statistics for CA Foundation

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