A relationship r2 = 1 - 500/300 is not possible

Option a: True. Solution: Checking the validity of r2 = 1 - 500/300 : r2 = 1 - 500/300 = 1 - 1.6 = -0.6 We know that r2 is the coefficient of determination, which represents the square of the correlation coefficient. Key property: Since r2 is a square of a real number, it must satisfy: 0 ≤ r2 ≤ 1 Here, r2 = -0.6 < 0 , which is impossible since the square of any real number cannot be negative. Therefore, the relationship r2 = 1 - 500/300 is indeed not possible. The statement is True. Hence, Option A is the correct answer.

A relationship $r^2 = 1 - \\frac{500}{300}$ is not possible

The correct answer is Option a: True. **Checking the validity of $r^2 = 1 - \\frac{500}{300}$:** $$r^2 = 1 - \\frac{500}{300} = 1 - 1.\\overline{6} = -0.\\overline{6}$$ We know that $r^2$ is the **coefficient of determination**, which represents the square of the correlation coefficient. **Key property:** Since $r^2$ is a square of a real number, it must satisfy: $$0 \\leq r^2 \\leq 1$$ Here, $r^2 = -0.\\overline{6} < 0$, which is **impossible** since the square of any real number cannot be negative. Therefore, the relationship $r^2 = 1 - \\frac{500}{300}$ is indeed **not possible**. The statement is **True**. Hence, **Option A** is the correct answer.

Correlation and RegressionMCQPYQ May 18Question 3617 of 188

All Questions

A relationship $\displaystyle r^2 = 1 - \\frac{500}{300}$ is not possible

Options

ATrue

BFalse

CBoth (a) & (b)

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — True

All Options:

ATrue
BFalse
CBoth (a) & (b)
DNone of these

Detailed Solution & Explanation

**Checking the validity of

\displaystyle r^2 = 1 - \\frac{500}{300}

:**

r^2 = 1 - \\frac{500}{300} = 1 - 1.\\overline{6} = -0.\\overline{6}

We know that

\displaystyle r^2

is the **coefficient of determination**, which represents the square of the correlation coefficient. **Key property:** Since

\displaystyle r^2

is a square of a real number, it must satisfy:

0 \\leq r^2 \\leq 1

Here,

\displaystyle r^2 = -0.\\overline{6} < 0

, which is **impossible** since the square of any real number cannot be negative. Therefore, the relationship

\displaystyle r^2 = 1 - \\frac{500}{300}

is indeed **not possible**. The statement is **True**. 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.

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Correlation vs Regression: Statistics for CA Foundation

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A relationship r2=1−frac500300\displaystyle r^2 = 1 - \\frac{500}{300}r2=1−frac500300 is not possible