Correlation and RegressionMCQMTP Dec 22 Series IIQuestion 3757 of 188
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When two lines of regression become identical if

Options

AR=1\displaystyle R = 1
BR=−1\displaystyle R = -1
CR=0\displaystyle R = 0
Da\displaystyle a or b\displaystyle b
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Correct Answer

✅ Option d — a\displaystyle a or b\displaystyle b

All Options:

  • AR=1\displaystyle R = 1
  • BR=−1\displaystyle R = -1
  • CR=0\displaystyle R = 0
  • Da\displaystyle a or b\displaystyle b

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Detailed Solution & Explanation

The angle theta\displaystyle \\theta between the two lines of regression is related to the correlation coefficient r\displaystyle r by the formula:\ntantheta=frac1−r2∣r∣left(fracsigmaxsigmaysigmax2+sigmay2right)\\tan\\theta = \\frac{1-r^2}{|r|} \\left(\\frac{\\sigma_x \\sigma_y}{\\sigma_x^2 + \\sigma_y^2}\\right)\nFor the two regression lines to be identical (i.e., to coincide), the angle between them must be \displaystyle 0^\\circ, which means tantheta=0\displaystyle \\tan\\theta = 0:\ntantheta=0implies1−r2=0impliesr2=1impliesr=pm1\\tan\\theta = 0 \\implies 1 - r^2 = 0 \\implies r^2 = 1 \\implies r = \\pm 1\nThis implies that the correlation between the two variables must be perfect, meaning either r=1\displaystyle r = 1 (Option A) or r=−1\displaystyle r = -1 (Option B). Therefore, the correct option is Option D (a or b).\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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