Question

if van(x) =8.25,var ( y
)=33.96and cov (x,y) =10.2, than the correlation coefficient is?​

Answer 1

Answer:    

Correlation Coefficient is 0.61

Step-by-step explanation:

Given: Variance of X, var (X) = 8.25

          Variance of Y, var (Y) = 33.96

          Co variance of X and Y , cov(X,Y) = 10.2

To find: Correlation coefficient.

Formula for Correlation Coefficient, r is given by,

$r=\frac{cov(X,Y)}{\sigma_X\:\sigma_Y}\\\\where,\:\:\sigma_X\,=\,Standard\:Deviation\:of\:X\\\:\:\:\sigma_Y\,=\,Standard\:Deviation\:of\:Y$

Standard Deviation of X = $\sqrt{var(X)}=\sqrt{8.25}$

Standard Deviation of Y = $\sqrt{var(Y)}=\sqrt{33.96}$

Thus,

$r\:=\:\frac{10.2}{\sqrt{8.25}\:\sqrt{33.96}}$

$r\:=\:\frac{10.2}{\sqrt{8.25\times33.96}}$

$r\:=\:\frac{10.2}{\sqrt{280.17}}$

$r\:=\:\frac{10.2}{16.7}$

$r\:=\:0.61$

Therefore, Correlation Coefficient is 0.61.