Question

If for two variable x and y, the covariance, variance of x and variance of y are 40, 16 and 256 respectively, what is the value of the correlation coefficient

Answer 1

Answer:

Step-by-step explanation:

We know that

r × sdx × sdy = cov( x,y )

Hence,

r × 40 × 16 = 256

r × 20 × 8 = 256

160r= 256

160/256=r

0.625 = r

Answer 2

Answer:

Correlation Coefficient = 0.625

Step-by-step explanation:

The relationship between Correlation coefficient and covariance is:

$Cor(X,Y)=\frac{Cov(X,Y)}{\sqrt{V(X)V(Y)}}$

where, Cor(X,Y) = Correlation coefficient of X and Y

Cov(X,Y) = Covariance of X and Y = 40

V(X) = Variance of X = 16

V(Y) = Variance of Y = 256

Thus, $Cor(X,Y)=\frac{40}{\sqrt{16\times256}}$

⇒$Cor(X,Y)=\frac{40}{64}=0.625$