Correlation and RegressionMCQPYQ July 21Question 3641 of 188
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The coefficient of correlation between x\displaystyle x and y\displaystyle y is 0.5\displaystyle 0.5 the covariance is 16\displaystyle 16, variance of x\displaystyle x is 16\displaystyle 16 then standard deviation of y\displaystyle y is

Options

A4
B8
C16
D64
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Correct Answer

Option b8

All Options:

  • A4
  • B8
  • C16
  • D64

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Detailed Solution & Explanation

**Finding standard deviation of y\displaystyle y:** Given: - r=0.5\displaystyle r = 0.5 - textCov(x,y)=16\displaystyle \\text{Cov}(x, y) = 16 - textVar(x)=sigmax2=16Rightarrowsigmax=4\displaystyle \\text{Var}(x) = \\sigma_x^2 = 16 \\Rightarrow \\sigma_x = 4 **Using the formula:** r=fractextCov(x,y)sigmaxcdotsigmayr = \\frac{\\text{Cov}(x, y)}{\\sigma_x \\cdot \\sigma_y} Substituting: 0.5=frac164cdotsigmay0.5 = \\frac{16}{4 \\cdot \\sigma_y} 0.5times4timessigmay=160.5 \\times 4 \\times \\sigma_y = 16 2sigmay=162\\sigma_y = 16 sigmay=8\\sigma_y = 8 Hence, **Option B** 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

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