Correlation and RegressionMCQPYQ Nov. 19Question 3703 of 188
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If two line of regression are x+2y−5=0\displaystyle x + 2y - 5 = 0 and 2x+3y−8=0\displaystyle 2x + 3y - 8 = 0. So x+2y−5=0\displaystyle x + 2y - 5 = 0 is

Options

Ay\displaystyle y on x\displaystyle x
Bx\displaystyle x on y\displaystyle y
CBoth (a) & (b)
DNone of these
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Correct Answer

✅ Option a — y\displaystyle y on x\displaystyle x

All Options:

  • Ay\displaystyle y on x\displaystyle x
  • Bx\displaystyle x on y\displaystyle y
  • CBoth (a) & (b)
  • DNone of these

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Detailed Solution & Explanation

We are given the two regression equations: 1. x+2y−5=0\displaystyle x + 2y - 5 = 0 2. 2x+3y−8=0\displaystyle 2x + 3y - 8 = 0 To determine if x+2y−5=0\displaystyle x + 2y - 5 = 0 is the regression line of y\displaystyle y on x\displaystyle x or x\displaystyle x on y\displaystyle y: **Assumption 1:** Let x+2y−5=0\displaystyle x + 2y - 5 = 0 be the regression line of y\displaystyle y on x\displaystyle x. Expressing it in terms of y\displaystyle y: 2y=−x+5⇒y=−0.5x+2.52y = -x + 5 \Rightarrow y = -0.5x + 2.5 Here, the regression coefficient is byx=−0.5\displaystyle b_{yx} = -0.5. Let 2x+3y−8=0\displaystyle 2x + 3y - 8 = 0 be the regression line of x\displaystyle x on y\displaystyle y. Expressing it in terms of x\displaystyle x: 2x=−3y+8⇒x=−1.5y+42x = -3y + 8 \Rightarrow x = -1.5y + 4 Here, the regression coefficient is bxy=−1.5\displaystyle b_{xy} = -1.5. **Verification:** The coefficient of determination r2\displaystyle r^2 is the product of byx\displaystyle b_{yx} and bxy\displaystyle b_{xy}: r2=byx×bxy=(−0.5)×(−1.5)=0.75r^2 = b_{yx} \times b_{xy} = (-0.5) \times (-1.5) = 0.75 Since 0≤r2≤1\displaystyle 0 \le r^2 \le 1, this assumption is mathematically valid. Therefore, the line x+2y−5=0\displaystyle x + 2y - 5 = 0 is indeed the regression line of y\displaystyle y on x\displaystyle 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.

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Correlation vs Regression: Statistics for CA Foundation

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