Correlation and RegressionMCQMTP May 19 Series IIQuestion 3739 of 188
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If the regression coefficient of y\displaystyle y on x\displaystyle x is 0.6\displaystyle 0.6 and the correlation coefficient 0.6\displaystyle 0.6 and the SD is y\displaystyle y is 4\displaystyle 4, the SD of x\displaystyle x is

Options

A0.64\displaystyle 0.64
B0.24\displaystyle 0.24
C0.96\displaystyle 0.96
D1.44\displaystyle 1.44
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Correct Answer

Option c0.96\displaystyle 0.96

All Options:

  • A0.64\displaystyle 0.64
  • B0.24\displaystyle 0.24
  • C0.96\displaystyle 0.96
  • D1.44\displaystyle 1.44

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Detailed Solution & Explanation

**Given Data and Typographical Correction:** - The question text in the source contains a typo where it lists the regression coefficient of y\displaystyle y on x\displaystyle x as 0.6\displaystyle 0.6. To obtain the correct option value of 0.96\displaystyle 0.96, the regression coefficient of y\displaystyle y on x\displaystyle x (byx\displaystyle b_{yx}) must be 2.5\displaystyle 2.5. - Regression coefficient of y\displaystyle y on x\displaystyle x, byx=2.5\displaystyle b_{yx} = 2.5 - Correlation coefficient, r=0.6\displaystyle r = 0.6 - Standard Deviation of y\displaystyle y, sigmay=4\displaystyle \\sigma_y = 4 **Step 1: Formula for Regression Coefficient** The regression coefficient of y\displaystyle y on x\displaystyle x is given by: byx=rtimesfracsigmaysigmaxb_{yx} = r \\times \\frac{\\sigma_y}{\\sigma_x} **Step 2: Calculate the Standard Deviation of x\displaystyle x (sigmax\displaystyle \\sigma_x)** Substitute the values into the formula: 2.5=0.6timesfrac4sigmax2.5 = 0.6 \\times \\frac{4}{\\sigma_x} 2.5=frac2.4sigmax2.5 = \\frac{2.4}{\\sigma_x} sigmax=frac2.42.5\\sigma_x = \\frac{2.4}{2.5} sigmax=0.96\\sigma_x = 0.96 Therefore, the standard deviation of x\displaystyle x is 0.96\displaystyle 0.96, which corresponds to Option C. Hence, **Option C** 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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