Question

If Var $\left(x\right)=8.25$ , Var $\left(y\right)=33.96$ and Covariance $(x,y)=10.2$ , then the correlation coefficient is

• A. $0.89$
• B. $–0.98$
• C. $0.61$
• D. $–0.16$

Answer 1

The correct option is C

$0.61$

Explanation for the correct option:

Finding the correlation coefficient:

The correlation coefficient of variables $x,y$ is

$\left(r_{xy}\right)$$=$covariance $\frac{\left(x,y\right)}{\left(\sqrt{var\left(x\right),var\left(y\right)}\right)}$

here,

Covariance $\left(x,y\right)$ $=10.2$

var $\left(x\right)=8.25$

var $\left(y\right)=33.96$

Now putting all the values in the above formula, we get

$\begin{array}{rcl}{r}_{xy}& =& \frac{10.2}{\sqrt{\left(8.25\right)\left(33.96\right)}}\\ & =& .61\end{array}$

Hence, the correct option is C.