Following is a random sample of price per piece of plywood X

Following is a random sample of price per piece of plywood, X, and quantity sold, Y (in thousands):

(6, 80)             (7, 60)             (8, 70)             (9, 40)             (10, 0)

a. compute the covariance

b. compute the correlation coefficient

Solution

N=no of samples=5

Covariance= Sum of {(X-X\')*(Y-Y\')]/N

Covariance=-180/5=-36

S.D of X= {Sum of [(X-X\')^2]/N}^(0.5)=(10/5)^(0.5)= 1.4142136

S.D of Y= {Sum of [(Y-Y\')^2]/N}^(0.5)=(4000/5)^(0.5)= 1.4142136=28.284271

Correlation coefficient=Covariance/(S.D of X*S.D of Y)

Correlation coefficient =-36/(1.4142136*28.284271)=-0.9