Correlation and RegressionMCQMTP Nov 20Question 3738 of 188
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The regression coefficients remain unchanged due to

Options

AShift of origin
BShift of scale
CBoth (a) and (b)
D(a) or (b)
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Correct Answer

✅ Option a — Shift of origin

All Options:

  • AShift of origin
  • BShift of scale
  • CBoth (a) and (b)
  • D(a) or (b)

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Detailed Solution & Explanation

**Understanding Shift of Origin and Shift of Scale:** Let the new variables u\displaystyle u and v\displaystyle v be defined by shifting the origin and scale of variables x\displaystyle x and y\displaystyle y: u=fracx−ah,quadv=fracy−bku = \\frac{x - a}{h}, \\quad v = \\frac{y - b}{k} where a,b\displaystyle a, b are shifts of origin, and h,k\displaystyle h, k are scale factors. **Step 1: Relationship between regression coefficients** The relationship between the regression coefficients of the original variables (byx,bxy\displaystyle b_{yx}, b_{xy}) and the new variables (bvu,buv\displaystyle b_{vu}, b_{uv}) is: byx=left(frackhright)bvub_{yx} = \\left(\\frac{k}{h}\\right) b_{vu} bxy=left(frachkright)buvb_{xy} = \\left(\\frac{h}{k}\\right) b_{uv} **Step 2: Effect of Change of Origin and Scale** - **Shift of Origin (a,b\displaystyle a, b):** The regression coefficients are independent of the change of origin. Thus, shifting the origin does not change the coefficients. - **Shift of Scale (h,k\displaystyle h, k):** The regression coefficients depend on the change of scale because of the terms frackh\displaystyle \\frac{k}{h} and frachk\displaystyle \\frac{h}{k}. Hence, changing the scale alters the coefficients. Therefore, regression coefficients remain unchanged only due to a shift of origin. **Note on Typo:** The source file lists Option D as correct, which is a typo. The correct option is Option A. 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.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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