Pearson's Correlation coefficient between x and y is 2

Option d: (x,y)/Sx Sy. Solution: Definition of Pearson's Correlation Coefficient: Karl Pearson's correlation coefficient r is defined as the ratio of covariance between x and y to the product of their standard deviations: r = (x,y)Sx × Sy where: - (x,y) = covariance between x and y - Sx = standard deviation of x - Sy = standard deviation of y Verification of other options: - Option (a): (x,y) alone — not standardized, has units - Option (b): Sy/Sx Sy = 1 always — not a correlation formula - Option (c): (Sx Sy)2 — not related to correlation formula - Option (d): (x,y)Sx Sy — correct formula for r (Note: The question text says "is 2" which seems like a typo or OCR error — the question is asking which formula gives r ) Hence, Option D is the correct answer.

Pearson's Correlation coefficient between $x$ and $y$ is 2

The correct answer is Option d: $\\frac{cov(x,y)}{S_x S_y}$. **Definition of Pearson's Correlation Coefficient:** Karl Pearson's correlation coefficient $r$ is defined as the ratio of covariance between $x$ and $y$ to the product of their standard deviations: $$r = \\frac{\\text{Cov}(x,y)}{S_x \\cdot S_y}$$ where: - $\\text{Cov}(x,y)$ = covariance between $x$ and $y$ - $S_x$ = standard deviation of $x$ - $S_y$ = standard deviation of $y$ **Verification of other options:** - Option (a): $\\text{Cov}(x,y)$ alone — not standardized, has units - Option (b): $\\frac{S_x S_y}{S_x S_y} = 1$ always — not a correlation formula - Option (c): $(S_x S_y)^2$ — not related to correlation formula - Option (d): $\\frac{\\text{Cov}(x,y)}{S_x S_y}$ — **correct formula for $r$** (Note: The question text says "is 2" which seems like a typo or OCR error — the question is asking which formula gives $r$) Hence, **Option D** is the correct answer.

Correlation and RegressionMCQPYQ Dec 23Question 3646 of 188

All Questions

Pearson's Correlation coefficient between $\displaystyle x$ and $\displaystyle y$ is 2

Options

\displaystyle cov(x,y)

\displaystyle \\frac{S_x S_y}{S_x S_y}

\displaystyle (S_x S_y)^2

\displaystyle \\frac{cov(x,y)}{S_x S_y}

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Correct Answer

✅ Option d — $\displaystyle \\frac{cov(x,y)}{S_x S_y}$

All Options:

A $\displaystyle cov(x,y)$
B $\displaystyle \\frac{S_x S_y}{S_x S_y}$
C $\displaystyle (S_x S_y)^2$
D $\displaystyle \\frac{cov(x,y)}{S_x S_y}$

Detailed Solution & Explanation

**Definition of Pearson's Correlation Coefficient:** Karl Pearson's correlation coefficient

\displaystyle r

is defined as the ratio of covariance between

\displaystyle x

and

\displaystyle y

to the product of their standard deviations:

r = \\frac{\\text{Cov}(x,y)}{S_x \\cdot S_y}

where: -

\displaystyle \\text{Cov}(x,y)

= covariance between

\displaystyle x

and

\displaystyle y

\displaystyle S_x

= standard deviation of

\displaystyle x

\displaystyle S_y

= standard deviation of

\displaystyle y

**Verification of other options:** - Option (a):

\displaystyle \\text{Cov}(x,y)

alone — not standardized, has units - Option (b):

\displaystyle \\frac{S_x S_y}{S_x S_y} = 1

always — not a correlation formula - Option (c):

\displaystyle (S_x S_y)^2

— not related to correlation formula - Option (d):

\displaystyle \\frac{\\text{Cov}(x,y)}{S_x S_y}

— **correct formula for

\displaystyle r

** (Note: The question text says "is 2" which seems like a typo or OCR error — the question is asking which formula gives

\displaystyle r

) Hence, **Option D** 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

Correlation

A statistical measure that expresses the extent to which two variables are linearly related.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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Pearson's Correlation coefficient between x\displaystyle xx and y\displaystyle yy is 2