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If the covariance between x and y is 12, variance of x is 64 and variance of y is 36, then what is the correlation coefficient?
1. \(\rm \frac{1}{{4}}\)
2. \(\rm \frac{1}{{3}}\)
3. \(\rm \frac{1}{{2}}\)
4. \(\rm \frac{2}{{3}}\)

1 Answer

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Best answer
Correct Answer - Option 1 : \(\rm \frac{1}{{4}}\)

Concept:

Correlation coefficeient of x and y is given by, \(\rm r = \frac{cov(x, y)}{\sqrt{V(x)\times V(y)}}\)

Where cov(x, y) = covariance between x and y, V(x) = variance of x and V(y) = variance of y

 

Calculation:

Here, covariance(x, y) = 12, V(x) = 64, V(y) = 36

Correlation coefficeient,  \(\rm r = \frac{cov(x, y)}{\sqrt{V(x)\times V(y)}}\)

\(=\rm \frac{12}{\sqrt{64\times36}}\)

\(=\rm \frac{12}{{8\times6}}\)

\(=\rm \frac{1}{{4}}\)

Hence, option (1) is correct.

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