Which of the following formulas is the correct calculation for the unconditional correlation between variables X and Y?
A) $\frac { \operatorname { sCov } ( X , Y ) } { N - 1 }$
B) $$\frac { \operatorname { sCov } ( X , Y ) } { \sqrt { N - 1 } }$$
C) $$\frac { s \operatorname { Cov } ( X , Y ) } { \sqrt { s \operatorname { Var } ( X ) s \operatorname { Var } ( Y ) } }$$
D) $\frac { s \operatorname { Cov } ( X , Y ) } { \sqrt { s \operatorname { Var } ( X ) } }$

Question

Quizplus · Accepted Answer

The formula for the unconditional correlation between variables X and Y is given as:
$$r_{XY} = \frac { \operatorname { Cov } ( X , Y ) } { \sqrt { \operatorname { Var } ( X ) \operatorname { Var } ( Y ) } }$$
However, since we do not know the population variances, we use sample variances and covariances to estimate the population parameters. Therefore, the correct formula is:
$$r_{XY} = \frac { s \operatorname { Cov } ( X , Y ) } { \sqrt { s \operatorname { Var } ( X ) s \operatorname { Var } ( Y ) } }$$
where s is the sample standard deviation. Therefore, choice C provides the correct calculation for the unconditional correlation between variables X and Y.

Which of the Following Formulas Is the Correct Calculation for the Unconditional