Correlation and RegressionMCQMTP March 22Question 3752 of 188
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The regression coefficients remain unchanged by

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

Regression coefficients are independent of the change of origin, but they are dependent on the change of scale.\n\nSpecifically, if we transform variables x\displaystyle x and y\displaystyle y to u\displaystyle u and v\displaystyle v using the formulas:\nu=fracx−ahquadtextandquadv=fracy−bku = \\frac{x - a}{h} \\quad \\text{and} \\quad v = \\frac{y - b}{k}\n\nHere, a\displaystyle a and b\displaystyle b represent shifts of origin, while h\displaystyle h and k\displaystyle k represent changes in scale. The regression coefficients transform as follows:\nbyx=frackhbvuquadtextandquadbxy=frachkbuvb_{yx} = \\frac{k}{h} b_{vu} \\quad \\text{and} \\quad b_{xy} = \\frac{h}{k} b_{uv}\n\nThis shows that the regression coefficients remain unchanged by a shift of origin, but change when the scale is shifted. Therefore, they remain unchanged by a "Shift to origin" (Option A).\n\nNote: The source file indicating Option C (Always) is a typo.\n\nHence, **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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