Correlation and RegressionPYQ May 25Question 4390 of 188
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The correlation co-efficient between X and Y is 0.8. If we add a number 10 in the X variable and subtracted 20 from Y variable, then the new correlation co-efficient will be -

Options

A0.4
B0.6
C0.9
D0.8
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Correct Answer

Option d0.8

All Options:

  • A0.4
  • B0.6
  • C0.9
  • D0.8

Detailed Solution & Explanation

Let the original variables be X\displaystyle X and Y\displaystyle Y, with the correlation coefficient rXY=0.8\displaystyle r_{XY} = 0.8.
We perform a change of origin on both variables. Let the new variables be U\displaystyle U and V\displaystyle V defined by:
U=X+10U = X + 10 V=Y20V = Y - 20
A fundamental property of the product-moment correlation coefficient is that it is completely independent of the change of origin and scale (provided the signs of the scale factors are the same).
Since we are only adding/subtracting constants (which represents a change of origin), the correlation coefficient remains unchanged:
rUV=rXY=0.8r_{UV} = r_{XY} = 0.8
Hence, **Option D** 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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