If r = 0 , regression lines are:

Option a: Perpendicular. Solution: The angle between the two regression lines is given by the formula: = 1 - r2/|r| ( /2 + 2 ) r = 0 , the correlation coefficient is zero, which means → ∞ , implying = 90^ . this case, the regression line of y on x simplifies to y = (a horizontal line) and the regression line of x on y simplifies to x = (a vertical line). These two lines are perpendicular to each other.: The source file indicating Option C (they coincide) is a typo., Option A is the correct answer.

If $r = 0$, regression lines are:

The correct answer is Option a: Perpendicular. The angle $\\theta$ between the two regression lines is given by the formula:\n$$\\tan \\theta = \\frac{1 - r^2}{|r|} \\left( \\frac{\\sigma_x \\sigma_y}{\\sigma_x^2 + \\sigma_y^2} \\right)$$\n\nWhen $r = 0$, the correlation coefficient is zero, which means $\\tan \\theta \\to \\infty$, implying $\\theta = 90^\\circ$.\n\nIn this case, the regression line of $y$ on $x$ simplifies to $y = \\bar{y}$ (a horizontal line) and the regression line of $x$ on $y$ simplifies to $x = \\bar{x}$ (a vertical line). These two lines are perpendicular to each other.\n\nNote: The source file indicating Option C (they coincide) is a typo.\n\nHence, **Option A** is the correct answer.

Correlation and RegressionMCQMTP Nov 21Question 3748 of 188

All Questions

If $\displaystyle r = 0$ , regression lines are:

Options

APerpendicular

BParallel

CThey coincide

DCannot be determined

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Correct Answer

✅ Option a — Perpendicular

All Options:

APerpendicular
BParallel
CThey coincide
DCannot be determined

Detailed Solution & Explanation

The angle

\displaystyle \\theta

between the two regression lines is given by the formula:\n

\\tan \\theta = \\frac{1 - r^2}{|r|} \\left( \\frac{\\sigma_x \\sigma_y}{\\sigma_x^2 + \\sigma_y^2} \\right)

\n\nWhen

\displaystyle r = 0

, the correlation coefficient is zero, which means

\displaystyle \\tan \\theta \\to \\infty

, implying

\displaystyle \\theta = 90^\\circ

.\n\nIn this case, the regression line of

\displaystyle y

\displaystyle x

simplifies to

\displaystyle y = \\bar{y}

(a horizontal line) and the regression line of

\displaystyle x

\displaystyle y

simplifies to

\displaystyle x = \\bar{x}

(a vertical line). These two lines are perpendicular to each other.\n\nNote: The source file indicating Option C (they coincide) is a typo.\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

Regression

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

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Correlation vs Regression: Statistics for CA Foundation

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If r=0\displaystyle r = 0r=0, regression lines are: