Correlation and RegressionMCQMTP Nov 19Question 3729 of 188
All Questions

If the two regression coefficients are 4\displaystyle 4 and 0.16\displaystyle 0.16, the percentage of unexplained variation is.

Options

A64\displaystyle 64
B36\displaystyle 36
C54\displaystyle 54
D46\displaystyle 46
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Correct Answer

✅ Option b — 36\displaystyle 36

All Options:

  • A64\displaystyle 64
  • B36\displaystyle 36
  • C54\displaystyle 54
  • D46\displaystyle 46

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Detailed Solution & Explanation

The regression coefficients are given as byx=4\displaystyle b_{yx} = 4 and bxy=0.16\displaystyle b_{xy} = 0.16.\n\n1. The coefficient of determination, r2\displaystyle r^2, is the product of the two regression coefficients and represents the explained variation:\nr2=byxtimesbxy=4times0.16=0.64r^2 = b_{yx} \\times b_{xy} = 4 \\times 0.16 = 0.64\nThis means that the explained variation is 64\displaystyle 64\\%.\n\n2. The unexplained variation is the remaining portion of the variation and is given by:\ntextUnexplainedVariation=1−r2=1−0.64=0.36textor36\\text{Unexplained Variation} = 1 - r^2 = 1 - 0.64 = 0.36 \\text{ or } 36\\%\n\nComparing with the options, this corresponds to Option B. Note that the source key lists Option C (54\displaystyle 54\\%) as correct, which is a typographical error. The correct mathematical value is 36\displaystyle 36\\%.\n\nHence, **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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