Equations of two lines of regression are 4x + 3y = 7 and 3x + 4y = 0 , the mean of x and y are

Option d: none. Solution: The intersection point of the two regression lines is the point of their arithmetic means, (, ) . Therefore, we can find the means by solving the two regression equations simultaneously:1. 4x + 3y = 7 2. 3x + 4y = 0 equation (2), we can express y in terms of x : y = -3/4x this value of y into equation (1): 4x + 3(-3/4x) = 7 4x - 9/4x = 7 16x - 9x/4 = 7 7/4x = 7 x = 4 , substitute x = 4 back into the expression for y : y = -3/4(4) = -3 , the mean values are = 4 and = -3 . the coordinates (4, -3) are not represented by Option A, B, or C, the correct choice is Option D (none). Note that the source key incorrectly marks Option A as correct; however, the mathematical calculation clearly leads to Option D., Option D is the correct answer.

Equations of two lines of regression are $4x + 3y = 7$ and $3x + 4y = 0$, the mean of $x$ and $y$ are

The correct answer is Option d: none. The intersection point of the two regression lines is the point of their arithmetic means, $(\\bar{x}, \\bar{y})$. Therefore, we can find the means by solving the two regression equations simultaneously:\n\n1. $4x + 3y = 7$\n2. $3x + 4y = 0$\n\nFrom equation (2), we can express $y$ in terms of $x$:\n$$y = -\\frac{3}{4}x$$\n\nSubstituting this value of $y$ into equation (1):\n$$4x + 3\\left(-\\frac{3}{4}x\\right) = 7$$\n$$4x - \\frac{9}{4}x = 7$$\n$$\\frac{16x - 9x}{4} = 7$$\n$$\\frac{7}{4}x = 7 \\implies x = 4$$\n\nNow, substitute $x = 4$ back into the expression for $y$:\n$$y = -\\frac{3}{4}(4) = -3$$\n\nThus, the mean values are $\\bar{x} = 4$ and $\\bar{y} = -3$.\n\nSince the coordinates $(4, -3)$ are not represented by Option A, B, or C, the correct choice is Option D (none). Note that the source key incorrectly marks Option A as correct; however, the mathematical calculation clearly leads to Option D.\n\nHence, **Option D** is the correct answer.

Correlation and RegressionMCQMTP May 18Question 3728 of 188

All Questions

Equations of two lines of regression are $\displaystyle 4x + 3y = 7$ and $\displaystyle 3x + 4y = 0$ , the mean of $\displaystyle x$ and $\displaystyle y$ are

Options

\displaystyle -7/5

\displaystyle 6/7

\displaystyle -4/7

\displaystyle -11/7

\displaystyle 2

\displaystyle 4

Dnone

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — none

All Options:

A $\displaystyle -7/5$ & $\displaystyle 6/7$
B $\displaystyle -4/7$ & $\displaystyle -11/7$
C $\displaystyle 2$ & $\displaystyle 4$
Dnone

Detailed Solution & Explanation

The intersection point of the two regression lines is the point of their arithmetic means,

\displaystyle (\\bar{x}, \\bar{y})

. Therefore, we can find the means by solving the two regression equations simultaneously:\n\n1.

\displaystyle 4x + 3y = 7

\n2.

\displaystyle 3x + 4y = 0

\n\nFrom equation (2), we can express

\displaystyle y

in terms of

\displaystyle x

:\n

y = -\\frac{3}{4}x

\n\nSubstituting this value of

\displaystyle y

into equation (1):\n

4x + 3\\left(-\\frac{3}{4}x\\right) = 7

4x - \\frac{9}{4}x = 7

\\frac{16x - 9x}{4} = 7

\\frac{7}{4}x = 7 \\implies x = 4

\n\nNow, substitute

\displaystyle x = 4

back into the expression for

\displaystyle y

:\n

y = -\\frac{3}{4}(4) = -3

\n\nThus, the mean values are

\displaystyle \\bar{x} = 4

and

\displaystyle \\bar{y} = -3

.\n\nSince the coordinates

\displaystyle (4, -3)

are not represented by Option A, B, or C, the correct choice is Option D (none). Note that the source key incorrectly marks Option A as correct; however, the mathematical calculation clearly leads to Option D.\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.

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Correlation vs Regression: Statistics for CA Foundation

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Equations of two lines of regression are 4x+3y=7\displaystyle 4x + 3y = 74x+3y=7 and 3x+4y=0\displaystyle 3x + 4y = 03x+4y=0, the mean of x\displaystyle xx and y\displaystyle yy are