Question

Match each correlation coefficient with the type of association it indicates between the variables x and y.

r = 0.9
r = -1.0
r = -0.6
r = 0.1

a perfect linear association in which y increases as x increases

a perfect linear association in which y decreases as x increases

a strong linear association in which y increases as x increases

a strong linear association in which y decreases as x increases

a moderate linear association in which y increases as x increases

Answer 1

r = 0.9 (a strong linear association in which y increases as x increases)

r = -1.0 (a perfect linear association in which y decreases as x increases)

r = -0.6 (a moderate linear association in which y decreases as x increases)

r = 0.1 (no linear association or a very weak association)

Answer 2

r = 0.9
A value of 0.9 would indicate that the correlation is positive. Since it's also close to the value 1, it would also tell us that the correlation of y and x is strong. Therefore, r = 0.9 would be a strong linear association in which y increases as x increases.

r = -1.0
Since the value of r is negative, this would mean that the correlation is also negative. Furthermore, the value of r is also at the minimum point which is -1.0 thus this would tell us that the correlation is a perfect linear association in which y decreases as x increases.

r = -0.6
Likewise, this r value is also negative thus allowing us to know that y will decrease as x increases. The value of r, which is -0.6, is also close to -1.0. This allows us to tell that it is a strong relationship. Therefore, r = -0.6 is a strong linear association in which y decreases as x increases.

r = 0.1
For this correlation, the r value is positive. This would indicate that the value of y will increase as x increases. Since the r value is only 0.1, we cannot say that it is a strong relationship since it is far from the maximum value for a perfect relationship which is 1. Therefore, r = 0.1 is a moderate linear association in which y increases as x increases.