Covariance Questionbank

Calculate the covariance $s_{xy}$ for the following four pairs of data: $(1, 2), (2, 1), (3, 2), (4, 1)$.

Consider a small data set with three pairs of observations: $(1, 2), (2, 4), (3, 6)$. Find the covariance $s_{xy}$ of this data set.

If most points in a scatter plot lie in the Top Left Quadrant (TLQ) and the Bottom Right Quadrant (BRQ) relative to the mean point, the covariance $s_{xy}$ will most likely be:

In the derivation of the computational formula for covariance, the expression $\sum (x_i - \bar{x})(y_i - \bar{y})$ is expanded. Which of the following is an algebraically equivalent form of this numerator?

A bivariate data set $(x_1, y_1), \dots, (x_n, y_n)$ has a mean point at the origin, $(\bar{x}, \bar{y}) = (0, 0)$. If every data point in the set satisfies the condition $x_i y_i > 0$, which of the following statements about the covariance $s_{xy}$ must be true?

A small dataset consists of three pairs of observations: $(10, 100)$, $(20, 200)$, and $(30, 300)$. Calculate the covariance $s_{xy}$ for this dataset.

A student calculates the covariance of a data set to be $-12.5$. The scatter plot of this data is most likely to show:

Calculate the covariance $s_{xy}$ for the following three data points: $(1, 3), (3, 1), (5, 5)$. Round your answer to two decimal places.

True or False: If the covariance $s_{xy}$ of a bivariate data set is positive, it implies that for every pair of observations $(x_i, y_i)$ and $(x_j, y_j)$, if $x_i > x_j$ then $y_i$ must be greater than $y_j$.

A researcher is studying the relationship between the number of hours spent studying ($x$) and exam scores ($y$). If $\sum x = 40$, $\sum y = 320$, $\sum xy = 2650$, and $n = 5$, calculate the covariance $s_{xy}$.