Question

1. The covariance between X and Y is 6.5. Sx = 7.2 and Sy = 3.6 Hence, the value of rxy is: _________________ (1 point)

2. Given that r = + 0.32, Sx = 5.2, and Sy = 6.4, the covariance equals: _________________ (1 point)

3. For a particular set of data, Sx = 9.2 and Sy = 8.5. What is the largest possible value of the covariance?

_________________ (2 points)

4. For a particular set of data, Sx = 9.2 and Sy = 8.5. What is the smallest possible value of the covariance?

Answer 1

Question 1:

1. The covariance between X and Y is 6.5. Sx = 7.2 and Sy = 3.6 Hence, the value of rxy is:

r = Cov (X,Y) / Sx * Sy

r = 6.5 / (7.2 * 3.6)

r = 0.25

Question 2:

Given that r = + 0.32, Sx = 5.2, and Sy = 6.4, the covariance equals:

r = Cov (X,Y) / Sx * Sy

0.32 = Cov (X,Y) / (5.2*6.4)

0.32 = Cov (X,Y) / 33.28

Cov (X,Y) = 33.28 * 0.32

Cov (X,Y) = 10.65

Question 3:

For a particular set of data, Sx = 9.2 and Sy = 8.5. What is the largest possible value of the covariance?

We know that, Correlation coefficient (r) lies between -1 to +1

So, largest possible value for r = +1

r = Cov (X,Y) / Sx * Sy

1 = Cov (X,Y) / (9.2 * 8.5)

Cov (X,Y) = 78.2

Question 4:

For a particular set of data, Sx = 9.2 and Sy = 8.5. What is the smallest possible value of the covariance?

We know that, Correlation coefficient (r) lies between -1 to +1

So,  smallest possible value for r = -1

r = Cov (X,Y) / Sx * Sy

-1 = Cov (X,Y) / (9.2 * 8.5)

Cov (X,Y) = -78.2