Correlation and RegressionMCQMTP May 19Question 3623 of 188
All Questions

The covariance between two variables is

Options

AStrictly positive
BStrictly negative
CAlways 0\displaystyle 0
DEither positive or negative or zero.
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Correct Answer

✅ Option d — Either positive or negative or zero.

All Options:

  • AStrictly positive
  • BStrictly negative
  • CAlways 0\displaystyle 0
  • DEither positive or negative or zero.

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Detailed Solution & Explanation

**Definition and range of Covariance:** Covariance between two variables X\displaystyle X and Y\displaystyle Y is defined as: textCov(X,Y)=fracsum(X−barX)(Y−barY)n\\text{Cov}(X, Y) = \\frac{\\sum(X - \\bar{X})(Y - \\bar{Y})}{n} **Possible values:** - If X\displaystyle X and Y\displaystyle Y tend to increase together: textCov(X,Y)>0\displaystyle \\text{Cov}(X, Y) > 0 (positive) - If X\displaystyle X increases when Y\displaystyle Y decreases: textCov(X,Y)<0\displaystyle \\text{Cov}(X, Y) < 0 (negative) - If X\displaystyle X and Y\displaystyle Y are independent: textCov(X,Y)=0\displaystyle \\text{Cov}(X, Y) = 0 Therefore, covariance can be **positive, negative, or zero** — it has no fixed sign restriction unlike variance (which is always ≥0\displaystyle \geq 0). Note: The given `correct_option` says 'a' (Strictly positive), which is incorrect. Covariance has no fixed sign. 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.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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