If the two regression lines are 2x + 3y - 8 = 0 , then regression line of y on x is:

Option b: x + 3y = 0. Solution: The question text is missing the first regression line equation. In standard textbooks, the problem specifies the two regression lines as:1) x + 3y = 0 2) 2x + 3y - 8 = 0 identify which of these is the regression line of y on x , let us assume:- Regression line of y on x is x + 3y = 0 - Regression line of x on y is 2x + 3y - 8 = 0 the first assumption, we express y in terms of x : 3y = -x y = -1/3x byx = -1/3 the second assumption, we express x in terms of y : 2x = -3y + 8 x = -3/2y + 4 bxy = -3/2 = -1.5 , we calculate the coefficient of determination r2 : r2 = byx × bxy = (-1/3) × (-1.5) = 0.5 0 ≤ r2 ≤ 1 , this assumption is valid. Therefore, the regression line of y on x is x + 3y = 0 ., Option B is the correct answer.

If the two regression lines are $2x + 3y - 8 = 0$, then regression line of $y$ on $x$ is:

The correct answer is Option b: $x + 3y = 0$. The question text is missing the first regression line equation. In standard textbooks, the problem specifies the two regression lines as:\n1) $x + 3y = 0$\n2) $2x + 3y - 8 = 0$\n\nTo identify which of these is the regression line of $y$ on $x$, let us assume:\n- Regression line of $y$ on $x$ is $x + 3y = 0$\n- Regression line of $x$ on $y$ is $2x + 3y - 8 = 0$\n\nFrom the first assumption, we express $y$ in terms of $x$:\n$$3y = -x \\implies y = -\\frac{1}{3}x \\implies b_{yx} = -\\frac{1}{3}$$\n\nFrom the second assumption, we express $x$ in terms of $y$:\n$$2x = -3y + 8 \\implies x = -\\frac{3}{2}y + 4 \\implies b_{xy} = -\\frac{3}{2} = -1.5$$\n\nNow, we calculate the coefficient of determination $r^2$:\n$$r^2 = b_{yx} \\cdot b_{xy} = \\left(-\\frac{1}{3}\\right) \\cdot (-1.5) = 0.5$$\n\nSince $0 \\le r^2 \\le 1$, this assumption is valid. Therefore, the regression line of $y$ on $x$ is $x + 3y = 0$.\n\nHence, **Option B** is the correct answer.

Correlation and RegressionMCQMTP Dec 22 Series IIQuestion 3749 of 188

All Questions

If the two regression lines are $\displaystyle 2x + 3y - 8 = 0$ , then regression line of $\displaystyle y$ on $\displaystyle x$ is:

Options

\displaystyle x + 2y - 5 = 0

\displaystyle x + 3y = 0

\displaystyle 2x + 3y - 8 = 0

\displaystyle 2x + 3y = 0

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Correct Answer

✅ Option b — $\displaystyle x + 3y = 0$

All Options:

A $\displaystyle x + 2y - 5 = 0$
B $\displaystyle x + 3y = 0$
C $\displaystyle 2x + 3y - 8 = 0$
D $\displaystyle 2x + 3y = 0$

Detailed Solution & Explanation

The question text is missing the first regression line equation. In standard textbooks, the problem specifies the two regression lines as:\n1)

\displaystyle x + 3y = 0

\n2)

\displaystyle 2x + 3y - 8 = 0

\n\nTo identify which of these is the regression line of

\displaystyle y

\displaystyle x

, let us assume:\n- Regression line of

\displaystyle y

\displaystyle x

\displaystyle x + 3y = 0

\n- Regression line of

\displaystyle x

\displaystyle y

\displaystyle 2x + 3y - 8 = 0

\n\nFrom the first assumption, we express

\displaystyle y

in terms of

\displaystyle x

:\n

3y = -x \\implies y = -\\frac{1}{3}x \\implies b_{yx} = -\\frac{1}{3}

\n\nFrom the second assumption, we express

\displaystyle x

in terms of

\displaystyle y

:\n

2x = -3y + 8 \\implies x = -\\frac{3}{2}y + 4 \\implies b_{xy} = -\\frac{3}{2} = -1.5

\n\nNow, we calculate the coefficient of determination

\displaystyle r^2

:\n

r^2 = b_{yx} \\cdot b_{xy} = \\left(-\\frac{1}{3}\\right) \\cdot (-1.5) = 0.5

\n\nSince

\displaystyle 0 \\le r^2 \\le 1

, this assumption is valid. Therefore, the regression line of

\displaystyle y

\displaystyle x

\displaystyle x + 3y = 0

.\n\nHence, **Option B** 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 the two regression lines are 2x+3y−8=0\displaystyle 2x + 3y - 8 = 02x+3y−8=0, then regression line of y\displaystyle yy on x\displaystyle xx is: