Correlation and RegressionMCQPYQ Nov. 19Question 3704 of 188
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Find the coefficient of correlation. 2x+3y=2\displaystyle 2x + 3y = 2 4x+3y=4\displaystyle 4x + 3y = 4

Options

A-0.71
B0.71
C-0.5
D0.5
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Correct Answer

✅ Option a — -0.71

All Options:

  • A-0.71
  • B0.71
  • C-0.5
  • D0.5

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Detailed Solution & Explanation

Given equations: 1. 2x+3y=2\displaystyle 2x + 3y = 2 2. 4x+3y=4\displaystyle 4x + 3y = 4 We assume one is the regression line of y\displaystyle y on x\displaystyle x and the other is x\displaystyle x on y\displaystyle y: - Let 2x+3y=2\displaystyle 2x + 3y = 2 be the regression line of y\displaystyle y on x\displaystyle x: 3y=−2x+2⇒y=−23x+233y = -2x + 2 \Rightarrow y = -\frac{2}{3}x + \frac{2}{3} Thus, byx=−23\displaystyle b_{yx} = -\frac{2}{3}. - Let 4x+3y=4\displaystyle 4x + 3y = 4 be the regression line of x\displaystyle x on y\displaystyle y: 4x=−3y+4⇒x=−34y+14x = -3y + 4 \Rightarrow x = -\frac{3}{4}y + 1 Thus, bxy=−34\displaystyle b_{xy} = -\frac{3}{4}. **Step 1: Calculate r2\displaystyle r^2** r2=byx×bxy=(−23)×(−34)=612=0.5r^2 = b_{yx} \times b_{xy} = \left(-\frac{2}{3}\right) \times \left(-\frac{3}{4}\right) = \frac{6}{12} = 0.5 Since 0≤r2≤1\displaystyle 0 \le r^2 \le 1, this choice of regression lines is valid. **Step 2: Calculate the correlation coefficient (r\displaystyle r)** r=±r2=±0.5≈±0.707≈±0.71r = \pm \sqrt{r^2} = \pm \sqrt{0.5} \approx \pm 0.707 \approx \pm 0.71 Since both regression coefficients (byx\displaystyle b_{yx} and bxy\displaystyle b_{xy}) are negative, the correlation coefficient r\displaystyle r must also be negative: r≈−0.71r \approx -0.71 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.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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