Correlation and RegressionMCQPYQ Nov 18Question 3698 of 188
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The two line of regression interested at the point

Options

AMean
BMode
CMedian
DNone of these
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Correct Answer

✅ Option a — Mean

All Options:

  • AMean
  • BMode
  • CMedian
  • DNone of these

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Detailed Solution & Explanation

By definition, the regression line of y\displaystyle y on x\displaystyle x is: y−yˉ=byx(x−xˉ)y - \bar{y} = b_{yx} (x - \bar{x}) And the regression line of x\displaystyle x on y\displaystyle y is: x−xˉ=bxy(y−yˉ)x - \bar{x} = b_{xy} (y - \bar{y}) If we substitute the mean coordinates (x,y)=(xˉ,yˉ)\displaystyle (x, y) = (\bar{x}, \bar{y}) into both equations: 1. For the y\displaystyle y on x\displaystyle x line: yˉ−yˉ=byx(xˉ−xˉ)⇒0=0\bar{y} - \bar{y} = b_{yx} (\bar{x} - \bar{x}) \Rightarrow 0 = 0 2. For the x\displaystyle x on y\displaystyle y line: xˉ−xˉ=bxy(yˉ−yˉ)⇒0=0\bar{x} - \bar{x} = b_{xy} (\bar{y} - \bar{y}) \Rightarrow 0 = 0 Both equations are satisfied at the point (xˉ,yˉ)\displaystyle (\bar{x}, \bar{y}). This mathematically proves that the two lines of regression always intersect at the point of their arithmetic means, (xˉ,yˉ)\displaystyle (\bar{x}, \bar{y}). *Note: The source/textbook lists the correct option as Option C (Median), which is incorrect. The correct intersection point is the Mean (Option A).* 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.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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