Correlation and RegressionMCQPYQ Jan. 21Question 3707 of 188
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Regression coefficients remain unchanged due to

Options

AA shift to scale
BA shift to origin
CReplacing x\displaystyle x - values by 1x\displaystyle \frac{1}{x}
DReplacing y\displaystyle y values by 1y\displaystyle \frac{1}{y}
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Correct Answer

✅ Option b — A shift to origin

All Options:

  • AA shift to scale
  • BA shift to origin
  • CReplacing x\displaystyle x - values by 1x\displaystyle \frac{1}{x}
  • DReplacing y\displaystyle y values by 1y\displaystyle \frac{1}{y}

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Detailed Solution & Explanation

Let the change of origin and scale for the variables x\displaystyle x and y\displaystyle y be defined as: u=x−ahandv=y−bku = \frac{x - a}{h} \quad \text{and} \quad v = \frac{y - b}{k} where a\displaystyle a and b\displaystyle b represent shifts in origin, and h\displaystyle h and k\displaystyle k represent shifts in scale. The relationship between the regression coefficient of the original variables (byx\displaystyle b_{yx}) and the new variables (bvu\displaystyle b_{vu}) is given by: 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} From these formulas, we can see that: 1. The regression coefficients depend on the scale factors h\displaystyle h and k\displaystyle k. Thus, they change due to a change of scale. 2. The regression coefficients do not depend on the origin parameters a\displaystyle a and b\displaystyle b. Therefore, they remain unchanged (invariant) due to a shift or change of origin. 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

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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