Correlation and RegressionMCQPYQ Dec 23Question 3723 of 188
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If the Regression coefficient (rxy\displaystyle r_{xy}) of y\displaystyle y on x\displaystyle x is greater than unity, then other Regression coefficient (ryx\displaystyle r_{yx}) of x\displaystyle x on y\displaystyle y is:

Options

ALess than one
BGreater than one
CEqual to one
DEqual to zero
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Correct Answer

Option aLess than one

All Options:

  • ALess than one
  • BGreater than one
  • CEqual to one
  • DEqual to zero

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Detailed Solution & Explanation

The coefficient of determination r2\displaystyle r^2 is the product of the two regression coefficients: r2=byx×bxyr^2 = b_{yx} \times b_{xy} We know that the correlation coefficient r\displaystyle r must lie between 1\displaystyle -1 and 1\displaystyle 1 (inclusive), which means the coefficient of determination r2\displaystyle r^2 must lie between 0\displaystyle 0 and 1\displaystyle 1: 0r21    0byx×bxy10 \le r^2 \le 1 \implies 0 \le b_{yx} \times b_{xy} \le 1 Therefore: byx×bxy1b_{yx} \times b_{xy} \le 1 If one of the regression coefficients is greater than unity (greater than 1\displaystyle 1), say byx>1\displaystyle b_{yx} > 1, then the other regression coefficient bxy\displaystyle b_{xy} must be less than unity (less than 1\displaystyle 1) so that their product does not exceed 1\displaystyle 1: bxy1byx<1b_{xy} \le \frac{1}{b_{yx}} < 1 Thus, if one regression coefficient is greater than one, the other must be less than one. 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

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