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

Option b: $36$. Solution: The regression coefficients are given as byx = 4 and bxy = 0.16 .1. The coefficient of determination, r2 , is the product of the two regression coefficients and represents the explained variation: r2 = byx × bxy = 4 × 0.16 = 0.64 means that the explained variation is $64% .2. The unexplained variation is the remaining portion of the variation and is given by: Variation = 1 - r2 = 1 - 0.64 = 0.36 or 36% with the options, this corresponds to Option B. Note that the source key lists Option C ($54% ) as correct, which is a typographical error. The correct mathematical value is $36%$., Option B is the correct answer.

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

The correct answer is Option b: $36$. The regression coefficients are given as byx = 4 and bxy = 0.16 .1. The coefficient of determination, r2 , is the product of the two regression coefficients and represents the explained variation: r2 = byx × bxy = 4 × 0.16 = 0.64 means that the explained variation is $64% .2. The unexplained variation is the remaining portion of the variation and is given by: Variation = 1 - r2 = 1 - 0.64 = 0.36 or 36% with the options, this corresponds to Option B. Note that the source key lists Option C ($54% ) as correct, which is a typographical error. The correct mathematical value is $36%$., Option B is the correct answer.

Correlation and RegressionMCQMTP Nov 19Question 3729 of 188

All Questions

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

Select Your Answer (Keyboard: A, B, C, D)

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Correct Answer

✅ Option b — $36$

All Options:

A$64$
B$36$
C$54$
D$46$

Detailed Solution & Explanation

The regression coefficients are given as

\displaystyle b_{yx} = 4

and

\displaystyle b_{xy} = 0.16

.\n\n1. The coefficient of determination,

\displaystyle r^2

, is the product of the two regression coefficients and represents the explained variation:\n

r^2 = b_{yx} \

\nThis means that the explained variation is $64\\%

\displaystyle .\n\n2. The unexplained variation is the remaining portion of the variation and is given by:\n<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mspace linebreak="newline"></mspace><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi><mrow><mi>U</mi><mi>n</mi><mi>e</mi><mi>x</mi><mi>p</mi><mi>l</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>e</mi><mi>d</mi><mi>V</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow><mo>=</mo><mn>1</mn><mo>−</mo><msup><mi>r</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn><mo>−</mo><mn>0.64</mn><mo>=</mo><mn>0.36</mn><mspace linebreak="newline"></mspace><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi><mrow><mi>o</mi><mi>r</mi></mrow><mn>36</mn><mspace linebreak="newline"></mspace></mrow><annotation encoding="application/x-tex">\

) as correct, which is a typographical error. The correct mathematical value is $36\\%$.\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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If the two regression coefficients are 4\displaystyle 44 and $0.16$, the percentage of unexplained variation is.