Correlation and RegressionMCQPYQ Dec 22Question 3714 of 188
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The regression coefficients remain unchanged due

Options

AShift to origin
BShift to scale
CAlways
DNever
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Correct Answer

✅ Option a — Shift to origin

All Options:

  • AShift to origin
  • BShift to scale
  • CAlways
  • DNever

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Detailed Solution & Explanation

Let the variables x\displaystyle x and y\displaystyle y undergo a change of origin and scale: u=x−ahandv=y−bku = \frac{x - a}{h} \quad \text{and} \quad v = \frac{y - b}{k} where a,b\displaystyle a, b are the shift constants of the origin and h,k\displaystyle h, k are the scale factors. The regression coefficient of y\displaystyle y on x\displaystyle x is given by: byx=rσyσxb_{yx} = r \frac{\sigma_y}{\sigma_x} Substituting the transformed variables: σy=∣k∣σvandσx=∣h∣σu\sigma_y = |k| \sigma_v \quad \text{and} \quad \sigma_x = |h| \sigma_u This yields: byx=khbvub_{yx} = \frac{k}{h} b_{vu} Similarly, for x\displaystyle x on y\displaystyle y: bxy=hkbuvb_{xy} = \frac{h}{k} b_{uv} Since the expressions for byx\displaystyle b_{yx} and bxy\displaystyle b_{xy} do not involve the origin shift parameters a\displaystyle a and b\displaystyle b, the regression coefficients are completely independent of any shift in origin. Hence, they remain unchanged due to a shift to origin. 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

Regression

A statistical method used for estimating the relationships between a dependent variable and one or more independent variables.

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Correlation vs Regression: Statistics for CA Foundation

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