Question

If the covariance between x and y is $30$, variance of x is $25$ and variance of y is $144$, then what is the correlation coefficient?

• A. $0.4$
• B. $0.5$
• C. $0.6$
• D. $0.7$

Answer 1

Answer: (B)

$0.5$

Given:-

$Cov(x,y)=30$

$V\left(x\right)=25$

$V\left(y\right)=144$

As we know formula of Corelation coefficient is$:-$

Let $r$ be Corelation coefficient of $x,y$

Then,

$r=\frac{Covariance(x,y)}{\sqrt{V\left(x\right)\times V\left(y\right)}}$

on solving$:-$

$\Rightarrow r=\frac{30}{\sqrt{25\times 144}}$

$\Rightarrow r=0.5$