The sample covariance can be calculated in any of the following ways, with the exception of: A) $\frac { 1 } { n - 1 } \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right) \left( Y _ { i } - \bar { Y } \right)$ B) $\frac { 1 } { n - 1 } \sum _ { i = 1 } ^ { n } X _ { i } Y _ { i } - \frac { n } { n - 1 } \overline { X Y }$ C) $\frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( X _ { i } - \mu _ { X } \right) \left( Y _ { i } - \mu _ { Y } \right)$ D)r_XYS_YS_Y, where r_XY is the correlation coefficient.

Question

Quizplus · Accepted Answer

The sample covariance is calculated using the formula $\frac { 1 } { n - 1 } \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right) \left( Y _ { i } - \bar { Y } \right)$ or $\frac { 1 } { n - 1 } \sum _ { i = 1 } ^ { n } X _ { i } Y _ { i } - \frac { n } { n - 1 } \overline { X Y }$. The formula $\frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( X _ { i } - \mu _ { X } \right) \left( Y _ { i } - \mu _ { Y } \right)$ is used to calculate the population covariance, not the sample covariance. The formula r_XYS_YS_Y, where r_XY is the correlation coefficient, is also used to calculate the covariance, but it is not one of the options given in the question.

The Sample Covariance Can Be Calculated in Any of the Following