Correlation and RegressionMCQMTP March 2021Question 3653 of 188
All Questions

Correlation coefficient rxy\displaystyle r_{xy}, byx\displaystyle b_{yx} and bxy\displaystyle b_{xy} are all have ______ signs

Options

ADifferent
BSame
CBoth
DNone
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option bSame

All Options:

  • ADifferent
  • BSame
  • CBoth
  • DNone

Ad

Detailed Solution & Explanation

**Sign consistency among correlation and regression coefficients:** **Key relationships:** r=pmsqrtbyxcdotbxyr = \\pm\\sqrt{b_{yx} \\cdot b_{xy}} byx=rcdotfracsigmaysigmax,quadbxy=rcdotfracsigmaxsigmayb_{yx} = r \\cdot \\frac{\\sigma_y}{\\sigma_x}, \\quad b_{xy} = r \\cdot \\frac{\\sigma_x}{\\sigma_y} **Analysis:** - Both sigmax\displaystyle \\sigma_x and sigmay\displaystyle \\sigma_y are positive (standard deviations are always positive) - Therefore, byx\displaystyle b_{yx} has the same sign as r\displaystyle r - Similarly, bxy\displaystyle b_{xy} has the same sign as r\displaystyle r - And since byxcdotbxy=r2geq0\displaystyle b_{yx} \\cdot b_{xy} = r^2 \\geq 0, both regression coefficients have the same sign **Conclusion:** rxy\displaystyle r_{xy}, byx\displaystyle b_{yx}, and bxy\displaystyle b_{xy} all have the **same sign** — all positive or all negative. 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

Related Comparison Tables

More Questions from Correlation and Regression

Ready to Master Correlation and Regression?

Practice all 188 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free