Correlation and RegressionMCQPYQ Sep 24Question 3727 of 188
All Questions

Which of the following statement is correct regarding both of the two regression coefficients?

Options

AMust be positive
BNo limit
COne positive and the other negative
DProduct of the regression coefficients must be numerically less than unity
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Correct Answer

✅ Option d — Product of the regression coefficients must be numerically less than unity

All Options:

  • AMust be positive
  • BNo limit
  • COne positive and the other negative
  • DProduct of the regression coefficients must be numerically less than unity

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Detailed Solution & Explanation

Let the two regression coefficients be byx\displaystyle b_{yx} (regression coefficient of y\displaystyle y on x\displaystyle x) and bxy\displaystyle b_{xy} (regression coefficient of x\displaystyle x on y\displaystyle y).\n\n1. The correlation coefficient r\displaystyle r and the regression coefficients are related by the equation:\nr2=byxtimesbxyr^2 = b_{yx} \\times b_{xy}\n\n2. Since the value of the correlation coefficient r\displaystyle r always lies between −1\displaystyle -1 and 1\displaystyle 1 (inclusive), i.e., −1lerle1\displaystyle -1 \\le r \\le 1, the square of the correlation coefficient r2\displaystyle r^2 must be less than or equal to 1\displaystyle 1:\n0ler2le1impliesbyxtimesbxyle10 \\le r^2 \\le 1 \\implies b_{yx} \\times b_{xy} \\le 1\n\n3. This implies that the product of the two regression coefficients must be numerically less than or equal to unity. Therefore, Option D is the correct statement.\n\nHence, **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.

Key Concepts to Understand

Regression

A statistical method used for estimating the relationships between a dependent variable and one or more independent variables.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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