Correlation and RegressionMCQMTP Dec 22 Series IIQuestion 3764 of 188
All Questions

If both the regression coefficients are negative, what will be coefficient of correlation?

Options

ANegative
BPositive
CCan be either positive of negative
DCannot be determined
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Correct Answer

✅ Option a — Negative

All Options:

  • ANegative
  • BPositive
  • CCan be either positive of negative
  • DCannot be determined

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Detailed Solution & Explanation

The correlation coefficient r\displaystyle r is related to the regression coefficients byx\displaystyle b_{yx} and bxy\displaystyle b_{xy} by the formula:\nr=pmsqrtbyxtimesbxyr = \\pm \\sqrt{b_{yx} \\times b_{xy}}\n\nA key property of regression and correlation coefficients is that the correlation coefficient r\displaystyle r, the regression coefficient of y\displaystyle y on x\displaystyle x (byx\displaystyle b_{yx}), and the regression coefficient of x\displaystyle x on y\displaystyle y (bxy\displaystyle b_{xy}) must all have the same sign. \n\nTherefore, if both regression coefficients are negative (byx<0\displaystyle b_{yx} < 0 and bxy<0\displaystyle b_{xy} < 0), the correlation coefficient r\displaystyle r must also be negative. (Taking the negative square root, r=−sqrtbyxtimesbxy\displaystyle r = -\\sqrt{b_{yx} \\times b_{xy}}).\n\nHence, **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

Correlation

A statistical measure that expresses the extent to which two variables are linearly related.

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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