Correlation and RegressionMCQMTP Dec 23 Series IQuestion 3766 of 188
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Two regression lines are perpendicular each other of r=\displaystyle r =

Options

A0\displaystyle 0
Bpm1\displaystyle \\pm 1
C-1
D1
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Correct Answer

✅ Option a — 0\displaystyle 0

All Options:

  • A0\displaystyle 0
  • Bpm1\displaystyle \\pm 1
  • C-1
  • D1

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Detailed Solution & Explanation

The angle theta\displaystyle \\theta between two regression lines is given by the formula: tantheta=frac1−r2∣r∣cdotfracsigmaxsigmaysigmax2+sigmay2\\tan \\theta = \\frac{1 - r^2}{|r|} \\cdot \\frac{\\sigma_x \\sigma_y}{\\sigma_x^2 + \\sigma_y^2} For the two regression lines to be perpendicular to each other, the angle between them must be \displaystyle 90^\\circ. Since \displaystyle \\tan 90^\\circ = \\infty, the denominator of the term containing r\displaystyle r must be zero, or the term frac1−r2∣r∣\displaystyle \\frac{1 - r^2}{|r|} must approach infinity. This occurs when the correlation coefficient r=0\displaystyle r = 0. Specifically, when r=0\displaystyle r = 0, the regression lines are parallel to the coordinate axes (and thus perpendicular to each other) with equations y=bary\displaystyle y = \\bar{y} and x=barx\displaystyle x = \\bar{x}. 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

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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