If X and Y are two variables with $\sigma _ { z } ^ { 2 } = 3.25$ , $\sigma _ { y } ^ { 2 } = 5.8$ , and COV(X, Y) = 14.703, then the coefficient of correlation $\rho$ = 0.78.

Question

Quizplus · Accepted Answer

The correlation coefficient $\rho$ is calculated using the formula $\rho = \frac{\text{COV}(X, Y)}{\sigma_X \sigma_Y}$. The given variances are $\sigma_X^2 = 3.25$ and $\sigma_Y^2 = 5.8$, so $\sigma_X = \sqrt{3.25}$ and $\sigma_Y = \sqrt{5.8}$. Calculating $\rho$ with these values does not equal 0.78.

If X and Y Are Two Variables With σz2=3.25\sigma _ { z } ^ { 2 } = 3.25σz2​=3.25

If X and Y Are Two Variables With $\sigma _ { z } ^ { 2 } = 3.25$