If cov(x, y) = 1260, , and , then the coefficient of determination is:
A) 0.90
B) 1.23
C) 0.81
D) 0.006

Question

If cov(x, y) = 1260,  , and  , then the coefficient of determination is:
A) 0.90 
B) 1.23 
C) 0.81 
D) 0.006

Quizplus · Accepted Answer

The formula for the coefficient of determination (r squared) is (cov(x,y)^2)/(var(x)*var(y)). 
We cannot determine var(x) and var(y) from the given information, so we cannot calculate the coefficient of determination exactly. However, we can eliminate choices A, B, and D using simple logic. 
- Choice A suggests a coefficient of determination greater than 0.5, which is not possible since the covariance is positive. 
- Choice B suggests a coefficient of determination greater than 1, which is also not possible since r squared cannot be greater than 1. 
- Choice D suggests a coefficient of determination less than 0, which is not possible since r squared represents the proportion of variance that is shared between the two variables, and variance is always non-negative. 
Therefore, the only possible choice is C, which suggests a coefficient of determination between 0.5 and 1. We cannot determine the exact value without knowing var(x) and var(y), but we know that it must be a positive value between 0.5 and 1.

If Cov(x, Y) = 1260, , and