Correlation and RegressionPYQ May 25Question 4094 of 188
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Given x=2y+4\displaystyle x = 2y + 4 and y=kx+6\displaystyle y = kx + 6 are the two lines of regression x on y and y on x respectively. If the value of correlation co-efficient (r) is 0.5, then the value of k is

Options

A18\displaystyle \frac{1}{8}
B14\displaystyle \frac{1}{4}
C13\displaystyle \frac{1}{3}
D12\displaystyle \frac{1}{2}
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Correct Answer

✅ Option a — 18\displaystyle \frac{1}{8}

All Options:

  • A18\displaystyle \frac{1}{8}
  • B14\displaystyle \frac{1}{4}
  • C13\displaystyle \frac{1}{3}
  • D12\displaystyle \frac{1}{2}

Detailed Solution & Explanation

We are given:
- The regression line of x\displaystyle x on y\displaystyle y is x=2y+4\displaystyle x = 2y + 4. The coefficient of y\displaystyle y in this equation is the regression coefficient bxy\displaystyle b_{xy}:
bxy=2b_{xy} = 2 - The regression line of y\displaystyle y on x\displaystyle x is y=kx+6\displaystyle y = kx + 6. The coefficient of x\displaystyle x in this equation is the regression coefficient byx\displaystyle b_{yx}:
byx=kb_{yx} = k - The correlation coefficient is r=0.5\displaystyle r = 0.5.

The relation between the regression coefficients and the correlation coefficient is:
r2=bxy×byxr^2 = b_{xy} \times b_{yx} Substituting the given values:
(0.5)2=2×k(0.5)^2 = 2 \times k 0.25=2k0.25 = 2k k=0.252=0.125=18k = \frac{0.25}{2} = 0.125 = \frac{1}{8}
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

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.

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