Correlation and RegressionMCQPYQ Dec 23Question 3724 of 188
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If 4y6x=18\displaystyle 4y - 6x = 18 is regression line of y\displaystyle y on x\displaystyle x and coefficient of correlation between x\displaystyle x and y\displaystyle y is 0.8\displaystyle 0.8, then value of regression coefficient of x\displaystyle x on y\displaystyle y is?

Options

A0.2548
B0.4267
C0.5733
D0.7441
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Correct Answer

Option b0.4267

All Options:

  • A0.2548
  • B0.4267
  • C0.5733
  • D0.7441

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Detailed Solution & Explanation

We are given: 1) The regression line of y\displaystyle y on x\displaystyle x: 4y6x=184y - 6x = 18 2) The correlation coefficient, r=0.8\displaystyle r = 0.8 First, let's find the regression coefficient byx\displaystyle b_{yx} by rewriting the regression line of y\displaystyle y on x\displaystyle x in the standard form y=a+byxx\displaystyle y = a + b_{yx}x: 4y=6x+18    y=64x+184    y=1.5x+4.54y = 6x + 18 \implies y = \frac{6}{4}x + \frac{18}{4} \implies y = 1.5x + 4.5 Thus, the regression coefficient of y\displaystyle y on x\displaystyle x is: byx=1.5b_{yx} = 1.5 The relationship between the correlation coefficient r\displaystyle r and the regression coefficients is: r2=byx×bxyr^2 = b_{yx} \times b_{xy} We compute r2\displaystyle r^2: r2=(0.8)2=0.64r^2 = (0.8)^2 = 0.64 Substitute r2\displaystyle r^2 and byx\displaystyle b_{yx} into the equation to find the regression coefficient of x\displaystyle x on y\displaystyle y (bxy\displaystyle b_{xy}): 0.64=1.5×bxy0.64 = 1.5 \times b_{xy} bxy=0.641.50.42667b_{xy} = \frac{0.64}{1.5} \approx 0.42667 Rounding to four decimal places, we get bxy0.4267\displaystyle b_{xy} \approx 0.4267. Hence, **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

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