Correlation and RegressionMCQMTP Dec 22 Series IIQuestion 3751 of 188
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If the two regression lines are 3X=Y\displaystyle 3X = Y and 8Y=6X\displaystyle 8Y = 6X then the value of correlation coefficient is:

Options

A−0.5\displaystyle -0.5
B0.5\displaystyle 0.5
C0.75\displaystyle 0.75
D−0.80\displaystyle -0.80
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Correct Answer

✅ Option b — 0.5\displaystyle 0.5

All Options:

  • A−0.5\displaystyle -0.5
  • B0.5\displaystyle 0.5
  • C0.75\displaystyle 0.75
  • D−0.80\displaystyle -0.80

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Detailed Solution & Explanation

We are given the two regression lines:\n1) 3X=YimpliesX=frac13Y\displaystyle 3X = Y \\implies X = \\frac{1}{3}Y\nIf we assume this is the regression line of X\displaystyle X on Y\displaystyle Y, the regression coefficient is:\nbxy=frac13b_{xy} = \\frac{1}{3}\n\n2) 8Y=6XimpliesY=frac68X=frac34X\displaystyle 8Y = 6X \\implies Y = \\frac{6}{8}X = \\frac{3}{4}X\nIf we assume this is the regression line of Y\displaystyle Y on X\displaystyle X, the regression coefficient is:\nbyx=frac34b_{yx} = \\frac{3}{4}\n\nThe coefficient of determination is:\nr2=bxycdotbyx=frac13cdotfrac34=frac14=0.25r^2 = b_{xy} \\cdot b_{yx} = \\frac{1}{3} \\cdot \\frac{3}{4} = \\frac{1}{4} = 0.25\n\nSince 0ler2le1\displaystyle 0 \\le r^2 \\le 1, our assumptions are valid. The correlation coefficient is the geometric mean of the regression coefficients. Since both bxy\displaystyle b_{xy} and byx\displaystyle b_{yx} are positive, r\displaystyle r must be positive:\nr=sqrt0.25=0.5r = \\sqrt{0.25} = 0.5\n\nNote: The source file indicating Option D is a typo.\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

Correlation

A statistical measure that expresses the extent to which two variables are linearly related.

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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