Correlation and RegressionMCQPYQ Dec 22Question 3716 of 188
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The regression equations are 2x+3y+1=0\displaystyle 2x + 3y + 1 = 0 and 5x+6y+1=0\displaystyle 5x + 6y + 1 = 0, then Mean of x\displaystyle x and y\displaystyle y are:

Options

A-1, -1
B1, -1
C1, -1
D2, 3
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Correct Answer

Option c1, -1

All Options:

  • A-1, -1
  • B1, -1
  • C1, -1
  • D2, 3

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Detailed Solution & Explanation

The point of intersection of the two regression lines is the point of their arithmetic means (xˉ,yˉ)\displaystyle (\bar{x}, \bar{y}). Therefore, we can find the means of x\displaystyle x and y\displaystyle y by solving the two regression equations simultaneously: 1) 2x+3y+1=0\displaystyle 2x + 3y + 1 = 0 2) 5x+6y+1=0\displaystyle 5x + 6y + 1 = 0 To solve these equations, multiply equation (1) by 2\displaystyle 2: 4x+6y+2=0— (Equation 3)4x + 6y + 2 = 0 \quad \text{--- (Equation 3)} Now, subtract Equation (3) from Equation (2): (5x+6y+1)(4x+6y+2)=0(5x + 6y + 1) - (4x + 6y + 2) = 0 x1=0    x=1x - 1 = 0 \implies x = 1 Therefore, the mean of x\displaystyle x is: xˉ=1\bar{x} = 1 Substitute x=1\displaystyle x = 1 back into Equation (1): 2(1)+3y+1=02(1) + 3y + 1 = 0 3y+3=0    3y=3    y=13y + 3 = 0 \implies 3y = -3 \implies y = -1 Therefore, the mean of y\displaystyle y is: yˉ=1\bar{y} = -1 Thus, the arithmetic means are xˉ=1\displaystyle \bar{x} = 1 and yˉ=1\displaystyle \bar{y} = -1. Hence, **Option C** 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

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